Yasuhide Fukumoto | Last modified date：2024.05.07 |

Professor /
Division of Applied Mathematics /
Institute of Mathematics for Industry

**Presentations**

1. | Yasuhide Fukumoto, Rong Zou, Particle-relabeling as variational and divergence symmetries for ideal fluid dynamics and magnetohydrodynamics, OCAMI Workshop: The Grad Conjecture in Fluid Mechanics and Magnetohydrodynamics: Theory and Applications, 2024.03. |

2. | Yasuhide Fukumoto, Rong Zou, Isovortical perturbation and wave energy of compressible neutral and conducting fluids based on Frieman-Rotenberg equation, GEOTOP-A International Conference Applications of Geometry and Topology, 2024.01. |

3. | Yasuhide Fukumoto, Rong Zou, Topological invariants and Nambu bracket for ideal fluid dynamics and magnetohydrodynamics, IASM-BIRS Workshop Vortex Dynamics: the Crossroads of Mathematics, Physics and Applications, 2023.12. |

4. | Yasuhide Fukumoto, Fengnan Liu, Xiaopeng Zhao, Efficient algorithms for solving Richards equation: from linearized finite element method to deep learning, CREST 2023 2nd International Symposium on Construction Resources for Environmentally Sustainable Technologies, 2023.11. |

5. | Yasuhide Fukumoto, Rong Zou, Kazuo Matsuura, Nobutaka Taniguchi, Compressibility effect on Kelvin-Helmholtz and Rayleigh-Taylor instabilities, 20th International Conference on Flow Dynamics (ICFD2023), 2023.11. |

6. | Yasuhide Fukumoto, Rong Zou, Kazuo Matsuura, Nobutaka Taniguchi, Effect of compressibility on Kelvin-Helmholtz and Rayleigh-Taylor instabilities, Exploration Conference: Interfaces and Mixing in Fluids, Plasmas, Materials, 2023.10. |

7. | Yasuhide Fukumoto, Rong Zou, Kazuo Matsuura, Nobutaka Taniguchi, Compressible Kelvin-Helmholtz and Rayleigh-Taylor instabilities, 10th International Congress on Industrial and Applied Mathematics (ICIAM2023 Tokyo), 2023.08. |

8. | Yasuhide Fukumoto, Rong Zou, Kazuo Matsuura, Nobutaka Taniguchi, Compressible Kelvin-Helmholtz and Rayleigh-Taylor instabilities, IUPAP 28th International Conference on Statistical Physics (STATPHYS28), 2023.08. |

9. | Yasuhide Fukumoto, Alejandro Mendez Rojas, Global time evolution of a vortex pair in a viscous fluid, 22nd ECMI Conference on Industrial and Applied Mathematics (ECMI 2023), 2024.06. |

10. | Yasuhide Fukumoto, Optimal design of observation holes on strainers for groundwater measurement, 173 ESGI (European Study Group with Industry), 2023.06. |

11. | Yasuhide Fukumoto, Okabe & Inoue's contribution to formation and metamorphoses of a vortex ring, 13th International School for Young Scientists "WAVES AND VORTICES IN COMPLEX MEDIA", 2022.12. |

12. | Yasuhide Fukumoto, Rong ZOU, Nambu brackets and induced Lie-Poisson brackets for fluid mechanics and magnetohydrodynamics, 75th Annual Meeting of the APS Division of Fluid Dynamics, 2022.11. |

13. | Yasuhide Fukumoto, Rong ZOU, Compact Nambu brackets for fluid and MHD equations, 19th International Conference on Flow Dynamics (ICFD2022), 2022.11. |

14. | Yasuhide Fukumoto, Toward an analytical approach for simulating motion of a helical vortex tube: Legacy of Valery Okulov, International Workshop on Turbulence, Vorticity Dynamics and Wind Energy, 2022.09. |

15. | 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. |

16. | Kazuo Matsuura, Yasuhide Fukumoto, "Hierarchical Clustering of Vortical Regions in Transitional Boundary Layers, Invited workshop "Liutex and Third Generation of Vortex Identification for Engineering Applications" in "Aerospace and Aeronautics World Forum", 2021.12. |

