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Yasuhide Fukumoto Last modified date:2023.11.22

Graduate School
Undergraduate School

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 Reseacher Profiling Tool Kyushu University Pure
Academic Degree
Country of degree conferring institution (Overseas)
Field of Specialization
fluid mechanics
Total Priod of education and research career in the foreign country
Outline Activities
I am engaged in the mathematical study of problems arising in fluid
mechanics. Fluid motion governed by the Navier-Stokes equations is a
nonlinear dynamical system of infinite degrees of freedom, with a
hierarchy of modes of various scales coupling with each other, and
exhibits a complicated irregular behavior. From a viewpoint vortices and
waves as fundamental elements, I make an effort to understand fluid
phenomena and then to build mathematical and numerical models for
analyzing them. My interest is also in solar magnetic fields and
magnetohydrodynamics in space.
Recently, I have been working on nonlinear analyses of the
three-dimensional vortex motion. By invoking ideas and machinery in
integrable systems and Hamiltonian dynamical systems, I derived an
accurate formula of translation speed of a vortex ring and discovered
its new instability mode.
I have been appointed as an Editor of Fluid Dyn. Research. Also I have
been a member of organizing committee of a couple of domestic Conferences.

My graduate students are encouraged to tackle with original problems
for their Master Theses. I have a foreign student. I invited a few
foreign scholars from Italy, Croatia and Russia for short terms.

Based on my experience, I wrote the Chapter "Vortex Dynamics" in the
"Dictionary of Flows" (Maruzen, 2004). Since 2005, I have been writing a
series of expository articles ``Fundamentals of Vortex Motion" in
``Nagare", a bimonthly Journal edited by the Japan Society of Fluid
Mechanics. I gave an introductory lecture on "topological aspect of
vortex and its relation to a variational principle" at Mathematical
Physics Summer School 2003, held at Tokyo University, September 2003,
and published its Lecture Note (2005).
Research Interests
  • Nambu bracket for ideal fluid and MHD equations and their applications

    keyword : Nambu bracket, Casimir invariant, Isovortical perturbation
  • Numerical analysis of infiltration of water into soil
    keyword : Richards equation, nonlinear parabolic partial differential equation, numerical analysis, explicit finite difference scheme, stability
  • Effect of compressibility on instability of a premixed flame front
    keyword : Combustion, Premixed flame, Laminar flame speed, Markstein effect, Darrieous-Landau instability
  • Topological invariants of flows of a neutral and an electrically conducting fluids and their characterization by Noether theorem
    keyword : Topological invariants, Cross-helicity, Noether theorem, Euler-Poincare equation
  • Local stability analyses of magnetohydrodynamics and magnetorotational instability
    keyword : Magnetorotational instability, WKB method, Frieman-Rotenberg equation, Hain-Lust方程式, Taylor instability
  • Three-domentional stability of vortices in a fluid
    keyword : Elliptic vortex, Vortex ring, Three-dimensional stablility, Krein's theory of Hamiltonian spectra, WKB method
    1999.04I investigate three-dimensional instability of a vortex tube to infinitesimal perturbations of long and short wavelengths. An elliptic vortex column serves as a universal model for strained vortices. Three-dimensional instability of a vortex tube subjected to a weak strain is investigated from the viewpoint of Krein's theory for Hamiltonian spectra. Energetic aspect of instability is clarified. Kirchhoff's elliptic vortex is subjected to finite strain. Three-dimensional linear stability of Kirchhoff's elliptic vortex, based on the Euler equation, is numerically investigated. To supplement this result, we made a local stability analysis of potential flows, using the WKB method. We verified rigorously that the parametric resonance is absent in this case. A new instability mode originating from vortex-line curvature is found for a vortex ring. This finding is supported by a local stability analysis using the WKB method..
