Crowe, MN; Taylor, JR; (2019) The evolution of a front in turbulent thermal wind balance. Part 2. Numerical simulations. Journal of Fluid Mechanics , 880 pp. 326-352. 10.1017/jfm.2019.688.

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Abstract

we described a theory for the evolution of density fronts in a rotating reference frame subject to strong vertical mixing using an asymptotic expansion in small Rossby number, Ro . We found that the front reaches a balanced state where vertical diffusion is balanced by horizontal advection in the buoyancy equation. The depth-averaged buoyancy obeys a nonlinear diffusion equation which admits a similarity solution corresponding to horizontal spreading of the front. Here we use numerical simulations of the full momentum and buoyancy equations to investigate this problem for a wide range of Rossby and Ekman numbers. We examine the accuracy of our asymptotic solution and find that many aspects of the solution are valid for Ro=O(1) . However, the asymptotic solution departs from the numerical simulations for small Ekman numbers where the dominant balance in the momentum equation changes. We trace the source of this discrepancy to a depth-independent geostrophic flow that develops on both sides of the front and we develop a modification to the theory described in Crowe & Taylor (2018) to account for this geostrophic flow. The refined theory closely matches the numerical simulations, even for Ro=O(1) . Finally, we develop a new scaling for the intense vertical velocity that can develop in thin bands at the edges of the front.

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