Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1063/1.2061427

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DOI： 10.1017/S0022112003006025

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DOI： 10.1063/1.1606446

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DOI： 10.1140/epjb/e2002-00279-5

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DOI： 10.1017/S0022112000008995

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DOI： 10.1088/0305-4470/29/24/025

Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： https://doi.org/10.1016/j.physleta.2023.129264

Language：English   Publishing type：Research paper (scientific journal)  

DOI： https://doi.org/10.1021/acs.jpca.3c05887

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DOI： 10.1007/s41614-023-00113-8

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.054703

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.physleta.2022.128073

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DOI： 10.1016/j.mlwa.2022.100265

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DOI： 10.3389/fenrg.2022.817941

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DOI： 10.1080/00102202.2021.2019234

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DOI： 10.1080/00036811.2021.1992395

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DOI： 10.1134/S0021894421030196

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The paper presents an analytical solution for helical vortices with a Gaussian vorticity distribution in the core, which is confirmed by experimental and numerical simulations. This result is obtained by extending the Dyson method to the Biot–Savart law. Previously, analytical solutions were found and studied only for vortices with constant vorticity distribution in the core (a Rankine-type vortex core). One of the important issues raised during the discussion is the difference between self-induced movements of helical structures with both types of vortex core. The proposed solutions are important for the fundamental understanding and description of the behavior of helical eddy flows in various fields of industry and in nature. Examples include tip vortices behind the rotors of wind or hydro turbines, tornadoes, or axial vortices in aerodynamic devices such as vortex apparatuses and generators; cyclone separators, combustion chambers, etc.

DOI： 10.1134/S0869864320040022

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/978-3-030-62497-2_26

Language：English   Publishing type：Research paper (scientific journal)  

We study singular modes of volume singular integral equations describing problems of scattering of electromagnetic wave in anisotropic dielectric structures. An explicit form of these modes is obtained for a certain class of anisotropic media. Example of real media in which singular modes can exist are considered.

DOI： 10.1134/S0012266120090104

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/978-3-030-62497-2_19

Language：English   Publishing type：Research paper (scientific journal)  

In this work, we prove some regularity criteria for a Ginzburg-Landau-Navier-Stokes in superfluidity in ℝ𝑛(𝑛≥3) .

DOI： 10.1002/mma.6397

Language：English   Publishing type：Research paper (scientific journal)  

The Richards equation is a degenerate nonlinear PDE that models a flow through saturated/unsaturated porous media. Research on its numerical methods has been conducted in many fields. Implicit schemes based on a backward Euler format are widely used in calculating it. However, it is difficult to obtain stability with a numerical scheme because of the strong nonlinearity and degeneracy. In this paper, we establish a linearized semi-implicit finite difference scheme that is faster than backward Euler implicit schemes. We analyze the stability of this scheme by adding a small positive perturbation ϵ to the coefficient function of the Richards equation. Moreover, we show that there is a linear relationship between the discretization error in the L^∞-norm and ϵ. Numerical experiments are carried out to verify our main results.

DOI： 10.1007/s10915-020-01196-y

Language：English   Publishing type：Research paper (scientific journal)  

A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In addition, we introduce an extra term in the difference scheme which is used to relax the time step restriction for improving the stability condition. With the augmented terms, we prove the stability using the induction method. Numerical experiments show the validity and the accuracy of the scheme, along with its efficiency.

DOI： 10.3390/e22030352

Language：English   Publishing type：Research paper (scientific journal)  

In this work, we prove some regularity criteria for a Ginzburg-Landau-Navier-Stokes in superfluidity in (Formula presented.).

DOI： 10.1002/mma.6397

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, by using Fourier splitting method and the properties of decay character r^*, we consider the decay rate on higher order derivative of solutions to 3D incompressible electron inertial Hall-MHD system in Sobolev space H^s(R³) × H^{s +1}(R³) for s ∈ N⁺. Moreover, based on a parabolic interpolation inequality, bootstrap argument and some weighted estimates, we also address the space-time decay properties of strong solutions in R³

DOI： 10.3934/cpaa.2019136

Language：English   Publishing type：Research paper (scientific journal)  

We examine a frictional effect on the linear stability of an interface of discontinuity in tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the other, and the bottom surface is assumed to exert drag force, quadratic in velocity, on the thin fluid layer. In the absence of the drag, the instability of the Kelvin-Helmholtz type is suppressed for U>8c, with c being the propagating speed of the gravity wave. We find by asymptotic analyses for both small and large values of the drag strength that the drag, regardless of its strength, makes the flow unstable for the whole range of the Froude number U/c.

DOI： 10.1016/j.physleta.2019.125839

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In this paper, the properties of weak and strong solutions for the Hall-magnetohydrodynamic system augmented by the effect of elec- tron inertia are studied. First, we establish the existence and uniqueness of local-in-time strong solutions; Then, we prove the existence of global strong solutions under the condition that ∥u ₀ ∥ _{H˙ 1/2} +∥B ₀ ∥ _{H˙ 1/2} +∥∇B ₀ ∥ _{H˙ 1/2} is sufficiently small. Moreover, by applying a cut-off function and gen- eralized energy inequality, we show that the weak solution of electron inertia Hall-MHD system approaches zero as the time t → ∞. Finally, the algebraic decay rate of the weak solution of electron inertia Hall- MHD system is established by using Fourier splitting method and the properties of decay character.

Language：English   Publishing type：Research paper (scientific journal)  

We develop a general matrix method to analyze from a far field the dynamics of an accelerated interface between incompressible ideal fluids of different densities with interfacial mass flux and with negligible density variations and stratification. We rigorously solve the linearized boundary value problem for the dynamics conserving mass, momentum, and energy in the bulk and at the interface. We find a new hydrodynamic instability that develops only when the acceleration magnitude exceeds a threshold. This critical threshold value depends on the magnitudes of the steady velocities of the fluids, the ratio of their densities, and the wavelength of the initial perturbation. The flow has potential velocity fields in the fluid bulk and is shear-free at the interface. The interface stability is set by the interplay of inertia and gravity. For weak acceleration, inertial effects dominate, and the flow fields experience stable oscillations. For strong acceleration, gravity effects dominate, and the dynamics is unstable. For strong accelerations, this new hydrodynamic instability grows faster than accelerated Landau-Darrieus and Rayleigh-Taylor instabilities. For given values of the fluids' densities and their steady bulk velocities, and for a given magnitude of acceleration, we find the critical and maximum values of the initial perturbation wavelength at which this new instability can be stabilized and at which its growth is the fastest. The quantitative, qualitative, and formal properties of the accelerated conservative dynamics depart from those of accelerated Landau-Darrieus and Rayleigh-Taylor dynamics. New diagnostic benchmarks are identified for experiments and simulations of unstable interfaces.

DOI： 10.1063/1.5008648

Language：English   Publishing type：Research paper (scientific journal)  

We propose a two-phase-fluid model for a full-cone turbulent round jet that describes its dynamics in a simple but comprehensive manner with only the apex angle of the cone being a disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium. To derive the model, we impose conservation of the initial volume and total momentum fluxes. Our model equations admit analytical solutions for the composite density and velocity of the two-phase fluid, both as functions of the distance from the nozzle, from which the dynamic pressure and the mass entrainment rate are calculated. Assuming a far-field approximation, we theoretically derive a constant entrainment rate coefficient solely in terms of the cone angle. Moreover, we carry out experiments for a single-phase turbulent air jet and show that the predictions of our model compare well with this and other experimental data of atomizing liquid jets.

DOI： 10.7566/JPSJ.86.034401

Language：English   Publishing type：Research paper (scientific journal)  

To protect coastal structures from the damage caused by the impact force of a tsunami, a new concept of using waste tires behind such structures is introduced in this paper. A physical model for tsunami impact force simulation was developed to evaluate the reduction effect of tsunami impact force by the tire structures. Model tests also were performed to evaluate the stiffness of tire structures. From an esthetic point of view, cultivation of suitable plants inside the tires is also proposed. Field tests on planting trees that can grow in saline soil conditions were performed to see whether such a structure can preserve the greenery of the area. Results show that the tsunami impact force could be reduced considerably by placing filled tires (with a suitable material) behind seawalls, and this technique can protect the structures from the tsunami impact force and the resulting scouring. The greening effect could be maintained by the appropriate selection of the shrubs and trees planted inside the tires, making it one of the most cost-effective methods for recycling waste tires.

