Horton Wendell, Hasegawa Akira
Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712Department of Communication Engineering, Osaka University 2-1 Yamadaoka, Suita 565, Japan.
Chaos. 1994 Jun;4(2):227-251. doi: 10.1063/1.166049.
In the lowest order of approximation quasi-two-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mima (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in nonideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.
在最低近似阶次下，行星大气和磁场中等离子体的准二维动力学可以用一个共同的对流涡旋方程——查尼（Charney）方程和长谷川-三马（Hasegawa-Mima，CHM）方程来描述。与二维纳维-斯托克斯方程不同，CHM方程在均匀极限下允许“屏蔽涡旋解”，并且在存在不均匀性时允许线性波（行星大气中的“罗斯比波”和等离子体中的“漂移波”）。由于这些特性，CHM方程所描述的非线性动力学提供了丰富的解，这些解涉及湍流行为、相干行为和波动行为。引入诸如电阻率等非理想效应，会使等离子体方程与大气方程显著不同，出现诸如由电阻率和密度梯度驱动的漂移波不稳定性等新效应。该模型方程偏离了CHM方程，并与麦克斯韦方程耦合。本文从理想模型方程（CHM方程）的引入开始，回顾等离子体和行星大气准二维方面的线性和非线性动力学，并延伸到等离子体湍流的最新进展。
