| Classic models of baroclinic instability, notably the Eady model, depend on the Rossby (or
Richardson) number as the sole non-dimensional parameter. Inclusion of a sloping bottom
requires an additional parameter, the slope Burger number, Bu = αNf-1, where α is the
bottom slope. Numerical simulations of the evolution of instabilities along the edge
of a coastally trapped buoyant flow suggest that the slope may help to stabilize
the flow when the deformation radius is similar to or larger than the with of the
buoyant flow, that is, the flow is stable when the slope Burger number is larger
than about 0.3. In unstable cases, Bu < 0.3, baroclinic instabilities in the flow
cause the isopycnals to relax, thereby increasing the local Burger number until the
critical condition, Bu -ă 0.3, is met. At this point the instabilities no longer grow
in time, preventing further offshore buoyancy flux by the eddies. This final state
corresponds approximately to the case where the slope of the ground is similar to the
slope of the mean isopycnal surfaces. The nonlinear, three-dimensional numerical
simulations are in basic agreement with one-dimensional linear stability analysis,
with a few key exceptions. Notably, numerical simulations suggest that cross-shelf
buoyancy fluxes are strongest in within the bottom boundary layer, showing a similar
pattern to continental shelf waves in the vertical structure of current and tracer
variability. Idealized simulations show a marked similarity to instabilities along the
Mississippi/Atchafalaya plume front, as seen in observations and realistic regional models.
These eddies have been shown to be important in Lagrangian transport of surface
particles, notably oil spill trajectory prediction, and create patchiness in bottom
dissolved oxygen distributions during periods of summertime seasonal hypoxia. |