DOI： 10.1061/(ASCE)GM.1943-5622.0000687

Language：English   Publishing type：Research paper (scientific journal)  

We consider the general problem of laser pulse heating of a spherical dielectric particle embedded in a liquid. The discussed range of the problem parameters is typical for medical and biological applications. We focus on the case, when the heat diffusivity in the particle is of the same order of magnitude as that in the fluid. We perform quantitative analysis of the heat transfer equation based on interplay of four characteristic scales of the problem, namely the particle radius, the characteristic depth of light absorption in the material of the particle and the two heat diffusion lengths: in the particle and in the embedding liquid. A new quantitative characteristic of the laser action, that is the cooling time, describing the temporal scale of the cooling down of the particle after the laser pulse is over, is introduced and discussed. Simple analytical formulas for the temperature rise in the center of the particle and at its surface as well as for the cooling time are obtained. We show that at the appropriate choice of the problem parameters the cooling time may be by many orders of magnitude larger the laser pulse duration. It makes possible to minimize the undesirable damage of healthy tissues owing to the finite size of the laser beam and scattering of the laser radiation, simultaneously keeping the total hyperthermia period large enough to kill the pathogenic cells. An example of application of the developed approach to optimization of the therapeutic effect at the laser heating of particles for cancer therapy is presented.

DOI： 10.1364/BOE.7.002781

Language：Japanese  

Language：English   Publishing type：Research paper (scientific journal)  

The basic solution for the velocity induced by helical vortex filament is well known as Hardin's solution, published in 1982. A study of early publications on helical vortices now shows that the Japanese scientist Kawada from Tokyo Imperial University also produced many of these results in 1936, which predates Hardin by 46 years. Consequently, in order to honor both, we have studied their derivations to establish the originality of both solutions.

DOI： 10.1115/1.4031964

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1088/0169-5983/47/1/015509

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1088/0031-8949/90/1/018002

Language：English   Publishing type：Research paper (scientific journal)  

A novel linear stability criterion is established for the equilibria of general three-dimen- sional (3D) rotating ows of an ideal gas satisfying Boyle–Charles' law by a newly refined energy-Casimir convexity (ECC) method that can exploit a larger class of Casimir in- variants. As the conventional ECC method cannot be applied directly to stratified shear ows, in our new approach, rather than checking the local convexity of a Lyapunov func- tional L ≡ E + C_E defined as a sum of the total energy and a certain Casimir, we seek the condition for nonexistence of unstable manifolds: orbits (physically realisable ow in phase space) on the leaves of invariants including L as well as other Casimirs connecting a given equilibrium point O and other points in the neighbourhood of it. We argue that the separatrices of the second variation of L (δ²L = 0) generally consist of such unstable manifolds as well as pseudo unstable ones for which either the total energy or Casimirs actually serve as a barrier for escaping orbits. The significance of the new method lies in the fact that it eliminates the latter so as to derive a condition for O being an isolated equilibrium point in terms of orbital connections.

DOI： 10.4171/PRIMS/166

Language：English   Publishing type：Research paper (scientific journal)  

This paper proves a regularity criterion for the density-dependent Hallmagnetohydrodynamics with positive density.

DOI： 10.4171/ZAA/1539

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1093/ptep/ptu139

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1017/jfm.2014.614

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1088/1751-8113/47/46/465501

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DOI： 10.1002/zamm.201400102

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Using the Wentzel–Kramers–Brillouin (WKB) approximation we perform a linear stability analysis for a rotational flow of a viscous and electrically conducting fluid in an external azimuthal magnetic field that has an arbitrary radial profile $B_{\phi}(R)$. In the inductionless approximation, we find the growth rate of the three-dimensional perturbation in a closed form and demonstrate in particular that it can be positive when the velocity profile is Keplerian and the magnetic field profile is slightly shallower than $R^{-1}$.

DOI： doi:10.1088/0169-5983/46/3/031403

Language：English   Publishing type：Research paper (scientific journal)  

Using the Wentzel-Kramers-Brillouin (WKB) approximation we perform a linear stability analysis for a rotational flow of a viscous and electrically conducting fluid in an external azimuthal magnetic field that has an arbitrary radial profile B_φ (R). In the inductionless approximation, we find the growth rate of the three-dimensional perturbation in a closed form and demonstrate in particular that it can be positive when the velocity profile is Keplerian and the magnetic field profile is slightly shallower than R ^-1.

DOI： 10.1088/0169-5983/46/3/031403

Language：English   Publishing type：Research paper (scientific journal)  

The linear stability of a helical vortex tube with axial flow, which is a model of helical vortices emanating from rotating wings, is studied by modal stability analysis. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube whose centreline is a helix of constant curvature and torsion. The helical vortex tube in an infinite domain, in which the free boundary condition is imposed at the surface of the tube, is our major target although the case of the rigid boundary condition is also considered in order to elucidate the effects of torsion and the combined effects of torsion and axial flow. The analysis is based on the linearized incompressible Euler equations expanded in ∈ which is the ratio of the core to curvature radius of the tube. The unstable growth rate can be evaluated using the leading-order neutral modes called the Kelvin waves with the expanded equations. At O(∈) the instability is a linear combination of the curvature instability due to the curvature of the tube and the precessional instability due to the axial flow, both parametric instabilities appearing at the same resonance condition. At the next order O(∈²) not only the effects of torsion but also the combined effects of torsion and axial flow appear, a fact which has been shown only for the short-wave limit. The maximum growth rate increases for the right-handed/left-handed helix with positive/negative helicity, in which the torsion makes the period of particle motion increase. All results converge to the previous local stability results in the short-wave limit. The differences between the two cases of different boundary conditions are due to the isolated mode of the free boundary case, whose dispersion curve depends strongly on the axial flow.

DOI： 10.1017/jfm.2013.591

Language：English   Publishing type：Research paper (international conference proceedings)  

A steady Euler flow of an inviscid incompressible fluid is characterized as an extremum of the total kinetic energy with respect to perturbations constrained to an isovortical sheet. We exploit the criticality in the Hamiltonian to calculate the energy of three-dimensional waves on a steady vortical flow, and, as a by-product, to calculate the mean flow, induced by nonlinear interaction of waves with themselves. We show that the energy of waves on a rotating flow is expressible in terms of a derivative of the dispersion relation with respect to the frequency.

Language：English   Publishing type：Research paper (scientific journal)  

The linear stability of a helical vortex tube with axial flow, which is a model of helical vortices emanating from rotating wings, is studied by modal stability analysis. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube whose centreline is a helix of constant curvature and torsion. The helical vortex tube in an infinite domain, in which the free boundary condition is imposed at the surface of the tube, is our major target although the case of the rigid boundary condition is also considered in order to elucidate the effects of torsion and the combined effects of torsion and axial flow. The analysis is based on the linearized incompressible Euler equations expanded in $\epsilon$ which is the ratio of the core to curvature radius of the tube. The unstable growth rate can be evaluated using the leading-order neutral modes called the Kelvin waves with the expanded equations. At $O(\epsilon)$ the instability is a linear combination of the curvature instability due to the curvature of the tube and the precessional instability due to the axial flow, both parametric instabilities appearing at the same resonance condition. At the next order $O(\epsilon^2)$ not only the effects of torsion but also the combined effects of torsion and axial flow appear, a fact which has been shown only for the short-wave limit. The maximum growth rate increases for the right-handed/left-handed helix with positive/negative helicity, in which the torsion makes the period of particle motion increase. All results converge to the previous local stability results in the short-wave limit. The differences between the two cases of different boundary conditions are due to the isolated mode of the free boundary case, whose dispersion curve depends strongly on the axial flow.

DOI： http://dx.doi.org/10.1017/jfm.2013.591

Language：English   Publishing type：Research paper (scientific journal)  

A weakly nonlinear stability theory is developed for a rotating flow confined in a cylinder of elliptic cross-section. The straining field associated with elliptic deformation of the cross-section breaks the SO(2)-symmetry of the basic flow and amplifies a pair of Kelvin waves whose azimuthal wavenumbers are separated by 2, being referred to as the Moore-Saffman-Tsai-Widnall (MSTW) instability. The Eulerian approach is unable to fully determine the mean flow induced by nonlinear interaction of the Kelvin waves. We establish a general framework for deriving the mean flow by a restriction to isovortical disturbances with use of the Lagrangian variables and put it on the ground of the generalized Lagrangian-mean theory. The resulting formula reveals enhancement of mass transport in regions dominated by the vorticity of the basic flow. With the mean flow at hand, we derive unambiguously the weakly nonlinear amplitude equations to third order for a nonstationary mode. By an appropriate normalization of the amplitude, the resulting equations are made Hamiltonian systems of four degrees of freedom, possibly with three first integrals identifiable as the wave energy and the mean flow.

