The nonlinear stabilization of a zonal shear flow instability
作者:
S.M. Churilov,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1989)
卷期:
Volume 46,
issue 3
页码: 159-175
ISSN:0309-1929
年代: 1989
DOI:10.1080/03091928908208909
出版商: Taylor & Francis Group
关键词: Shear flow;nonlinear stabilization;critical layer;small disturbances
数据来源: Taylor
摘要:
The development of initially small perturbations in a weakly supercritical zonal shear flow on a β-plane is studied. Two different scenarios of evolution are possible. If the supercriticality is sufficiently small, the growth of a perturbation is stopped in the viscous critical layer regime; for this case the evolution equation (corrected by the inclusion of a quintic nonlinearity) is derived. At greater supercriticality the nonlinearity cannot stop the growth of the perturbation in a linear (viscous or unsteady) critical layer regime, and the evolution is more complicated. Transition to a nonlinear critical layer regime leads to a reduction in the growth rate and to a slowing (but not a stopping) of the increase in amplitude,A. These are connected to the formation of a plateau (S=constant) of widthL=O(A½) in the profile of absolute vorticity,S. Careful analysis reveals that the growth in amplitude ceases only when the whole instability domain (where the slope of unperturbedS-profile is positive) becomes covered again by the plateau.
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