<Poster Presentation 16>Relations between statistical values along unstable periodic orbits in differential equation systems

[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA

Guiding Center Derivation of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields

Recently, a generalized Hasegawa-Mima (gHM) equation describing drift wave turbulence in curved magnetic fields has been derived in [N. Sato and M. Yamada, J. Plasma Phys. (2022), vol. 88, 905880319] for an ion-electron plasma modeled as a two-fluid system. In this work, we show that a mathematically equivalent GHM equation can be obtained within the kinetic framework of guiding center motion, and that the relevant drift wave turbulence ordering can be further relaxed, effectively generalizing the applicability of the equation to any magnetic field geometry and electron spatial density, in the sense that no ordering requirements involve spatial derivatives of the magnetic field or the electron spatial density.Comment: 13 pages, 5 table

Resonant interaction of Rossby waves in two-dimensional flow on a β plane

An incompressible two-dimensional flow on a β plane is considered. The β plane is a tangent plane of a sphere to approximately describe fluid motion on a rotating sphere assuming that the Coriolis parameter is a linear function of the latitude. Rossby waves are expected to dominate the β plane dynamics, and here in this paper, a mathematical support for the crucial role of the resonant pairs of the Rossby waves is given

Energy Transfer to Resonant Zonal Rossby Modes in Two-Dimensional Turbulence on a Rotating Sphere

The transfer of energy by the nonlinear interaction of Rossby waves in two-dimensional turbulence on a rotating sphere was investigated in this study. Although it has been suggested that three-wave resonant interaction dominates nonlinear interactions when the rotation rate of the sphere is sufficiently high, resonant interactions do not transfer energy to zonal Rossby waves, resulting in the nonresonant interaction of Rossby waves being responsible for the generation of zonal flows [Reznik, Piterbarg, and Kartashova, Dyn. Atmos. Oceans 18, 235 (1993); Obuse and Yamada, Phys. Rev. Fluids 4, 024601 (2019)]. The resonant and nonresonant interactions of Rossby waves were investigated in this study, and it was found that although energy is transferred to the zonal Rossby modes by the nonresonant three-wave interaction of Rossby waves, the target of this nonresonant energy transfer is only the resonant zonal Rossby waves

Nested invariant tori foliating a vector field and its curl: toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries

This paper studies the problem of finding a three-dimensional solenoidal vector field such that both the vector field and its curl are tangential to a given family of toroidal surfaces. We show that this question can be translated into the problem of determining a periodic solution with periodic derivatives of a two-dimensional linear elliptic second-order partial differential equation on each toroidal surface, and prove the existence of smooth solutions. An example of smooth solution foliated by toroidal surfaces that are not invariant under continuous Euclidean isometries is also constructed explicitly, and it is identified as an equilibrium of anisotropic magnetohydrodynamics. The problem examined here represents a weaker version of a fundamental mathematical problem that arises in the context of magnetohydrodynamics and fluid mechanics concerning the existence of regular equilibrium magnetic fields and steady Euler flows in bounded domains without continuous Euclidean isometries. The existence of such configurations represents a key theoretical issue for the design of the confining magnetic field in nuclear fusion reactors known as stellarators.Comment: 22 pages, 4 figure