DOI： 10.1088/0031-8949/2013/T155/014042

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, logarithmically improved regularity criteria for the generalized Navier-Stokes equations are established in terms of the velocity, vorticity and pressure, respectively. Here BMO, the Triebel-Lizorkin and Besov spaces are used, which extend usual Sobolev spaces much. Similar results for the quasi-geostrophic ows and the generalized MHD equations are also listed.

DOI： 10.3934/krm.2013.6.545

Language：English   Publishing type：Research paper (international conference proceedings)  

Noether's theorem associated with the particle relabeling symmetry group leads us to a unified view that all the topological invariants of a barotropic fluid are variants of the cross helicity. The similar is shown to be true of a baroclinic fluid. A cross-helicity representation is given to the Casimir invariant, a class of integrals including an arbitrary function of the specific entropy and the potential vorticity. We then develop a new energy-Casimir convexity method for three-dimensional stability of equilibria of general rotating flows of an ideal baroclinic gas, without appealing to the Boussinesq approximation. By fully exploiting the Casimir invariant, we have succeeded in ruling out a term including the gradient of a dependent variable from the energy-Casimir function and have established a sharp linear stability criterion, being an extension of the Richardson-number criterion.

DOI： 10.1016/j.piutam.2013.03.025

Language：English   Publishing type：Research paper (scientific journal)  

We construct the singular mode corresponding to a spatial essential spectrum of the integral operator for the scattering of the electromagnetic waves by a three-dimensional body of finite size with inhomogeneous and anisotropic dielectric permittivity tensor. The permittivity tensor field is assumed to be H\"older continuous throughout the whole space. The singular volume integral equation, transformed from Maxwell's equations, makes it feasible to deduce explicit form of both the continuous essential spectrum and the corresponding singular modes. The obtained singular mode is a natural extension of the previously obtained one for the isotropic case and is applicable to a much wider class of dielectric scattering bodies. A discussion is made of possibility for realizability of the electromagnetic waves, with finite energy, concentrated at a point in the body.

DOI： 10.1016/j.wavemoti.2012.11.001

Language：English   Publishing type：Research paper (scientific journal)  

An example is given of a mechanical system whose behavior does not follow Thomson-Tait-Chetayev's (TTC) theorem which states that, for a system with an unstable potential, a state stabilized by gyroscopic forces goes unstable after the addition of arbitrary dissipation. The example is brought by a system, closely related with a heavy symmetrical top, describing motion of a charged spherical pendulum subjected to the Lorentz force, in a magnetic-monopole field sitting at the sphere center, as well as the gravity force. A drag force proportional to the velocity is exerted on the pendulum. The upright state, an equilibrium stabilized by the Lorentz force, is shown to be exempted from the TTC theorem. The numerical calculation of the full nonlinear system is performed for precession. For the slow precession, the drag force acts to continuously tilt down the top axis toward vertically downward equilibrium, following the dissipation-induced instability. On the contrary, for the fast precession, the drag acts to continuously tilt up the axis against the gravity force, despite losing the energy.

DOI： 10.7566/JPSJ.82.043002

Language：English   Publishing type：Research paper (scientific journal)  

The magnetorotational instability (MRI) plays a key role for cosmic structure formation by triggering turbulence in the rotating flows of accretion disks that would be otherwise hydrodynamically stable. In the limit of smallmagnetic Prandtl number, the helical and the azimuthal versions of MRI are known to be governed by a quite different scaling behavior than the standard MRI with a vertical app ied magnetic field. Using the short-wavelength approximation for an incompressible, resistive, and viscous rotating fluid, we present a unified description of helical and azimuthal MRI, and we identify the universal character of the Liu limit 2(1−2^{1/2})= 0.8284 for the critical Rossby number. From this universal behavior we are also led to the prediction that the instability will be governed by a mode with an azimuthal wavenumber that is proportional to the ratio of axial to azimuthal applied magnetic field, when this ratio becomes large and the Rossby number is close to the Liu limit.

DOI： 10.1088/0004-637X/756/1/83

Language：English  

Kinematic variational principle for vortical structure of Euler flows and beyond (Modern approach and developments to Onsager's theory on statistical vortices)

Language：English   Publishing type：Research paper (scientific journal)  

The effects of axial flow on the stability of a helical vortex tube are studied by short-wavelength stability analysis. By axial flow we mean the flow along the helical tube inside the vortex core. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube. The exponential growth rate is obtained analytically as the magnitude of he sum of three O(1) and five O(2) complex numbers, where ϵ is the ratio of the core to curvature radius. At O(1) the effect of axial flow can be regarded as the effect of the Coriolis force; as a result the instability is the superposition of the curvature instability and the Coriolis or precessional instability since the two instabilities occur under the same resonance condition. At O(2) combined effects of the axial flow and the torsion appear; the maximum growth rate increases when the period of particle motion increases.

DOI： 10.1063/1.4717769

Language：English   Publishing type：Research paper (scientific journal)  

An analytical model describing vortex ring for low Reynolds numbers proposed previously by Kaplanski and Rudi [Phys. Fluids,17, 087101 (2005)], is extended to a vortex rings for high Reynolds numbers. The experimental results show that the vortex ring core takes the oblate ellipsoidal shape with increasing $Re$. In order to model this feature, we suggest an expression for the vorticity distribution, which corrects the linearized solution of the Navier-Stokes equation, with two disposable nondimensional parameters $\lambda$ and $\beta$ governing the shape of the vortex core, and derive the new expressions for the translation velocity, energy, circulation and streamfunction on the basis of it. The appropriate values of $\lambda$ and $\beta$ are calculated by equating the nondimensional energy $E_d$ and circulation $\Gamma_d$ of the theoretical vortex to the corresponding values obtained from the experimental or numerical vortex ring. To validate the model, the data adapted from the numerical study of vortex ring at $Re=1400$ performed by Danaila and Helie [Phys. Fluids,20, 073602 (2008)], is applied. It is shown that the temporal evolution of the translation velocity at high Reynolds numbers based on these data compares well with the experiments and numerical simulations.

DOI： 10.1063/1.3693276

Language：English   Publishing type：Research paper (international conference proceedings)  

We establish a Lagrangian method which provides us with an unambiguous definition of the wave energy and facilitates its calculation. A steady incompressible Euler flow is characterized as a state of the maximum of the total kinetic energy with respect to disturbances constrained to an isovortical sheet, and the isovortical disturbances are tractable only in terms of the Lagrangian variables. The criticality in energy of a steady flow allows us to work out the wave energy of Kelvin waves solely from the linear disturbance field. As a by-product, the mean flow of second order in amplitude, induced by the nonlinear interaction of Kelvin waves, is obtainable, which provides us with a bypass to enter into weakly nonlinear regime of amplitude evolution.

Language：English   Publishing type：Research paper (scientific journal)  

We revisit the local stability, to three-dimensional disturbances, of rotating flows with circular streamlines, whose rotation axis executes constant precessional motion about an axis perpendicular to itself. In the rotating frame, the basic flow is steady velocity field linear in coordinates in an unbounded domain constructed by Kerswell (1993), and admits the use of the WKB method. For small precession frequency, we recover Kerswell's result. A novel instability is found at large frequency for which the axial wavenumber executes an oscillation around zero; drastic growth of disturbance amplitude occurs only in an extremely short time interval around the time where the axial wavenumber vanishes. In the limit of infinite precession frequency, the growth rate exhibits singular behavior with respect to a parameter characterizing the tilting angle of the wave vector.