17. | Yasuhide Fukumot, Rong ZOU, Nambu-mechanics representation of Euler and MHD equations, Mathematical Aspects of the Contemporary Continuum Mechanics, 2021.11. |

18. | Yasuhide Fukumoto, Rong ZOU, Noether's theorem, relabeling symmetry, Casimir invariants, generalized Bianchi identity, 18h International Conference on Flow Dynamics (ICFD2021), 2021.10. |

19. | Yasuhide Fukumoto, Rong ZOU, Particle relabeling symmetry and Noether's first and second theorems for fluid and MHD equations, OCAMI Joint Usage/Research: Helicity and space-time symmetry ― a new perspective of classical and quantum systems, 2021.10. |

20. | Yasuhide Fukumoto, Rong ZOU, Nambu bracket and induced Lie-Poisson bracket for ideal MHD equation, 5th Asia-Pacific Conference on Plasma Physics (AAPPS-DPP2021), 2021.09. |

21. | Yasuhide Fukumoto, Keigo Wada, Compressibility effect on vorticity production and Darrieus-Landau instability of a premixed flame front, 25th International Congress of Theoretical and Applied Mechanics (ICTAM 2020+1), 2021.08. |

22. | Yasuhide Fukumoto,Fengnan Liu,Xiaopeng Zhao, A finite difference scheme for the Richards equation under variable-flux boundary conditions, 1st International Symposium on Construction Resources for Environmentally Sustainable Technologies (CREST2020), 2021.03, 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.. |

23. | Kazuo Matsuura, Yasuhide Fukumoto, Pedestrian stream flow analysis to detect people conglomerates and disperse states for COVID-19 prevention measures in crowded spaces, 1st Virtual International Study Group on Mathematical Solutions to Industrial and Social Problems, 2020.12, [URL]. |

24. | Yasuhide Fukumoto,Rong ZOU, Topological invariants and Nambu brackets in fluid mechanics and magnetohydrodynamics, 17h International Conference on Flow Dynamics (ICFD2020), 2020.10, 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.. |

25. | 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。. |

26. | Nambu-mechanics representation of Euler and MHD equations. |

27. | Topological invariant of MHD revisited. |

28. | 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. |

29. | Yasuhide Fukumoto & Thi Thai LE, Stability of finite shear layer of shallow-water flow, 10-th International School for Young Scientists "WAVES AND VORTICES IN COMPLEX MEDIA", 2019.12. |

30. | Yasuhide Fukumoto, Keigo Wada & Abarzhi Snezhana, Effect of compressibility on laminar flame speed and its influence on the Darrieus-Landau instability of a planar front of premixed flame, 72th Annual Meeting of the APS Division of Fluid Dynamics, 2020.06. |

31. | Yasuhide Fukumoto & Keigo Wada, Effect of compressibility in the reaction zone of a premixed flame and its implication to the Darrieus-Landau instability, MATRIX: Conservation Laws, Interfaces, and Mixing, 2019.11. |

32. | Yasuhide Fukumoto, Topological aspects of fluid dynamics with application to vortex motion, JASSO平成31年度帰国外国人留学生研究指導事業, 2019.10. |

33. | Yasuhide Fukumoto, Initiative of APCMfI for promoting international collaboration of industrial mathematics in East, The 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), 2019.07. |

34. | Keigo Wada, Yasuhide Fukumoto, Effect of compressibility on laminar flame speed and its stabilizing effect on Darrieus-Landau instability of a premixed flame front, 12th Asia-Pacific Conference on Combustion, ASPACC 2019, 2019.07, The compressibility effect on a premixed flame front is investigated for small Mach numbers Ma in terms of M^{2} expansions. We extend the method of matched asymptotic expansions to O(Ma^{2}) 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(Ma^{2}) effect, this dramatic decrease in S-_{L} brings in stabilization of the Darrieus-Landau instability, the linear instability of a plane flame front.. |

