TRANSIENT DYNAMICS OF STREAK AND LONGITUDINAL VORTICES IN SHEAR FLOW WITH WAVE

Abstract

Langmuir circulations are alternating right and left helical vortices in the ocean having horizontal axes parallel to the wind. They are manifested by floating material on the ocean surface as streaks. The laboratory wind driven shear flow demonstrate streak feature with/without wave condition. When the wave is present the explanation of results with Craik-Leibovich instability mechanism, originally proposed for weak current shear in ocean, is not appropriate for some problem as in the laboratory the current shear is strong. The existing normal mode analysis based on the generalized Lagrangian mean formulation for wave with strong shear is not able to capture the fully dynamics of streak and longitudinal vortices. We extend Craik-Leibovich theory to strong shear in Eulerian framework but focusing on the fully perturbation evolution dynamics. Transient dynamics of perturbation is studied with an initial value problem. In this approach the effect of shear and wave and its interaction are made clear. The transient growth in the time period without wave is significant and is crucial to the initial preferred wave number observed in the experiments. The optimal longitudinal vortex form perturbation is searched and the preferred spanwise wave number predicted is well consistent with experimental data of wind shear and wave.