DOI： 10.1088/0169-5983/43/5/055502

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DOI： 10.1088/0031-8949/2010/T142/011003

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Spectrum and Energy of Waves in Mean Shear Flows (Mathematical Analysis in Fluid and Gas Dynamics)

Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：Japanese  

7. Three-dimensional motion of vortex tubes(Fundamentals of Vortex Motion)

DOI： 10.11426/nagare1982.25.391

Language：Japanese  

6. Vortex Ring(Fundamentals of Vortex Motion)

DOI： 10.11426/nagare1982.25.265

Language：Japanese  

3. Vortex sheet(Fundamentals of Vortex Motion)

DOI： 10.11426/nagare1982.24.443

Language：Japanese  

2. Point Vortices(Fundamentals of Vortex Motion)

DOI： 10.11426/nagare1982.24.327

Language：English  

In XeCl excimer Laser interactions with Co-coated steel surfaces, we have seemingly realized a quasi-linear array of vortex rings. These form from instabilities on an array of vortex filaments which emerge and then lead to a series of loops. Finally the collapse-and-reconnection process yields a cascade of nearby vortex rings. Since the filament array is subjected to randomly distributed local multipolar strains, unstable waves can develop on the vortex rings. These deformed shapes are frozen permanently by ultrafast cooling, following the last laser pulse. Using a modal analysis, an attempt is made to relate the wave structures to a parametric resonance instability which is caused by dipolar and a quadrupolar fields. Multipulse laser-matter interactions are thus capable of nonselective excitation of vortex ring instabilities of various sizes and various modal structures. (c) 2005 Published by The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.

DOI： 10.1016/j.fluiddyn.2004.06.005

Language：Japanese  

1. Kinematics and Dynamics of Vorticity(Fundamentals of Vortex Motion)

DOI： 10.11426/nagare1982.24.207

Language：English  

A global stability analysis of Kelvin's vortex ring to three-dimensional disturbances of infinitesimal amplitude is made. The basic state is a steady asymptotic solution of the Euler equations, in powers of the ratio epsilon of the core radius to the ring radius, for an axisymmetric vortex ring with vorticity proportional to the distance from the symmetric axis. The effect of ring curvature appears at first order, in the form of a dipole field, and a local straining field, which is a quadrupole field, follows at second order. The eigenvalue problem of the Euler equations, retaining the terms to first order, is solved in closed form, in terms of the Bessel and the modified Bessel functions. We show that the dipole field causes a parametric resonance instability between a pair of Kelvin waves whose azimuthal wavenumbers are separated by 1. The most unstable mode occurs in the short-wavelength limit, under the constraint that the radial and the azimuthal wavenumbers are of the same magnitude, and the limiting value of maximum growth rate coincides with the value 165/256 epsilon obtained by Hattori A Fukumoto (Phys. Fluids, vol. 15, 2003, p. 3151) by means of the geometric optics method. The instability mechanism is traced to stretching of disturbance vorticity in the toroidal direction. In the absence of viscosity, the dipole effect outweighs the straining field effect of O(epsilon(2)) known as the Moore-Saffman-Tsai-Widnall instability. The viscosity acts to damp the former preferentially and these effects compete with each other.

DOI： 10.1017/S0022112004002678

Language：Japanese  

4. Vortex patch(Fundamentals of Vortex Motion)

DOI： 10.11426/nagare1982.24.553

Language：English  

DOI： 10.1017/S0022112004002678

Language：English  

Language：English  

Curvature instability of a vortex ring (Mathematical Analysis in Fluid and Gas Dynamics)

Language：English  

DOI： 10.1134/1.1831533

Language：English   Publishing type：Research paper (scientific journal)  

Language：English  

We revisit the Moore-Saffman-Tsai-Widnall instability, a parametric resonance between left- and right-handed bending waves of infinitesimal amplitude, on the Rankine vortex strained by a weak pure shear flow. The results of Tsai & Widnall (1976) and Eloy & Le Dizes (2001), as generalized to all pairs of Kelvin waves whose azimuthal wavenumbers m are separated by 2, are simplified by providing an explicit solution of the linearized Euler equations for the disturbance flow field. Given the wavenumber k(0) and the frequency coo of an intersection point of dispersion curves, the growth rate is expressible solely in terms of the modified Bessel functions, and so is the unstable wavenumber range. Every intersection leads to instability. Most of the intersections correspond to weak instability that vanishes in the short-wave limit, and dominant modes are restricted to particular intersections. For helical waves m = +/-1, the growth rate of non-rotating waves is far larger than that of rotating waves. The wavenumber width of stationary instability bands broadens linearly in k(0), while that of rotating instability bands is bounded. The growth rate of the stationary instability takes, in the long-wavelength limit, the value of epsilon/2 for the two-dimensional displacement instability, and, in the short-wavelength limit, the value of 9epsilon/16 for the elliptical instability, being larger at large but finite values of k(0). Here E is the strength of shear near the core centre. For resonance between higher azimuthal wavenumbers m and m + 2, the same limiting value is approached as ko --> infinity, along sequences of specific crossing points whose frequency rapidly converges to m + 1, in two ways, from above for a fixed m and from below for m --> infinity. The energy of the Kelvin waves is calculated by invoking Cairns' formula. The instability result is compatible with Krein's theory for Hamiltonian spectra.

DOI： 10.1017/S0022112003006025

Language：English  

The linear stability of thin vortex rings are studied by short-wavelength stability analysis. The modified Hill-Schrodinger equation for vortex rings, which incorporates curvature effect, is derived. It is used to evaluate growth rates analytically. The growth rates are also evaluated by numerical calculation and they agree well with analytical values for small epsilon which is the ratio of core radius to ring radius. Two types of vortex rings are considered: Kelvin's vortex ring and a Gaussian vortex ring. For Kelvin's vortex ring the maximum first-order growth rate is found to be 165/256 epsilon. For the Gaussian vortex ring the first-order growth rate is large in the skirts of the vortex core. The first-order instability is significant for both vortex rings. (C) 2003 American Institute of Physics.

DOI： 10.1063/1.1606446

Language：English  

We have studied the string-like structure generated in nanosecond laser-matter interactions. An attempt is made at gaining, from a frozen picture, information on the vortex-filament dynamics by estimating the hydrodynamic parameters of the shear layer of molten metal surface. The parameter values are consistent with the filament instability, and are in a range that admits breakup of waves, formation of loop solitons and reconnections of filaments. (C) 2003 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0375-9601(03)00069-0

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S0375-9601(03)00069-0

Language：English  

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter c, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(epsilon(3)), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy.

DOI： 10.1140/epjb/e2002-00279-5

Language：English  

We explore the flow field around a thin axisymmetric vortex ring steadily translating in an ideal fluid, with vorticity proportional to distance from the axis of symmetry, originally treated by Dyson (Pihilos. Trans. R. Soc. 184 (1893) 1041). By making a higher-order extension of the method of matched asymptotic expansions in a small. parameter epsilon, the ratio of the core radius to the ring radius R-0, an explicit form of the streamfunction is derived, to O(epsilon(3)), both inside and outside the core. The pressure and velocity fields are written out in full to the same order. It is shown that the circle of minimum pressure coincides, to O(epsilon(2)R(0)), with the circle of stagnation points viewed from the frame moving with the core. (C) 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0169-5983(01)00044-2

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S0169-5983(01)00044-2

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：Others  

Asymptotic expansions for the motion of a curved vortex filament and the localized induction hierarchy (Mathematical Analysis in Fluid and Gas Dynamics)

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：English  

DOI： 10.1143/JPSJ.69.2700

Language：English   Publishing type：Research paper (scientific journal)  

Language：English  

A large-Reynolds-number asymptotic solution of the Navier-Stokes equations is sought for the motion of an axisymmetric vortex ring of small cross-section embedded in a viscous incompressible fluid. In order to take account of the influence of elliptical deformation of the core due to the self-induced strain, the method of matched asymptotic expansions is extended to a higher order in a small parameter epsilon = (nu/Gamma)(1/2), where nu is the kinematic viscosity of fluid and Gamma is the circulation. Alternatively, epsilon is regarded as a measure of the ratio of the core radius to the ring radius, and our scheme is applicable also to the steady inviscid dynamics.
We establish a general formula for the translation speed of the ring valid up to third order in epsilon. This is a natural extension of Fraenkel-Saffman's first-order formula, and reduces, if specialized to a particular distribution of vorticity in an inviscid fluid, to Dyson's third-order formula. Moreover, it is demonstrated, for a ring starting from an infinitely thin circular loop of radius R-0, that viscosity acts, at third order, to expand the circles of stagnation points of radii R-s(t) and (R) over tilde(s)(t) relative to the laboratory frame and a comoving frame respectively, and that of peak vorticity of radius R-p(t) as R-s approximate to R-0 + [2 log(4R(0)/root nu t) + 1.4743424] nu t/R-0, (R) over tilde(s) approximate to R-0 + 2.5902739 nu t/R-0, and R-p approximate to R-0 + 4.5902739 nu t/R-0. The growth of the radial centroid of vorticity, linear in time, is also deduced. The results are compatible with the experimental results of Sallet & Widmayer (1974) and Weigand & Gharib (1997).
The procedure of pursuing the higher-order asymptotics provides a clear picture of the dynamics of a curved vortex tube; a vortex ring may be locally regarded as a line of dipoles along the core centreline, with their axes in the propagating direction, subjected to the self-induced flow field. The strength of the dipole depends not only on the curvature but also on the location of the core centre, and therefore should be specified at the initial instant. This specification removes an indeterminacy of the first-order theory. We derive a new asymptotic development of the Biot-Savart law for an arbitrary distribution of vorticity, which makes the non-local induction velocity from the dipoles calculable at third order.

