Yasuhide Fukumoto | Last modified date：2019.07.02 |

Graduate School

Undergraduate School

Other Organization

Administration Post

Other

E-Mail

Phone

092-802-4440

Fax

092-802-4405

Academic Degree

PhD

Field of Specialization

fluid mechanics

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**

- 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**

- 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).

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).

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