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The evolution of a front in turbulent thermal wind balance. Part 2. Numerical simulations

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Crowe, MN 
Taylor, JR 

Abstract

jats:pIn Crowe & Taylor (jats:italicJ. Fluid Mech.</jats:italic>, vol. 850, 2018, pp. 179–211) 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, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019006888_inline1" />jats:tex-mathRo</jats:tex-math></jats:alternatives></jats:inline-formula>. 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 jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019006888_inline2" />jats:tex-mathRo=O(1)</jats:tex-math></jats:alternatives></jats:inline-formula>. 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 jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019006888_inline3" />jats:tex-mathRo=O(1)</jats:tex-math></jats:alternatives></jats:inline-formula>. Finally, we develop a new scaling for the intense vertical velocity that can develop in thin bands at the edges of the front.</jats:p>

Description

Keywords

4012 Fluid Mechanics and Thermal Engineering, 40 Engineering

Journal Title

Journal of Fluid Mechanics

Conference Name

Journal ISSN

0022-1120
1469-7645

Volume Title

880

Publisher

Cambridge University Press (CUP)

Rights

All rights reserved