DOI： 10.1017/S0022112000008995

Language：English   Publishing type：Research paper (scientific journal)  

Dyson's method for the Biot-Savart law revisited,
by Yasuhide Fukumoto,
Nagare Vol.19, No.3 (2000) pp.180-185

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：English  

We investigate the three-dimensional configurations of a thin vortex filament embedded in background flows of an inviscid incompressible fluid, based on the localized induction approximation. An analogy is found between stationary configurations of a vortex filament in a steady flow and trajectories of a charged particle in a steady magnetic field. An analogy with trajectories of a sound ray in a steady low-Mach number flow is drawn as well. These analogies allow us to use the Lagrangian and Hamiltonian formalism of classical mechanics for calculating fully nonlinear forms of a vortex filament. The equations for the filament curve are integrable when the background flow has two spatial symmetries. Only integrable cases are explored in some detail. To illustrate the advantages of use of the analogy, we re-examine the invariant shapes of a vortex filament moving through a still fluid obtained by Kida (1981). Analogies of the Kida class with the motions of a heavy symmetrical top and a charged spherical pendulum in the field of a magnetic monopole are discussed. As next examples, we consider a point source (sink) and a line source (sink) flows. A filament takes the form of a non-uniform helix wound around a cone. The last example is a circular jet of a parabolic velocity profile. We construct a closed filament with azimuthal waves, lying on a plane orthogonal to the flow direction. Among them, an elliptic vortex ring is found to be distinct from higher waves.

DOI： 10.1098/rspa.1997.0067

Language：English  

An evolution equation of a curve is constructed by summing up the infinite sequence of commuting vector fields of the integrable hierarchy for the localized induction equation (LIE). It is shown to be equivalent to the Lund-Regge equation. The intrinsic equations governing the curvature and torsion are deduced in the form of integrodifferential evolution equations. A class of exact solutions which correspond to the permanent forms of a curve evolving by a steady rigid motion are presented. The analysis of the solutions reveals that, given the shape, there are two speeds of motion, one of which has no counterpart in the case of the LIE.

DOI： 10.1088/0305-4470/29/24/025

Language：English  

We investigate the linear stability of regions of two-dimensional steady irrotational flows in which streamlines are closed, with respect to three-dimensional perturbations of short wavelengths. The fluid is assumed to be inviscid and incompressible. The geometrical optics equations derived by Hameiri and Lifschitz are employed. It is demonstrated that, at large times, both short-wave perturbation velocity and vorticity grow in magnitude at most linearly in time. It implies that there are no exponentially growing short-wave instabilities in such a flow domain. The same result holds if the how field is steady relative to a suitably chosen steadily rotating frame and the net vorticity relative to the inertial frame is zero.

DOI： 10.1143/JPSJ.65.107

Language：English  

DOI： 10.1063/1.868719

Event date： 2017.9

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：Hotel Bonadis, Ravello   Country：Italy  

Event date： 2015.6 - 2015.7

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：Porquerolles Island, Hyeres   Country：France  

Event date： 2014.8

Language：English   Presentation type：Oral presentation (general)  

Venue：The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste   Country：Italy  

Event date： 2013.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Isaac Newton Institute for Mathematical Sciences，Cambridge   Country：United Kingdom  

Event date： 2012.7

Language：English   Presentation type：Oral presentation (general)  

Venue：Isaac Newton Institute for Mathematical Sciences, Cambridge   Country：United Kingdom  

Integrals of an arbitrary function of the vorticity, two-dimensional topological invariants of an ideal barotropic fluid, take different guise from the helicity. Noether's theorem associated with the particle relabeling symmetry group leads us to a unified view that all the topological invariants of a barotropic fluid are variants of the cross helicity. Baroclinic fluid flows admit, as the Casimir invariants, a class of integrals including an arbitrary function of the entropy and the potential vorticity. A consideration is given to them from the view point of Noether's theorem. We then develop a new energy-Casimir convexity method for a baroclinic fluid, and establish a novel linear stability criterion, to three-dimensional disturbances, for equilibria of general rotating flows of an ideal gas without appealing to the Boussinesq approximation. By exploiting a larger class of the Casimir invariants, we have succeeded in ruling out a term including the gradient of a dependent variable from the energy-Casimir function. For zonally symmetric flows, the resulting criterion is regarded as an extended Richardson number criterion for stratified rotating shear flows with compressibility taken into account.

Event date： 2009.7 - 2009.8

Presentation type：Oral presentation (general)  

Venue：The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy   Country：Italy  

Event date： 2008.10

Presentation type：Oral presentation (invited, special)  

Venue：Technical University of Denmark, Lyngby   Country：Denmark  

Event date： 2008.8

Presentation type：Oral presentation (general)  

Venue：Adelaide Convention Center, Adelaide   Country：Australia  

Presentation type：Oral presentation (invited, special)  

Venue：Centre Paul Langevin, Aussois   Country：France  

Presentation type：Oral presentation (invited, special)  

Venue：The Abdus Salam International Centre for Theoretical Physics (ICTP)   Country：Japan  

Presentation type：Oral presentation (invited, special)  

Venue：Steklov Mathematical Institute, Moscow, Russia   Country：Russian Federation  

Presentation type：Oral presentation (general)  

Venue：University of Washington, Seattle, Washington   Country：United States  

Event date： 2024.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Wroclaw University   Country：Poland  

Event date： 2024.3

Language：English   Presentation type：Oral presentation (general)  

Venue：I-site なんば, 大阪公立大学   Country：Japan  

Event date： 2024.1

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.12

Language：English   Presentation type：Oral presentation (general)  

Venue：Institute for Advanced Study in Mathematics (IASM), Hangzhou   Country：China  

Event date： 2023.11

Language：English   Presentation type：Oral presentation (general)  

Venue：福岡国際センター   Country：Japan  

Event date： 2023.11

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.10

Language：English   Presentation type：Oral presentation (general)  

Venue：Kavli Institute for Theoretical Physics, UC Santa Barbara   Country：United States  

Event date： 2023.9

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.9

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.8

Language：English   Presentation type：Oral presentation (general)  

Venue：Waseda Campus, Waseda University   Country：Japan  

Event date： 2023.8

Language：English   Presentation type：Oral presentation (general)  

Venue：Hongo Campus, University of Tokyo   Country：Japan  

Event date： 2023.6 - 2024.6

Language：English   Presentation type：Oral presentation (general)  

Venue：University of Limerick   Country：Ireland  

Event date： 2023.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.11 - 2022.12

Language：English   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

Event date： 2022.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Indiana Convention Center, Indianapolis   Country：United States  

Event date： 2022.11

Language：English   Presentation type：Oral presentation (general)  

Venue：仙台国際センター   Country：Japan  

Event date： 2022.9 - 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：京都大学吉田キャンパス   Country：Japan  

Event date： 2022.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東京工業大学大岡山キャンパス   Country：Japan  

Event date： 2022.9

Language：English   Presentation type：Oral presentation (general)  

Venue：University of Calgary   Country：Canada  

Event date： 2022.5

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：福岡大学   Country：Japan  

Event date： 2022.3

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Country：Japan  

Event date： 2021.12

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.11

Language：Japanese   Presentation type：Oral presentation (invited, special)  

