Relaxation and stationary vortex patterns for two dimensional channel flows
We study the dynamic evolution of two dimensional vorticity in a periodic (zonal) channel with slip boundary conditions using a semi-Lagrangian quasi-inviscid code. The inverse cascade (vortex mergers) drives the small-scale initial vorticity distribution to a large-scale quasi-stationary dipole- or multi-pole channel-wise blocking array. We examine the effect of aspect ratio a (channel width over its stream-wise period) on the resulting stationary pattern. As a increases, the relaxed flow undergoes a sequence of bifurcations, whereby dipole number decreases to a single pair at about α～0.25-0.5. Further increase brings about geometric changes in the shape of circulation cells, pushing vortex cores away from the equator towards the channel walls, and deforming cell boundaries. Another bifurcation occurs at α = 1. The meandering jet splits into a eastward-westward pair, by surrounding a single symmetric equatorial vortex, and squeezing its separated dipole partner to the channel walls. For intermediate values of a, the stream-vorticity relation will obey a sinh-Poisson equation and an approximate analytical description for such dipoles in terms of the Jacobi elliptic functions is derived. Parameters of these dipoles are estimated analytically, and are shown to be in good agreement with numeric simulations.
D.Gurarie L.P.Yip K.W.Chow D.H. Zhang
Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong, China
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
951-958
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）