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Parameterization of Frontal Symmetric Instabilities. I: Theory for Resolved Fronts

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Bachman, SD 
Fox-Kemper, B 
Taylor, JR 
Thomas, LN 


A parameterization is proposed for the effects of symmetric instability (SI) on a resolved front. The parameterization is dependent on external forcing by surface buoyancy loss and/or down-front winds, which reduce potential vorticity (PV) and lead to conditions favorable for SI. The parameterization consists of three parts. The first part is a specification for the vertical eddy viscosity, which is derived from a specified ageostrophic circulation resulting from the balance of the Coriolis force and a Reynolds momentum flux (a turbulent Ekman balance), with a previously proposed vertical structure function for the geostrophic shear production. The vertical structure of the eddy viscosity is constructed to extract the mean kinetic energy of the front at a rate consistent with resolved SI. The second part of the parameterization represents a near-surface convective layer whose depth is determined by a previously proposed polynomial equation. The third part of the parameterization represents diffusive tracer mixing through small-scale shear instabilities and SI. The diabatic, vertical component of this diffusivity is set to be proportional to the eddy viscosity using a turbulent Prandtl number, and the along-isopycnal tracer mixing is represented by an anisotropic diffusivity tensor. Preliminary testing of the parameterization using a set of idealized models shows that the extraction of total energy of the front is consistent with that from SI-resolving LES, while yielding mixed layer stratification, momentum, and potential vorticity profiles that compare favorably to those from an extant boundary layer parameterization (Large et al., 1994). The new parameterization is also shown to improve the vertical mixing of a passive tracer in the LES.



Symmetric instability, Front, Submesoscale, Geostrophic shear production, Parameterization, Mixed layer

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Ocean Modelling

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Elsevier BV
Natural Environment Research Council (NE/J010472/1)
SDB and BFK were funded in part by a Grant from BP/The Gulf of Mexico Research Initiative. SDB and JRT were funded through support from the Natural Environment Research Council, award NE/J010472/1. BFK’s contribution was also made possible by NSF OCE 1350795, 1258907, and 0934737. LNT was funded through NSF Grants OCE 1260312 and 1459677.