Coupling of damped and growing modes in unstable shear flow
Abstract
Analysis of the saturation of the KelvinHelmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewisecontinuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injectionscale sink of the fluctuation energy similar to what has been found for gyroradiusscale driftwave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to small scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.
 Publication:

Physics of Plasmas
 Pub Date:
 June 2017
 DOI:
 10.1063/1.4985322
 arXiv:
 arXiv:1610.06142
 Bibcode:
 2017PhPl...24f2304F
 Keywords:

 Physics  Plasma Physics
 EPrint:
 23 pages, 6 figures, accepted for publication in Physics of Plasmas, June 2017