Is Langmuir Circulation Driven by Surface Waves or Surface Cooling?

Abstract

The ratio of the buoyancy force driving thermal convection to the surface wave vortex-force driving Langmuir circulation in the Craik?Leibovich mechanism involves the Hoenikker number Ho. The critical value Hoc, at which wave forcing and thermal convection contribute equally to the circulation, is found to increase with decreasing Langmuir number La and approaches 3 in the small La limit. For a typical wind speed and surface cooling, Ho is of order O(10?2) to O(10?1). Thus, wave forcing dominates over thermal convection in driving Langmuir circulation. Stratification induced by strong surface heating suppresses the circulation generated by wave forcing and could completely inhibit the CL instability. In the physically plausible range of ?0.1 < Ho < 0, however, this does not happen for small La and the dynamical effect of heating is very small. For a given heat flux, the temperature difference between the regions of surface divergence and convergence in Langmuir circulation depends on Ho, Pr, and La and on the depth distribution of the heating, but is typically 0(10?2) K.