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

- A new parameterization for forced symmetric instability (SI) is developed.
- A vertical viscosity is specified using results from SI-resolving LES, which reduces the geostrophic shear.
- A bulk-PV criterion is used to specify the boundary layer depth.
- Dimensional analysis and a rotation tensor are used to specify along-isopycnal mixing coefficients.
- The parameterized fluxes compare favorably to KPP in conditions ripe for the development of SI.

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.