Quasi‐two‐dimensional dynamics of plasmas and fluids

Horton, Wendell; Hasegawa, Akira

doi:doi:10.1063/1.166049

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Successes and failures of shallow-water interpretations of Voyager wind data

Studying the dynamics of Jupiter’s atmosphere is a rewarding experience, in part because the planet’s cloud-top circulations are easy to track from space, the jet streams flow in straight lines eastward or westward, and there is enough room for the vortices to usually keep out of each other’s way. Earth, in contrast, is a planet with global circulations that are not easy to track from space, with jet streams that make wide, fluctuating arcs as they negotiate mountain ranges, and with vortices th...

Steady vortices in plasmas and geophysical flows

A number of two‐dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions. A simple and general method that consists of two steps is used. First the dispersion relation is calculated, to find all possible values of the phase velocity of the linear waves. Then an integral relation that determines the center‐of‐mass velocity of localized structures must be found. The existence condition is tha...

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.