Maximum entropy state of the quasi-geostrophic bi-disperse point vortex system: bifurcation phenomena under periodic boundary conditions

Autor:	Tomoyoshi Sato, Takeshi Miyazaki, Satoshi Funakoshi
Rok vydání:	2012
Předmět:	Fluid Flow and Transfer Processes Laplace's equation Mechanical Engineering Principle of maximum entropy Mathematical analysis General Physics and Astronomy Statistical mechanics Vortex Classical mechanics Periodic boundary conditions Laplace operator Bifurcation Mathematics Sign (mathematics)
Zdroj:	Fluid Dynamics Research. 44:031407
ISSN:	1873-7005 0169-5983
DOI:	10.1088/0169-5983/44/3/031407
Popis:	We investigate the statistical mechanics of quasi-geostrophic point vortices of mixed sign (bi-disperse system) numerically and theoretically. Direct numerical simulations under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics (GRAPE-DR). Clustering of point vortices of like sign is observed and two-dimensional (2D) equilibrium states are formed. It is shown that they are the solutions of the 2D mean-field equation, i.e. the sinh-Poisson equation. The sinh-Poisson equation is generalized to study the 3D nature of the equilibrium states, and a new mean-field equation with the 3D Laplace operator is derived based on the maximum entropy theory. 3D solutions are obtained at very low energy level. These solution branches, however, cannot be traced up to the higher energy level at which the direct numerical simulations are performed, and transitions to 2D solution branches take place when the energy is increased.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d8206a7b8b8da6aeb050fbf37111ef62 https://doi.org/10.1088/0169-5983/44/3/031407 Zobrazit plný text záznamu