Venue：オンライン (愛知工業大学)   Country：Japan  

Event date： 2021.10

Language：English   Presentation type：Oral presentation (general)  

Venue：Online   Country：Japan  

Event date： 2021.10

Language：English   Presentation type：Oral presentation (general)  

Venue：Online (大阪市立大学杉本キャンパス)   Country：Japan  

Event date： 2021.9 - 2021.10

Language：English   Presentation type：Oral presentation (general)  

Venue：Online (Kyushu University)   Country：Japan  

Event date： 2021.9

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：オンライン（東京大学生産技術研究所）   Country：Japan  

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

Event date： 2021.8

Language：English   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Italy  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

オイラー方程式・電磁流体方程式は非正準ポアソン方程式の形に書き表わせる．ポアソン構造は退化しており，カシミール不変量の存在を許す．このカシミール不変量を陽に利用して，ポアソン括弧を南部括弧で表現する．

Event date： 2021.3

Language：English   Presentation type：Oral presentation (general)  

Venue：九州大学伊都キャンパス   Country：Japan  

The Richards equation is a degenerate nonlinear partial differential equation which serves as a model for the percolation of water into a porous medium under the influence of gravity. Recently even in regions of mid latitudes, heavy rains or showers attack with a larger frequency. This trend is more so as years pass by. Typhoons and hurricanes also have a tendency to grow strong, accompanied by concentrated rains as well as strongly blowing wind, due to the temperature rise of the sea surface. A drastically heavy rain may cause floods of rivers. In case a heavy rain lasts for a long time, landslides may take place in regions at the foot of a mountain and under a cliff. Prevention of such natural disasters associated with heavy rains is an issue of the highest demand for saving human lives. This investigation develops numerical method for the one-dimensional Richards equation. Implicit schemes based on a backward Euler format have been widely used in calculating it. However, it is difficult to obtain stability with a numerical scheme because of the strong nonlinearity and degeneracy. We establish a linearized semi-implicit finite difference scheme that is faster than backward Euler implicit schemes. We analyze the stability of this scheme by adding a small perturbation to the coefficient function of the Richards equation. It is found that there is a linear relationship between the discretization error in a certain norm and the perturbation strength.

Event date： 2020.12

Language：English   Presentation type：Symposium, workshop panel (public)  

Venue：Online (Faculty of Science, Autonomous,University of Baja California, Mexico)   Country：Mexico  

Other Link： https://en-gb.facebook.com/events/1146685609084632/

Event date： 2020.10

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：オンライン   Country：Japan  

The dynamics of a neutral and an electrically conducting fluids is governed by the Lie-Poisson equation. This is a non-canonical Hamiltonian equation, and the degeneracy of the Hamiltonian structure admits Casmir invariants. The Lie-Poisson bracket is rewritten in terms of the Nambu bracket, which manifests the Casimirs hidden in it. The Casimirs are characterized, by Noether's theorem, as the integral invariants corresponding to the particle relabeling symmetry group.

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

Nambu-mechanics representation of Euler and MHD equations

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

Topological invariant of MHD revisited

Event date： 2020.6

Language：English  

Venue：Washington State Convention Center, Seattle   Country：United States  

Event date： 2019.12

Language：English   Presentation type：Oral presentation (general)  

Venue：Moscow in Institute for Problems in Mechanics of Russian Academy of Science (IPMech RAS)   Country：Russian Federation  

Event date： 2019.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Creswick Campus of the University of Melbourne．Creswick   Country：Australia  

Event date： 2019.10

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：Zhejiang Normal University, Jinhua   Country：China  

Event date： 2019.7

Language：English   Presentation type：Oral presentation (general)  

Venue：Campus de Blasco Ibanez of the Universitat de Valencia   Country：Spain  

Event date： 2019.7

Language：English  

Venue：Fukuoka   Country：Japan  

The compressibility effect on a premixed flame front is investigated for small Mach numbers Ma in terms of M² expansions. We extend the method of matched asymptotic expansions to O(Ma²) in which a flame front consists of he reaction and the preheat zones, By an asymptotic analysis of the reaction zone, we establish a rapid decrease of the laminar flame speed S-_L with Ma and a volumetric heat loss, of compressibility origin, brought by the pressure variation in the heat-conduction equation, which has been gone neglected in the zero-Mach-number limit. Together with O(Ma²) effect, this dramatic decrease in S-_L brings in stabilization of the Darrieus-Landau instability, the linear instability of a plane flame front.

Event date： 2019.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Scripps Forum, Scripps Institution of Oceanography (SIO), La Jolla   Country：United States  

Event date： 2019.6

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：La Trobe University’s City Campus, Melbourne   Country：Australia  

Event date： 2018.12

Language：English   Presentation type：Oral presentation (general)  

Venue：九州大学マス・フォア・インダストリ研究所   Country：Japan  

Event date： 2018.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Mathematical Sciences Research Institute (MSRI), Berkeley   Country：United States  

Event date： 2018.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Georgia World Congress Center, Atlanta   Country：United States  

Event date： 2018.11

Language：English   Presentation type：Oral presentation (general)  

Venue：仙台国際センター   Country：Japan  

Event date： 2018.9

Language：English   Presentation type：Oral presentation (general)  

Venue：New Century Hall, Embassy of Japan, Seoul   Country：Korea, Republic of  

Event date： 2018.8 - 2020.8

Language：English   Presentation type：Oral presentation (general)  

Venue：POI Cape Schultz Marine Experimental Station, Vladivostok   Country：Russian Federation  

Event date： 2018.8

Language：English   Presentation type：Oral presentation (general)  

Venue：V. I. Il’ychev Pacific Oceanological Institute, Far-Eastern Branch, Russian Academy of Sciences. Vladivostok   Country：Russian Federation  

Event date： 2018.3

Language：English   Presentation type：Oral presentation (general)  

Venue：Venture Business Labolatory, 名古屋大学   Country：Japan  

Event date： 2017.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Colorado Convention Center, enver   Country：United States  

Event date： 2017.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Moscow in Institute for Problems in Mechanics of Russian Academy of Science   Country：Russian Federation  

Event date： 2017.11

Language：English   Presentation type：Oral presentation (general)  

Venue：仙台国際センター   Country：Japan  

Event date： 2017.8

Language：English   Presentation type：Oral presentation (general)  

Venue：V.I. Il’ichev Pacific Oceanological Institute, Russian Academy of Sciences, Vladivostok   Country：Russian Federation  

Event date： 2017.8

Language：English   Presentation type：Oral presentation (general)  

Venue：The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste   Country：Italy  

Event date： 2017.8

Language：English  

Venue：Malang   Country：Indonesia  

We study the motion of a counter-rotating vortex pair with the circulations ±Γ move in incompressible fluid. The assumption is made that the core is very thin, that is the core radius σ is much smaller than the vortex radius d such that ϵ = σ/d ≤ 1. With this condition, the method of matched asymptotic expansion is employed. The solutions of the Navier-Stokes equations and the Biot-Savart law, regarding the inner and outer solutions respectively, are constructed in the form of a small parameter. An asymptotic expansion of the Biot-Savart law near the vortex core provides with the matching condition for an asymptotic expansion for limiting the Navier-Stokes equations for large radius r. The general formula of an anti-parallel vortex pair is established. At leading order O(ϵ), we apply the special case in inviscid fluid, the Rankine vortex, a circular vortex of uniform vorticity. Furthermore at leading order O(ϵ⁵) we show the traveling speed of a vortex pair.

