Semigeostrophic Frontal Boundary Layer

The viscous semigeostrophic solutions obtained for the baroclinic Eady wave fronts are analyzed for the generation of the cross-frontal temperature gradient in the boundary layer. In the case of free-slip boundaries, the cross-frontal gradient is maximally generated at the surface by meridional temperature advection. In the case of no-slip boundaries, surface friction reduces the meridional temperature advection in the boundary layer: The maximum generation occurs above the surface layer and the temperature gradient at the surface is maintained by vertical diffusion. The no-slip solution is compared with the Ekman-layer model solution. Errors are quantified for the use of the Ekman-layer model in the mature state of frontogenesis.The surface frontogenesis is found to be affected by diffusivity both directly and indirectly. The direct effect of diffusivity is represented explicitly by the diffusion term in the potential temperature equation. The indirect effect of diffusivity is related implicitly to the temperature advection caused by the viscous part of the ageostrophic motion whose horizontal velocity component is defined by the frictional wind deflection (away from the geostrophy). The direct effect of diffusivity is frontolytical, whilst theindirect effect of diffusivity is frontogenetic in the mesoscale vicinity of the front. The indirect effect of diffusivity contributes dominantly to the mesoscale surface frontogenesis for the free-slip case, but it is offset by the divergence of the dynamic part of the ageostrophic motion at the surface level for the non-slip case.