  • Motion of a vortex ring in a viscous fluid
    keyword : Vortex ring, Navier-Stokes equations, Matched asymptotic expansions, Dyson's method
    1996.08A 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. The method of matched asymptotic expansions is extended to a third order in a small parameter, the ratio of core to ring radii. It is demonstrated that viscosity acts to expand, linearly in time, the ring radius. By exploiting the formulas of kinetic energy and impulse, Fraenkel-Saffman's first-order formula (1970) for translation speed is successfully extended to third order..
  • Three-dimensional dynamics of a vortex filament in a fluid
    keyword : Vortex filament, Biot-Savart law, Localized induction approximation, Integrable system, Laser-matter interaction
    1998.01Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated based on the Euler equations. The method of matched asymptotic expansions in a small parameter, the ratio of core to curvature radii, is extended to a higher order and thereby torsion and nonuniformity in curvature along the center curve is taken into consideration. We devise a systematic method for an asymptotic development of the Biot-Savart law. The velocity of a vortex filament is derived to third order. In the localized induction approximation, the resulting equation of filament motion is reducible to a completely integrable evolution equation among the localized induction hierarchy. We have studied the string-like structure generated by irradiating nano-second XeCl excimer laser pulses on Co-coated substrate. 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..
Current and Past Project
  • The Russian team led by a fluid dynamicist who is actively working in Denmark, featured by wind power generation, and the Japanese team, of which the members are developing the frontier of fluid dynamics, specifically vortex dynamics and turbulence, are jointed together to tackle with problems of wind power generation, in three ways of theoretical analysis, large-scale numerical simulations, and experiments, specifically, "Estimation and optimization of power generation efficiency by wind turbines (= rotors) based on helical vortices"
  • The aim of the program is to activate local economies through realization of a locally-generated and locally-used energy that is not dependent on the power grid, and by circulating cash produced with clean energy within the community. Various technologies and systems for clean energy will be used such as high-accuracy supply and demand estimation of power, support for electric power procurement planning, energy management system, “Pay-As-You-Save” (PAYS) payment scheme for electric utility expenses, and imbalance compensation utilizing electric vehicles (EV) or hydrogen. By utilizing the capital funds, we will be able to provide transportation options to those who are mobility disadvantaged, offer ICT monitoring services to promote "safety and security" to those who are socially disadvantaged, and take measures to revitalize the activities of local residents that have a stay-at-home tendency.
  • Topological vorticity dynamics in the physical and biological sciences
  • We study the stability of vortices with swirl. The effects of swirl on a helical vortex tube which is a model of rotating wingtip vortices is investigated by linear stability analysis and DNS.
Academic Activities
1. Handbook of Fluid Mechanics, Ver.2, Chap.5 "Vortex" (ed. by the Japan Society of Fluid Mechanics, Maruzen)
by Yasuhide Fukumoto, Takeshi Miyazaki.
1. R. Zou, J. Labarbe, O. N. Kirillov, Y. Fukumoto, Analysis of azimuthal magnetorotational instability of rotating magnetohydrodynamic flows and Tayler instability via an extended Hain-Lüst equation, Physical Review E, 10.1103/PhysRevE.101.013201, 101, 1, 2020.01, We consider a differentially rotating flow of an incompressible electrically conducting and viscous fluid subject to an external axial magnetic field and to an azimuthal magnetic field that is allowed to be generated by a combination of an axial electric current external to the fluid and electrical currents in the fluid itself. In this setting we derive an extended version of the celebrated Hain-Lüst differential equation for the radial Lagrangian displacement that incorporates the effects of the axial and azimuthal magnetic fields, differential rotation, viscosity, and electrical resistivity. We apply the Wentzel-Kramers-Brillouin method to the extended Hain-Lüst equation and derive a comprehensive dispersion relation for the local stability analysis of the flow to three-dimensional disturbances. We confirm that in the limit of low magnetic Prandtl numbers, in which the ratio of the viscosity to the magnetic diffusivity is vanishing, the rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. In the analysis of the dispersion relation we find evidence of a new long-wavelength instability which is caught also by the numerical solution of the boundary value problem for a magnetized Taylor-Couette flow..
2. Ummu Habibah, Hironori Nakagawa, Yasuhide Fukumoto, Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers, Fluid Dynamics Research, 10.1088/1873-7005/aaa5c8, 50, 3, 2018.03, We establish a general formula for the translational speed of a counter-rotating vortex pair, valid for thick cores, moving in an incompressible fluid with and without viscosity. We extend to higher order the method of matched asymptotic expansions developed by Ting and Tung (1965 Phys. Fluids 8 1039-51). The solution of the Euler or the Navier-Stokes equations is constructed in the form of a power series in a small parameter, the ratio of the core radius to the distance between the core centers. For a viscous vortex pair, the small parameter should be where ν is the kinematic viscosity of the fluid and Γ is the circulation of each vortex. A correction due to the effect of finite thickness of the vortices to the traveling speed makes its appearance at fifth order. A drastic simplification is achieved of expressing it solely in terms of the strength of the second-order quadrupole field associated with the elliptical deformation of the core. For a viscous vortex pair, we exploit the conservation law for the hydrodynamic impulse to derive the growth of the distance between the vortices, which is cubic in time..
3. Yasuhide Fukumoto, M. Hirota, Elliptical instability of a vortex tube and drift current induced by it, Physica Scripta, Vol.T132, 014041 (9 pages), 2008.10.
4. Yasuhide Fukumoto, H. K. Moffatt, Kinematic variational principle for motion of vortex rings, Physica D, Vol.237, No.14-17, pp.2210-2217, 2008.08.
5. Yasuhide Fukumoto, V. L. Okulov, The velocity field induced by a helical vortex tube, Physics of Fluids, 10.1063/1.2061427, 17, 10, Vol. 17, No.10, pp. 107101-1-19, 2005.10.
6. Yasuhide Fukumoto, The three-dimensional instability of a strained vortex tube revisited, Journal of Fluid Mechanics, 10.1017/S0022112003006025, 493, 287-318, Vol.493, pp.287-318, 2003.10.
7. Yuji Hattori, Yasuhide Fukumoto, Short-wavelength stability analysis of thin vortex rings, Physics of Fluids, 10.1063/1.1606446, 15, 10, 3151-3163, Vol.15, No.10, pp.3151-3163, 2003.10.
8. Yasuhide Fukumoto, Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy, European Physical Journal B, 10.1140/epjb/e2002-00279-5, 29, 2, 167-171, Vol.29, No.2, pp.167-171, 2002.09.
9. Yasuhide Fukumoto, H. K. Moffatt, Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity, Journal of Fluid Mechanics, 10.1017/S0022112000008995, 417, 1-45, Vol.417, pp.1-45, 2001.08.
10. Yasuhide Fukumoto, Stationary configurations of a vortex filament in background flows, Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, Vol.453, No.1961, pp.1205-1232, 1997.06.
11. Yasuhide Fukumoto, Mitsuharu Miyajima, The localised induction hierarchy and the Lund-Regge equation, Journal of Physics A - Mathmatical and General, 10.1088/0305-4470/29/24/025, 29, 24, 8025-8034, Vol.29, No.24, pp.8025-8034, 1996.12.
1. Yasuhide Fukumoto, Rong ZOU, Nambu bracket for ideal fluid and MHD equations and their applications, International School of Mathematics ≪Guido Stampacchia≫ & Workshop: Topological Methods in Mathematical Physics, 2022.09.
2. Yasuhide Fukumot, Rong ZOU, Nambu-mechanics representation of Euler and MHD equations, Mathematical Aspects of the Contemporary Continuum Mechanics, 2021.11.
3. Yasuhide Fukumoto,Rong ZOU, Casimirs and Nambu brackets for fluid dynamics and magnetohydrodynamics, 大阪市立大学数学研究所・共同利用研究 pace-time topology behind formation of micro-macro magneto-vertical structure manifested by Nambu mechanics, 2020.09, 電磁流体の運動(MHD)においては、全質量、全エントロピー、磁気ヘリシティに加えて、クロスヘリシティがカシミール不変量である。この4個のカシミール不変量を用いて、MHDのリー・ポアッソン方程式(Morrison and Green 1980)が南部括弧によって表現できることを示した。クロスヘリシティがカシミール不変量でないことが、20世紀末からの懸案であったが、南部力学表現はこの問題を自動的に完全解決する。.
4. Yasuhide Fukumoto & Keigo Wada, Effect of compressibility in the reaction zone of a premixed flame and its implication to the Darrieus-Landau instability, KIAS Workshop on Mathematics of Fluid Motion III: Theory and Computation, 2019.12.
5. Yasuhide Fukumoto & Valery L. Okulov, Asymptotic expansions for motion of a curved vortex filament tube will elliptically deformed core, 4th International Retreat on Vortical Flow and Aerodynamics (IRVA4), 2018.10.
6. Yasuhide Fukumoto, Introduction to topological fluid dynamics and magnetohydrodynamics, ISTITUTO NAZIONALE DI ALTA MATEMATICA (INdAM), GRUPPO NAZIONALE PER LA FISICA MATEMATICA (GNFM) , 2017.09.
7. Yasuhide Fukumoto, Hironori Nakagawa & Ummu Habibah, Motion of a vortex pair and its application to industry, Workshop / Summer School on "Fluid-structure interactions and vortex dynamics in aerodynamics", 2015.06.
8. Yasuhide Fukumoto, Rong Zou, Azimuthal and helical magnetorotational instabilities to non-axisymmetric perturbations, Turbulent Mixing and Beyond Workshop: Mixing in Rapidly Changing Environment - Probing Matter at the Extremes, 2014.08.
9. Yasuhide Fukumoto, Are all the topological invariants representable as cross helicities?, JSPS/UK Meeting "Topological Vorticity Dynamics in the Physical Sciences", 2013.09.
10. Yasuhide Fukumoto, Hirofumi Sakuma, A unified view of topological invariants of barotropic and baroclinic fluids and their application to formal stability analysis of three-dimensional ideal gas flows, IUTAM symposium "Topological Fluid Dynamics", 2012.07, 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..
Educational Activities
I direct students in the Master and Doctor Courses. Seminar classes are
held for Graduate students, the third and fourth year students of the
Undergraduate Course. In seminars, students read textbooks in the field
of fluid mechanics and dynamical systems chosen in conformity with their
knowledge and interest. The students are trained to make original
research for their Master Theses.
I give lectures for graduate and undergraduate students of mathematics,
and have courses on "industrial mathematics" in Faculty of Engineering
and on "calculus" in general education. For the fourth year students of
mathematics, I give an introductory lecture on "fluid mechanics" and
"dynamical systems". For graduate students, topics are chosen from the
latest topics in "vortex dynamics" and "magnetohydrodynamics".
I gave an intensive course in Hiroshima University (2003).
 I made an effort to supervise PhD students of the Functional Mathematics Course. So far, 6 students of mine made the long-term (over 3 months) research internship at research institutes of industry. I also accept many overseas students. So far, 7 students of mine received PhD.
Other Educational Activities
  • 2020.03, I gave a lecture on a topic of fluid dynamics to about 15 graduate students of the Department of Mathematics at the University of Yangon and Mandalay University (Myanmar) who stayed at Kyushu University for 10 days..
  • 2019.10, Under the support of JASSO's program of short-term visit, I visited Zhejiang Normal University for 9 days and conducted joint research with a former student (now a lecturer at Zhejiang Normal University). During my stay, I gave 4 seminars to professors and graduate students for research exchange..