Event date： 2017.7

Language：English   Presentation type：Oral presentation (general)  

Venue：知のフォーラム, 東北大学片平キャンパス, 仙台   Country：Japan  

Event date： 2017.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Carry-le-Rouet, Marseilles   Country：France  

Event date： 2016.11

Language：English   Presentation type：Oral presentation (general)  

Venue：京都大学数理解析研究所   Country：Japan  

Event date： 2016.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Punta Arenas & Puerto Natales   Country：Chile  

Event date： 2016.8

Language：English   Presentation type：Oral presentation (general)  

Venue：Palais des congres, Montreal   Country：Canada  

Event date： 2016.6

Language：English   Presentation type：Oral presentation (general)  

Venue：関西セミナーハウス, 京都   Country：Japan  

Event date： 2016.5 - 2016.6

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Kutateladze Institute of Thermophysics, SB RAS, Novosibirsk   Country：Russian Federation  

Event date： 2016.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Palazzo Franchetti, Venice   Country：Jordan  

Event date： 2016.2

Language：English   Presentation type：Oral presentation (general)  

Venue：nstitute for Advanced Study, La Trobe University, Mebourne   Country：Australia  

Event date： 2016.1

Language：English   Presentation type：Oral presentation (general)  

Venue：京都大学理学部   Country：Japan  

Event date： 2015.12

Language：English   Presentation type：Oral presentation (general)  

Venue：University of Yangon   Country：Myanmar  

Event date： 2015.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Hynes Convention Center, Boston   Country：United States  

Event date： 2015.11

Language：English   Presentation type：Oral presentation (general)  

Venue：西新プラザ, 九州大学   Country：Japan  

Event date： 2015.11

Language：English   Presentation type：Oral presentation (general)  

Venue：早稲田大学・西早稲田キャンパス   Country：Japan  

Event date： 2015.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Hotel “VOLNA”, Svetlogorsk, Kaliningrad   Country：Russian Federation  

Event date： 2015.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Independent University, Moscow   Country：Russian Federation  

Event date： 2014.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Moscone (West) Convention Center, San Francisco   Country：United States  

Event date： 2014.11

Language：English   Presentation type：Oral presentation (general)  

Venue：早稲田大学西早稲田キャンパス   Country：Japan  

Event date： 2014.11

Language：English   Presentation type：Oral presentation (general)  

Venue：The University of Mandalay   Country：Myanmar  

Event date： 2014.9

Language：English  

Venue：Kyoto   Country：Japan  

In March 11, 2011 tsunami activated by the 2011 off the pacific coast of Tohoku Earthquake led to several compound disasters in Japan. Many coastal protection structures such as seawalls and breakwaters were damaged seriously but, surprisingly a waste tire retaining wall, located just about 150 m away from a completely collapsed seawall was found to be undamaged. In order to demonstrate how effectively these tires will function against the earthquake and tsunami to protect seawall, a new model was developed and tsunami impact force experiments were performed for a sea wall with model tires behind it (land side). Results from the tsunami impact force experiments showed a better performance of the sea wall when protected with tires placed behind the seawall. At the same time, field test were conducted by cultivating different kind of plants inside the actual tires to maintain the environment. The field test results showed that the greening effect could be maintained by planting trees inside the tires.

Event date： 2014.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東北大学川内北キャンパス   Country：Japan  

Event date： 2014.9 - 2014.8

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：中部大学春日井キャンパス   Country：Japan  

Event date： 2014.3

Language：English   Presentation type：Oral presentation (general)  

Venue：北海道大学, 札幌   Country：Japan  

Event date： 2013.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：核融合科学研究所, 土岐市   Country：Japan  

Event date： 2013.11

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：Zhejiang Normal University, Jinhua   Country：China  

Event date： 2013.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：徳島大学 常三島キャンパス, 徳島市   Country：Japan  

Event date： 2013.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東京農工大学小金井キャンパス, 小金井市, 東京   Country：Japan  

Event date： 2013.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Exeter University, Exeter   Country：United Kingdom  

Event date： 2013.8

Language：English   Presentation type：Oral presentation (general)  

Venue：Shanghai Sun Island Resort, 上海   Country：China  

Event date： 2013.7

Language：English   Presentation type：Oral presentation (general)  

Venue：札幌コンベンションセンター, 札幌   Country：Japan  

Event date： 2013.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Russian State Hydrometeorological University, St.-Petersburg   Country：Russian Federation  

Event date： 2013.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東海大学 湘南キャンパス, 平塚市   Country：Japan  

Event date： 2013.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：広島大学東広島キャンパス   Country：Japan  

Event date： 2013.3

Language：English  

Venue：九州大学医学部百年講堂   Country：Japan  

Event date： 2012.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Banff International Research Station for Mathematical Innovation and Discovery (BIRS), Banff   Country：Canada  

A steady Euler flow of an inviscid incompressible fluid is characterized as an extremum of the total kinetic energy (=the Hamiltonian) with respect to perturbations constrained to an isovortical sheet (=coadjoint orbits). We exploit the criticality in the Hamiltonian to calculate the energy of three-dimensional waves on a steady vortical flow, and, as a by-product, to calculate the mean flow, induced by nonlinear interaction of waves with themselves.
　We apply these formulas to the linear and weakly nonlinear stability of a rotating flow confined in a cylinder of elliptic cross-section. The linear instability, parametric resonance between a pair of Kelvin waves, is known as the Moore-Saffman-Tsai-Widnall (MSTW) instability. The linear stability characteristics is well captured from the viewpoint of Krein's theory of Hamiltonian spectra. Furthermore, with the mean flow induced by the Kelvin waves, a hybrid method of combining the Eulerian and the Lagrangian approaches is developed to deduce the amplitude equations to third order.

Event date： 2012.10

Language：English   Presentation type：Oral presentation (general)  

Venue：大阪大学豊中キャンパス   Country：Japan  

Event date： 2012.9

Presentation type：Oral presentation (general)  

Venue：東洋大学・白山キャンパス   Country：Japan  

Event date： 2012.8

Language：English   Presentation type：Oral presentation (general)  

Venue：China National Convention Center (CNCC)   Country：China  

Event date： 2012.6

Presentation type：Oral presentation (general)  

Venue：熊本大学・黒髪キャンパス   Country：Japan  

Event date： 2012.6

Presentation type：Oral presentation (general)  

Venue：University of Nottingam, Nottingam   Country：United Kingdom  

Event date： 2012.3

Presentation type：Oral presentation (general)  

Venue：関西学院大学・西宮上ケ原キャンパス, 西宮   Country：Japan  

Event date： 2012.3

Presentation type：Oral presentation (general)  

Venue：関西学院大学・西宮上ケ原キャンパス, 西宮   Country：Japan  

Event date： 2012.3

Presentation type：Oral presentation (general)  

Venue：東京大学生産技術研究所, 目黒区   Country：Japan  

Event date： 2012.2

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：Mandalay University   Country：Myanmar  

Event date： 2011.12

Presentation type：Oral presentation (invited, special)  

Venue：愛媛大学理学部   Country：Japan  

Event date： 2011.12

Presentation type：Oral presentation (general)  

Venue：東京大学本郷キャンパス・山上会館   Country：Japan  

Event date： 2011.11

Presentation type：Symposium, workshop panel (public)  

Venue：九州大学応用力学研究所, 春日   Country：Japan  

Event date： 2011.11

Venue：ホテルメトロポリタン仙台   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：V.I.Il`ichev Pacific Oceanological Institute, Vladivostok   Country：Russian Federation  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：Zhejiang Normal University, Jinhua   Country：China  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：富山大学五福キャンパス, 富山   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：首都大学東京・南大沢キャンパス, 八王子   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：首都大学東京・南大沢キャンパス, 八王子   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：パシフィコ横浜   Country：Japan  

Event date： 2011.8

Presentation type：Oral presentation (invited, special)  

Venue：アピカルイン京都   Country：Japan  

Event date： 2011.8

Presentation type：Oral presentation (invited, special)  

Venue：The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste   Country：Italy  

回転流や立つ3次元波をケルヴィン波といい、軸対称性や並進対称性を破る摂動を加えると2個のケルヴィン波が共鳴不安定を起こす。ハミルトン力学系のスペクトル理論によると、ケルヴィン波のエネルギーの符号が不安定化の鍵を握る。ラグランジュ変位を基本変数にとって撹乱を渦なしに限定することによって、波の非線形相互作用によって誘起される振幅について2次の平均流を計算できることを示した。渦なし撹乱の定義を循環保存と関係づけることによって、擬運動量が平均流とストークスドリフトの和と等しく、円筒容器中では後者が消えるので、擬運動量と平均流が等しいことを証明した。これらを利用することによって、軸対称波と楕円変形波との共鳴のからのハミルトン的ホップ分岐の成長をあらわす弱非線形振幅方程式の係数を3次まであいまいさなく求めることに初めて成功した。

Event date： 2011.8

Presentation type：Oral presentation (general)  

Venue：北海道大学理学部   Country：Japan  

Event date： 2011.7

Presentation type：Oral presentation (general)  

Venue：京都大学数理解析研究所   Country：Japan  

Event date： 2011.7

Presentation type：Oral presentation (general)  