35. | Yasuhide Fukumoto, Abarzhi Snezhana & Keigo Wada, Effect of compressibility on Darrieus-Landau instability of a premixed flame front and role of vorticity production, IUTAM Symposium on Vortex dynamics in science, nature and technology, 2019.06. |

36. | Yasuhide Fukumoto, Liu Fengnan & Xiaopeng Zhao, A finite difference scheme for the Richards equation under variable-flux boundary conditions, Workshop ANDE 2019: Applications of Nonlinear Diffusion Equations, 2019.06. |

37. | Yasuhide Fukumoto, Keigo Wad, Thi Thai LE & Abarzhi Snezhana, Modeling compressible combustion flame and shear flow of a river by interfaces of velocity discontinuity, Ajou-Kyushu joint workshop on Industrial Mathematics, 2018.12. |

38. | Yasuhide Fukumoto & Yuki Miyachi , Gyroscopic analogy of a rotating stratified flow confined in a tilted spheroid with a heavy symmetrical top with the top axis misaligned from the axis of symmetry, Program: Hamiltonian systems, from topology to applications through analysis, Workshop: Hamiltonian systems, from topology to applications through analysis II, 2018.11. |

39. | Yasuhide Fukumoto, Keigo Wada & Abarzhi Snezhana, Compressibility effect on volumetric heat loss and its influence on the Darrieus-Landau instability of a planar front of premixed flame, 71th Annual Meeting of the APS Division of Fluid Dynamics, 2018.11. |

40. | Yasuhide Fukumoto, Keigo Wada & Abarzhi Snezhana, Generation of vorticity and its influence on the stability of a premixed flame front of a compressibile flow, 15h International Conference on Flow Dynamics (ICFD2018), 2018.11. |

41. | 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. |

42. | Yasuhide Fukumoto, Initiative for advanced innovation by promoting collaboration of mathematics and mathematical sciences with other fields and industry, Elsevier KOREA-JAPAN Symposium on The 4th Industrial Revolution, 2018.09. |

43. | Yasuhide Fukumoto & Yuki Miyachi, Mechanical Analogue of a rotating flow of a stratified fluid confined in a spheroid, International Workshop "Marine measurements in Hydrophysics and Geophysics", 2018.08. |

44. | Yasuhide Fukumoto & Thi Thai LE
, Frictional effect om Kelvin-Helmholtz problem of a shallow-water flow" International Conference "Flux and Structure in Fluids, International Conference "Flux and Structure in Fluids", 2018.08. |

45. | Yasuhide Fukumoto, Thi Thai LE & Liangbing JIN, Friction induced instability of surface of velocity discontinuity of a shallow-water flow, 5th International Conference on Mathematical Theory of Turbulence via Harmonic Analysis and Computational Fluid Dynamics, 2018.03. |

46. | Yasuhide Fukumoto & Yuki Miyachi, Gyroscopic analogy of a rotating stratified flow confined in a tilted spheroid and its implication to stability of a heavy symmetrical top, 70th Annual Meeting of the APS Division of Fluid Dynamics, 2017.11. |

47. | Yasuhide Fukumoto, Thi Thai LE & Liangbing JIN, Frictional effect on linear stability of interface of tangential velocity discontinuity in shallow water, 8-th International School for Young Scientists "WAVES AND VORTICES IN COMPLEX MEDIA", 2017.11. |

48. | Yasuhide Fukumoto & Yuki Miyachi, Gyroscopic analogy of Coriolis force for stabilizing a rotating stratified flow confined in a spheroid, 14h International Conference on Flow Dynamics (ICFD2017), 2017.11. |

49. | Yasuhide Fukumoto, Introduction to topological fluid dynamics and magnetohydrodynamics, ISTITUTO NAZIONALE DI ALTA MATEMATICA (INdAM), GRUPPO NAZIONALE PER LA FISICA MATEMATICA (GNFM) , 2017.09. |

50. | Yasuhide Fukumoto & Yuki Miyachi, Gyroscopic analogies of rotating flows of a strongly stratified fluid confined in a spheroid, International Conference Vortices and coherent structures: from ocean to microfluids, 2017.08. |

