Baroclinic instability of density current along a sloping bottom and the associated transport process

Abstract

Numerical experiments with a three‐dimensional nonhydrostatic ocean model have been carried out to investigate the dynamic processes of downslope density current and associated transport of dense water, focusing on the effects of bottom slope for the range of slope inclination S from 0 to 0.04. Bottom slope has two effects on baroclinic instability of the flow. One is the stabilizing effect due to the topographic β effect and to offshoreward increase in water depth. The other is the destabilizing effect due to steepened inclination of isopycnal surface, which increases available potential energy. Since the destabilizing effect over the upper slope overcomes the stabilizing one in the early stage, unstable waves develop more rapidly with increasing S. Nonlinear energy conversion due to Reynolds stresses also affects the flow stability and then the growth rate of instability increases linearly with S in this stage. After the unstable waves have finite amplitudes in the mature stage the stabilizing effect of bottom slope becomes dominant, especially over the lower slope. Thus vigorous unstable eddies are confined to the upper slope region in steep slope cases, while they cover the whole slope region in gentle slope cases, and this difference in the eddy field causes a drastic change in downslope transport of dense water. In gentle slope cases, efficiency of the transport becomes higher with increasing S since the destabilizing effect overcomes the stabilizing one as a whole. On the contrary, the efficiency becomes lower with increasing S in steep slope cases since the stabilizing effect surpasses the destabilizing one. As a result, the most effective transport is realized in the case with S = 0.005. Although the transport due to eddies in steep slope cases becomes weak over the lower slope, it is still larger than that due to the bottom Ekman current since the eddy transport occurs in the bottom layer with a thickness of 100∼200 m, which is 4∼8 times the Ekman layer thickness.