On the stabilization of a two-dimensional vortex strip by adverse shear

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Abstract
An isolated strip of anomalous vorticity in a two-dimensional, inviseid, incompressible, unbounded fluid is linearly unstable - or is it? It is pointed out that an imposed uniform shear, opposing the shear due to the isolated strip alone, can prevent all linear instabilities if the imposed shear is of sufficient strength, and that this is highly relevant to current thinking about ‘two-dimensional turbulence’ and related problems. The linear stability result has been known and goes back to Rayleigh, but its implications for the behaviour of the thin strips of vorticity that are a ubiquitous feature of nonlinear two-dimensional flows, as revealed for instance in high-resolution experiments, appear not to have been widely recognized. In particular, these thin strips, or filaments, almost always behave quasi-passively when being wrapped around intense coherent vortices, and do not roll up into strings of miniature vortices as would an isolated strip. Nonlinear calculations presented herein furthermore show that substantially less adverse shear than suggested by linear theory is required to preserve a strip of vorticity. Taken together, and in conjunction with results showing the further stabilizing effect of a large-scale strain field, these results explain the observed quasi-passive behaviour.