51. | Yasuhide Fukumoto & Yuki Miyachi, Gyroscopic analogy of Coriolis effect for stabilizing a rotating stratified flow confined in a spheroid, Turbulent Mixing and Beyond Workshop Sixth International Conference -Tenth Anniversary, 2017.08. |

52. | Ummu Habibah, Yasuhide Fukumoto, A counter-rotating vortex pair in inviscid fluid, International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017, 2017.08, 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(ϵ^{5}) we show the traveling speed of a vortex pair.. |

53. | Yasuhide Fukumoto & Yuki Miyachi, Gyroscopic analogy of a rotating stratified flow confined in a spheroid and its implication to stability, Tohoku Forum for Creativity Thematic Program 2017 Nonlinear PDE for Future Applications ー Evolution Eq. and Mathematical Fluid Dynamics ー, 2017.07. |

54. | Yasuhide Fukumoto & Yuki Miyachi, Gyroscopic analogy of Coriolis force on a rotating stratified flow confined in a spheroid, IUTAM symposium “Dynamics and Topology of Vorticity and Vortices”, 2017.06. |

55. | Yasuhide Fukumoto, Rong Zou and Oleg N. Kirillov, Short-wavelength analysis of magnetorotational instability of resistive MHD flow, 京大数理解Workshop: Applied Mathematics , 2016.11. |

56. | Yasuhide Fukumoto, IMI Activities with Industry, Second Chile-Japan Academic Forum at Patagonia, 2016.11. |

57. | Yasuhide Fukumoto & Ummu Habibah, Motion of a vortex pair at high and low Reynolds numbers, 24th International Congress of Theoretical and Applied Mechanics (ICTAM 2016), 2016.08. |

58. | Yasuhide Fukumoto, Lagrangian approach to spectra and energy of Kelvin waves on a vortex core, RIMS International Project Research 2016 Fluid Dynamics of Near-Wall Turbulence International Workshop on Theoretical Aspects of Near-Wall Turbulence Studies, 2016.06. |

59. | Yasuhide Fukumoto, Valery L. Okulov & David H. Wood, Kawada's contribution to induced velocity by helical vortices with its application to propeller theory, EUROMECH Colloquium 581 "Dynamics of Concentrated Vortices", 2016.05. |

60. | Yasuhide Fukumoto, Are all the topological invariants of vorticity representable as cross-helicities?, IUTAM symposium “Helicity, Structures and Singularity in Fluid and Plasma Dynamics”, 2016.04. |

61. | Yasuhide Fukumoto & H. K. Moffatt, Topological idea combined with asymptotic expansions for vortex motion, IMI-La Trobe Joint Conference "Mathematics for Materials Science and Processing", 2016.02. |

62. | Yasuhide Fukumoto & Ummu Habibah , Motion of a counter-rotating vortex pair in a viscous fluid, Second International ACCA-JP/UK Workshop, 2016.01. |

63. | Yasuhide Fukumoto, Hironori Nakagawa & Ummu Habibah, A higher-order asymptotic formula for velocity of a viscous vortex pair, The Eighth International Conference on Sciences and Mathematics Education in Developing Countries, 2015.12. |

64. | Yasuhide Fukumoto & Ummu Habibah, A higher-order asymptotic formula for velocity of a viscous vortex pair, 68th Annual Meeting of the APS Division of Fluid Dynamics, 2015.11. |

65. | Yasuhide Fukumoto, Valery L. Okulov & David H. Wood, The contribution of Kawada to the analytical solution for the velocity induced by a helical vortex filament and modern applications of helical vortices, 15th International Conference CoMFoS15: Mathematical Analysis of Continuum Mechanics and Industrial Applications, 2015.11. |

66. | Yasuhide Fukumoto, Hironori Nakagawa & Ummu Habibah, A higher-order asymptotic formula for traveling speed of a counter-rotating vortex pair, International Workshop on “the Multi-Phase Flow; Analysis, Modelling and Numerics", 2015.11. |

