Pattern Selection, Wave Formation, Turbulence, and Vortex Breakdown in SpiralFlows

摘要

Landau type amplitude equations for the small-gap Taylor problem were derived andanalyzed; the equations obtained are global and are more complete than those determined by a formal two-timing analysis. Transition solutions (i.e., heteroclinic orbits) connecting the trivial Couette flow with bifurcating steady flows were obtained by solving singular evolution equations in infinite-dimensional spaces. (2) The existence of a continuum of periodic waves for a class of spiral flow problems was established; the general method was applied to rotating plane Couette flow to obtain an analytic description of turbulent-like flows. The usual Hopf bifurcation theory does not apply to such problems and new methods using singular evolution equations were developed. It was shown that such methods apply also to Langmuir circulations in upper-ocean mixing problems and that the use of such methods leads to a number of new results for Langmuir circulations including mixing problems where the Stokes drift has a cross-wind component.