Geostrophic Adjustment and Restratification of a Mixed Layer with Horizontal Gradients above a Stratified Layer

Abstract

The restratification of a mixed layer with horizontal density gradients above a stratified layer is considered. Solutions are obtained on the assumption that the width across this front is much larger than the local radius of deformation Δbh̄/|f| based on the buoyancy change across the front Δb, mean mixed layer depth Rdh̄, and the Coriolis parameter f, where b is defined as Rd−g(ρ−ρ0)ρ0, but the fractional change in the mixed layer depth is not required to be small. For an initially quiescent mixed layer, created by homogenizing a fluid of constant stratification to a depth that varies horizontally, the isopycnals in the mixed layer tilt about their intersections with the top surface in the adjusted state, and the base of the mixed layer flattens slightly in the frontal region. Other cases considered include mixed layer fronts with initial momentum out of geostrophic balance, created by vertical mixing of a layer with horizontal gradients previously in thermal wind balance. For a wide front, the isopycnals pivot about the middepth for this case. In all cases, for a wide front, the new vertical buoyancy gradient is RdM4/f2h̄, where RdM2=|b|h̄ is the magnitude of the horizontal buoyancy gradient, and the Richardson number of the adjusted state is 1, as in an earlier constant depth case.