67. | 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. |

68. | Yasuhide Fukumoto & Yuki Miyachi, Mechanical analogue of a rotating flow of a strongly stratified fluid confined in an ellipsoid as mathematics for industry, 18h INTERNATIONAL CONFERENCE “FLUXES AND STRUCTURES IN FLUIDS”, 2015.06. |

69. | Yasuhide Fukumoto, Yohei Kawazura and Zensho Yoshida, Are all the topological invariants representable as cross-helicities?, Knots and Links in Fluid Flows - From Helicity to Knot Energy, 2015.06. |

70. | H. Hazarika, K. H. Pradhan, Y. Fukumoto, N. Yasufuku, R. Ishikura, N. Hirayu, Protection of seawall against earthquake and tsunami using flexible material, 14th International Conference of International Association for Computer Methods and Recent Advances in Geomechanics, IACMAG 2014, 2015.01, 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.. |

71. | Yasuhide Fukumoto, Rong Zou, Azimuthal magnetorotational instabilities to non-axisymmetric perturbations, 67th Annual Meeting of the APS Division of Fluid Dynamcs, 2014.11. |

72. | 福本 康秀, Rong Zou, Local and global analyses of azimuthal magnetorotational instability, The 8th CREST-SBM International Conference on Mathematical Fluid Dynamics, Present and Future, 2014.11. |

73. | Yasuhide Fukumoto, Rong Zou, Topological magnetohydrodynamics and its application to azimuthal magnetorotational instability, The Seventh International Conference on Sciences and Mathematics Education in Developing Countries, 2014.11. |

74. | 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. |

75. | Yasuhide Fukumoto, Lagrangian approach to weakly nonlinear stability of a columnar vortex, Workshop on Lagrangian Coherent Structures and Dynamical Systems", 2014.03. |

76. | Yasuhide Fukumoto, Derivation of magnetohydrodynamic equations with Hall effect, Magnetorotational instability (MRI) with and without Hall effect, Zhejiang Normal University 集中講義, 2013.11. |

77. | Yasuhide Fukumoto, Are all the topological invariants representable as cross helicities?, JSPS/UK Meeting "Topological Vorticity Dynamics in the Physical Sciences", 2013.09. |

78. | Yasuhide Fukumoto, Energy, pseudomomentum and Stokes drift of inertial waves and their application to stability of a columnar vortex, A mini-Conference "Topological Vorticity Dynamics and Magnetohydrodynamics", 2013.09. |

79. | Yasuhide Fukumoto, Motion of a vortex ring and a vortex pair in a viscous fluid, 2nd International Retreat on Vortex Dynamics and Vorticity Aerodynamics (IRVDVA), 2013.08. |

80. | Yasuhide Fukumoto, Energy, pseudomomentum and Stokes drift of inertial waves and their application to stability of a columnar vortex, The 6th Pacific RIM Conference on Mathematics 2013, 2013.07. |

81. | Yasuhide Fukumoto, Hirofumi Sakuma, Three-dimensional formal stability of stratified shear flows of an ideal gas, International Conference“FLUXES AND STRUCTURES IN FLUIDS”, 2013.06. |

82. | Yasuhide Fukumoto, Youichi Mie, Lagrangian approach to weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow, IUTAM Symposium on Vortex Dynamics: Formation, Structure and Function, 2013.03. |

83. | Yasuhide Fukumoto, Makoto Hirota, Youichi Mie, Lagrangian and Eulerian hybrid method for symmetric breaking bifurcation of a rotating flow, BIRS Workshop: Spectral Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems, 2012.11, 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.. |

84. | Yasuhide Fukumoto, Energy, Pseudomomentum and Stokes Drift of Kelvin Waves and Their Application to Weakly Nonlinear Stability of an Elliptic Vortex, Vortex Theory Now--Frontiers of Mathematical Physics, 2012.10. |

85. | Yasuhide Fukumoto, Youichi Mie, Lagrangian and Eulerian hybrid method for weakly nonlinear stability of a rotating flow in a cylinder of elliptic cross-section, 23rd International Congress of Theoretical and Applied Mechanics (ICTAM 2012), 2012.08. |

86. | 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.. |

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

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

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