The submesoscale, the finescale and their interaction at a mixed layer front

Abstract

Abstract The spindown of a geostrophically balanced density front in an upper-ocean mixed layer is simulated with a large eddy simulation (LES) model that resolves O(1000) m down to O(1) m scale. Our goal is to examine the interaction between the submesoscale and the turbulent finescale, and another related goal is to use the turbulence-resolving simulation to better characterize vertical transport, frontogenesis and dissipative processes. The flow passes through symmetric and baroclinic instabilities, spawns vortex filaments of O (100) m thickness as well as larger eddies with cross-front velocity as large as the along-front velocity, and develops turbulence that is spatially localized and organized. A O(100) m physical-space filter is applied to the simulated flow so that the coherent submesoscale is separated from the finescale in a decomposition that preserves the spatial organization of the flow unlike the typical practice of a split into a frontal average and a fluctuation that obscures the coherent submesoscale. The energy spectrum exhibits a change of slope at O(100) m with an approximately −5/3 slope over a subrange of the finescale. Analysis of the submesoscale vertical velocity (as large as 5mm/s) in the upper layer of the front reveals that downwelling is limited to the thin vortex filaments and the junction of the submesoscale eddies with these filaments while upwelling occurs over spatially extensive regions in the eddies. Conditional averaging shows that heavier (lighter) fluid is preferentially downwelled (upwelled) by these coherent submesoscale structures leading to an overall buoyancy flux that is restratifying. The submesoscale is unbalanced with local Rossby number as large as 5. The kinetic energy (KE) transport equations are evaluated separately for the submesoscale and the finescale to understand energy pathways in this problem. The buoyancy flux (associated with coherent motions) transfers the potential energy of the front and acts as the primary source of submesoscale KE which is then transported across the front with a fraction transferred to the finescale. The transfer, limited to thin regions of O(100) m horizontal width, is accomplished by primarily horizontal strain in the upper 10\u202fm and by vertical shear in the rest of the 50-m deep mixed layer. Frontogenetic mechanisms are diagnosed through analysis of the transport equation for squared buoyancy gradient. Horizontal strain is the primary frontogenetic term that is especially strong in the near-surface layer. The frontogenesis is counteracted primarily by horizontal diffusion in the top 10\u202fm while, further below, the balance is with the horizontal gradient of vertical velocity.