Deceleration of a finite-width, stratified current over a sloping bottom: Frictional spindown or buoyancy shutdown?

The deceleration of an unforced, two-dimensional, finite-width current over a sloping bottom in a stratified fluid is studied to quantify the relative importance of frictional spindown and buoyancy shutdown when both act simultaneously. Frictional spindown decelerates the current through Ekman suction and pumping at the current edges, which transmit stresses into the interior fluid. Buoyancy shutdown is the process by which lateral advection of density in the bottom boundary layer generates thermal wind shears that reduce the bottom stress, thereby halting deceleration. A theoretical model of a downwelling current suggests that buoyancy shutdown always reduces the deceleration timescale from that for frictional spindown alone and produces a nonzero steady along-isobath current overlying an arrested bottom mixed layer. The model is most sensitive to the Burger number S = Nalpha/f where N is the buoyancy frequency, alpha the bottom slope, and f the Coriolis parameter. Larger S produces a stronger steady current that is reached more rapidly. Buoyancy shutdown remains important in the deceleration process even when its individual timescale for adjustment is an order of magnitude longer than the frictional spindown timescale. The model suggests that buoyancy shutdown should influence currents over the continental shelf on timescales of about five days and greater. A primitive-equation numerical model is used to test the theory and its assumptions. Overall, the results are supportive of the theory, except that the theoretical model neglects the cross-isobath component of bottom stress and ignores vertical shears above the bottom mixed layer. As a result, the numerical model current initially decelerates more slowly and then continues to decelerate after the along-isobath stress has vanished, leaving a weaker steady flow, especially with stronger stratification. Interior vertical shears in the numerical model tend to decouple the near-surface flow from the bottom mixed layer, producing more variable steady flows. Details of the flow in the bottom mixed layer are highly dependent on the choice of turbulence closure scheme. Buoyancy shutdown is also important in the deceleration of upwelling currents, substantially reducing the time to reach steady state from that for frictional spindown alone. Details of both the deceleration and the steady state vary sharply with the turbulent closure scheme, so generalizations are difficult.