Venue：京都大学数理解析研究所   Country：Japan  

Event date： 2011.6 - 2011.7

Presentation type：Oral presentation (general)  

Venue：YIHE Hotel Guangzhou, Guangzhou   Country：China  

Event date： 2011.3

Presentation type：Oral presentation (general)  

Venue：新潟大学・五十嵐キャンパス   Country：Japan  

Event date： 2011.2

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：NZ Institute for Advanced Study, Massey University, Auckland   Country：New Zealand  

Event date： 2011.1

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：キャンパスプラザ京都   Country：Japan  

Event date： 2010.12

Presentation type：Oral presentation (general)  

Venue：福岡大学工学部   Country：Japan  

Event date： 2010.11

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：愛媛大学理学部, 松山   Country：Japan  

Event date： 2010.11

Venue：仙台国際センター   Country：Japan  

Event date： 2010.10

Presentation type：Oral presentation (general)  

Venue：九州大学・筑紫キャンパス，春日   Country：Japan  

Event date： 2010.9

Presentation type：Oral presentation (general)  

Venue：大阪府立大学・中百舌鳥キャンパス, 堺   Country：Japan  

Event date： 2010.9

Presentation type：Oral presentation (general)  

Venue：大阪府立大学・中百舌鳥キャンパス, 堺   Country：Japan  

Event date： 2010.9

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Country：Japan  

Event date： 2010.9

Presentation type：Oral presentation (general)  

Venue：北海道大学高等教育機能開発総合センター   Country：Japan  

Event date： 2010.9

Presentation type：Oral presentation (general)  

Venue：北海道大学高等教育機能開発総合センター   Country：Japan  

Event date： 2010.7

Presentation type：Oral presentation (general)  

Venue：Sheraton Hotel Newfoundland, St. John's   Country：Canada  

Event date： 2010.5

Presentation type：Oral presentation (general)  

Venue：Zhejiang Normal University and Wuxing Hotel, Jinhua   Country：China  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：岡山大学津島キャンパ   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：岡山大学津島キャンパス   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：早稲田大学 西早稲田キャンパス   Country：Japan  

Event date： 2010.3

Presentation type：Oral presentation (general)  

Venue：早稲田大学 西早稲田キャンパス   Country：Japan  

Event date： 2010.2

Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：Department of Mathematics, Zhejiang Normal University, Jinhua   Country：China  

Event date： 2009.12

Presentation type：Oral presentation (invited, special)  

Venue：Pontificia Universidade Catolica de Parana (PUCPR), Curitiba   Country：Brazil  

Event date： 2009.12 - 2010.12

Presentation type：Oral presentation (general)  

Venue：神戸大学六甲台キャンパス   Country：Japan  

Event date： 2009.12

Presentation type：Oral presentation (general)  

Venue：大阪大学基礎工学部   Country：Japan  

Event date： 2009.10

Presentation type：Oral presentation (general)  

Venue：京都大学大学院理学研究科   Country：Japan  

Event date： 2009.9

Presentation type：Oral presentation (general)  

Venue：熊本大学・黒髪キャンパス   Country：Japan  

Event date： 2009.9

Presentation type：Oral presentation (general)  

Venue：熊本大学・黒髪キャンパス   Country：Japan  

Event date： 2009.9

Presentation type：Oral presentation (general)  

Venue：東洋大学・白山キャンパス   Country：Japan  

Event date： 2009.7

Presentation type：Oral presentation (general)  

Venue：京都大学大学院人間環境学研究科   Country：Japan  

Event date： 2009.6

Presentation type：Oral presentation (general)  

Venue：名古屋大学Business Laboratory   Country：Japan  

Event date： 2009.5

Presentation type：Oral presentation (general)  

Venue：高知工科大学, 香美   Country：Japan  

Event date： 2009.4

Venue：大阪大学レーザーエネルギー学研究センター   Country：Japan  

Event date： 2009.3

Presentation type：Oral presentation (general)  

Venue：University of Karlsruhe (TH), Karlsruhe   Country：Germany  

Event date： 2008.1

Presentation type：Oral presentation (general)  

Venue：大阪大学レーザーエネルギー科学研究所，豊中市   Country：Japan  

Presentation type：Oral presentation (general)  

Venue：The Abdus Salam International Centre for Theoretical Physics (ICTP)   Country：Italy  

Presentation type：Oral presentation (general)  

Venue：岡山大学 (岡山市)   Country：Japan  

Linear stability of thin vortex rings in the short-wavelength limit
By Yuji Hattori and Yasuhide Fukumoto

Presentation type：Oral presentation (general)  

Venue：University of Birmingham   Country：United Kingdom  

Presentation type：Oral presentation (general)  

Venue：九州大学応用力学研究所 (福岡市)   Country：Japan  

Linear stability of thin vortex rings - Local stability analysis
By Yuji Hattori and Yasuhide Fukumoto

Presentation type：Oral presentation (general)  

Venue：St. Petersburg   Country：Russian Federation  

Presentation type：Oral presentation (general)  

Venue：Warsaw University of Technology, Warsaw   Country：Poland  

Presentation type：Oral presentation (general)  

Venue：University of Hyderabad, Hyderabad   Country：India  

Presentation type：Oral presentation (general)  

Venue：Rencontres Mathematiques de Rouen, INSA de Rouen   Country：France  

Presentation type：Oral presentation (general)  

Venue：Rencontres Mathematiques de Rouen, INSA de Rouen   Country：France  

Presentation type：Oral presentation (general)  

Venue：横浜シンポジア, 横浜   Country：Japan  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Topology and dynamics of vortex in the Euler-Poincare framework,
by Yasuhide Fukumoto
Bussei Kenkyu, Vol.81, No.3 (December, 2003) (Yukawa Institute, Kyoto University)

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Integrable systems associated with vortex filaments,
by Yasuhide Fukumoto
Supplements of Sugaku Seminar: Sugaku no Tanoshimi, No.25 (2001) pp.21-31 (Nihon-Hyoron-sha)

Type：Competition, symposium, etc. 

Number of participants：120

Type：Scientific advice/Review 

Type：Competition, symposium, etc. 

Number of participants：300

Type：Scientific advice/Review 

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：5

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：5

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0

Type：Competition, symposium, etc. 

Number of participants：120

Type：Competition, symposium, etc. 

Number of participants：70

Type：Competition, symposium, etc. 

Number of participants：90

Type：Competition, symposium, etc. 

Number of participants：40

Type：Academic society, research group, etc. 

Type：Competition, symposium, etc. 

Number of participants：120

Type：Competition, symposium, etc. 

Number of participants：120

Type：Competition, symposium, etc. 

Number of participants：80

Type：Competition, symposium, etc. 

Number of participants：60

Type：Competition, symposium, etc. 

Number of participants：80

Type：Competition, symposium, etc. 

Number of participants：30

Type：Competition, symposium, etc. 

Number of participants：60

Type：Competition, symposium, etc. 

Number of participants：120

Type：Competition, symposium, etc. 

Number of participants：20

Type：Competition, symposium, etc. 

Number of participants：40

Type：Competition, symposium, etc. 

Number of participants：120

Type：Competition, symposium, etc. 

Number of participants：20

Type：Competition, symposium, etc. 

Number of participants：40

Type：Academic society, research group, etc. 

Type：Academic society, research group, etc. 

Type：Academic society, research group, etc. 

Type：Competition, symposium, etc. 

Number of participants：40

Type：Competition, symposium, etc. 

Number of participants：60

Type：Competition, symposium, etc. 

Number of participants：100

Type：Competition, symposium, etc. 

Number of participants：60

Type：Competition, symposium, etc. 

Number of participants：100

Type：Competition, symposium, etc. 

Number of participants：70

Type：Competition, symposium, etc. 

Number of participants：59

Type：Competition, symposium, etc. 

Number of participants：40

Type：Competition, symposium, etc. 

Number of participants：61

Type：Competition, symposium, etc. 

Number of participants：50

Type：Competition, symposium, etc. 

Number of participants：100

Type：Competition, symposium, etc. 

Number of participants：70

Type：Competition, symposium, etc. 

Number of participants：120

Type：Competition, symposium, etc. 

Number of participants：70

Type：Competition, symposium, etc. 

Number of participants：500

Type：Competition, symposium, etc. 

Number of participants：500

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc.