Yasuhide Fukumoto | Last modified date：2023.11.22 |

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Undergraduate School

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##### https://kyushu-u.elsevierpure.com/en/persons/yasuhide-fukumoto

Reseacher Profiling Tool Kyushu University Pure

Phone

092-802-4440

Fax

092-802-4405

Academic Degree

PhD

Country of degree conferring institution (Overseas)

No

Field of Specialization

fluid mechanics

Total Priod of education and research career in the foreign country

02years00months

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).

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

**Research Interests**

- Nambu bracket for ideal fluid and MHD equations and their applications

keyword : Nambu bracket, Casimir invariant, Isovortical perturbation

2020.02～2023.06. - Numerical analysis of infiltration of water into soil

keyword : Richards equation, nonlinear parabolic partial differential equation, numerical analysis, explicit finite difference scheme, stability

2019.07～2021.06. - Effect of compressibility on instability of a premixed flame front

keyword : Combustion, Premixed flame, Laminar flame speed, Markstein effect, Darrieous-Landau instability

2016.04～2020.06. - 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

2007.04～2020.06. - Local stability analyses of magnetohydrodynamics and magnetorotational instability

keyword : Magnetorotational instability, WKB method, Frieman-Rotenberg equation, Hain-Lust方程式, Taylor instability

2012.04～2025.06. - 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**

**Books**

1. | Handbook of Fluid Mechanics, Ver.2, Chap.5 "Vortex" (ed. by the Japan Society of Fluid Mechanics, Maruzen) by Yasuhide Fukumoto, Takeshi Miyazaki. |

**Papers**

**Presentations**

Educational

**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.

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..

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