The stability and nonlinear dynamics of spatially-extended Langmuir circulation.

摘要

Langmuir circulation (LC) is a wind- and surface-wave-driven convective flow in the upper ocean that is operative on lateral scales from meters to several kilometers (the ocean submesoscales). Despite the importance of LC to the transfer of heat, mass, and momentum between the atmosphere and oceans, ocean general circulation models (OGCMs)---a key component of computational climate models---cannot resolve LC and other comparably fine-scale flows in the mixed layer (ML, the upper 50--100 meters of the ocean), whose effects must therefore be parameterized. While much is known about the physics of LC in small domains, having O(100) meter dimensions, a necessary prerequisite for parameterizing LC in OGCMs is a proper understanding of the stability and intrinsic nonlinear dynamics of horizontally-extended arrays of Langmuir cells.;In this theoretical investigation, a complement of linear and secondary stability analysis and direct numerical simulation is used to study three scenarios in which spatially-extended LC dynamics may be manifest. The simulations are strategically initialized using a superposition of the relevant base flow plus a small-amplitude contribution of the fastest-growing instability mode.;First, the influence of downwind modulation on the dynamics of Langmuir cells is investigated using an asymptotically reduced version of the Craik-Leibovich (CL) equations governing LC. The reduced CL (rCL) equations render numerical simulations in very long downwind domains feasible by filtering certain fast spatiotemporal dynamics. Secondary stability analysis and numerical simulations of the rCL equations confirm that the rCL equations admit dynamics reminiscent of LC. A key finding is a numerically-exact nonlinear defect traveling-wave solution of the rCL equations, associated with a novel downwind-modulated 2:1 spatial resonance phenomenon.;Next, the dynamics of LC in cross-wind extended domains is considered. For this purpose, downwind variability is suppressed. The effects of both density stratification and Coriolis accelerations are incorporated to study the effects of horizontal stratification, associated with submesoscale lateral fronts in the upper ocean, on LC. It is shown that LC, generally viewed as a prominent vertical mixing mechanism, may actually play a role in ML re-stratification.;Finally, the stability of steady downwind invariant LC states, in a stably vertically-stratified fluid, to long-wavelength cross-wind-varying disturbances is studied using spatial Floquet theory. A variety of secondary instabilities is identified and catalogued. Numerical simulations reveal the potential for certain long-wavelength instabilities to radically modify the uniformly patterned base state, deepening the ML in some cases and driving modulated internal-wave packets in others.