Geostrophic adjustment and restratification of a mixed layer with
horizontal gradients above a stratified layer
J. Phys. Oceanogr., 25, 10, 2229-2241, 1995.
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 then the local radius of deformation,
but the fractional change in 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 mid-depth for this case. In all cases, for a wide front, the new vertical buoyancy
gradient is M^4/f^2 where M^2 = abs(db/dx) 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.
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