Clustering and negative temperatute state of vortices in geophysical flow: Statistical mechanics of quasi-geostrophic point vortices

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400462
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Meteorology/Physical oceanography/Hydrology
• Research Institution: The University of Electro-Communications
• Principal Investigator: Miyazaki Takeshi 電気通信大学, 情報理工学(系)研究科, 教授 (50142097)
• Co-Investigator(Kenkyū-buntansha): TAKAHASHI Naoya 東京電機大学, 工学部, 教授 (40313423)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 地球流体運動 / 秩序渦構造 / 統計力学 / 準地衡風近似 / 最大エントロピー理論 / 負温度状態

Outline of Final Research Achievements

The statistical mechanics of quasi-geostrophic vortices is investigated numerically and theoretically. Direct numerical simulations of a point vortex system of mixed sign under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics. Clustering of point vortices of like sign is observed and a columnar dipole structure appears
as an equilibrium state.
These numerical results are explained from the viewpoint of the classical statistical mechanics. A three-dimensional mean field equation is derived based on the maximum entropy theory. The numerically obtained end states are shown to be the 2D sn-sn dipole solutions of the mean field equation. We present other branches of 2D and 3D solution of the mean field equation, whose entropy is smaller than that of the two-dimensional sn-sn dipole branch. These findings explain the reason why only the two-dimensional sn-sn dipole states are found in the numerical simulations of point vortices.

Free Research Field

流体物理学