The inviscid instability of O(ɛ) two-dimensional periodic flows to spanwise-periodic longitudinal vortex modes in parallel O(1) shear flows beneath deformable surface gravity waves is considered. In such cases, not only is the effect of fluctuations upon the mean state important but also the influence of the developing mean flow on the fluctuating part of the motion. The former is described by a generalized Lagrangian-mean formulation; the latter by a modified Rayleigh equation. Of specific interest is whether the spanwise distortion of the wave field feeds back to enhance or inhibit instability to longitudinal vortex form, and whether the free surface boundary conditions for wave distortion, which are spanwise dependent, act to give rise to a preferred spanwise spacing of the vortices. We find that wave distortion acts to inhibit, and in some circumstances curtail, instability for all but the shortest waves and that a preferred spanwise spacing can occur.
Bulletin of the American Physical Society: meeting abstracts of the 54th Annual Meeting of the Division of Fluid Dynamics, San Diego, California, United States, 18-20 November 2001,
abstract no. EL.006