same as in Fig.2 but for 8 days after. In contrast to the onset of the eddies, the transport of dense water occurs more effectively in the gentle slope case.
Figure 4 shows the horizontal velocity field at the same times as in Fig.3. The eddies in the gentle slope case move downslope more rapidly, than in the steep slope. These features reflect the above-mentioned dependence of dense water transport on the bottom slope that the transport in the gentle slope case is more effective than in the gentle slope.
These results suggest that the bottom slope has two effects operating oppositely on the descending process of dense water. That is, one is to enhance the instability of flow to promote the development of the eddies. The other is to prevent the eddies from moving downslope smoothly. The former leads to the effective downslope transport of dense water, while the latter prevents it.
Then, we examined the effect of the bottom slope on the stability of flow in more details. Table l shows the mean growth rates of the instability in the developing stage for all the cases with the contributions of the baroclinic and the barotropic energy conversions, where the former conversion is due to the energy transfer from potential energy (PE) to eddy kinetic energy (EKE) and the latter from mean kinetic energy (MKE) to EKE. As seen in this table, the baroclinic energy conversion is positive value for all the cases, while the barotropic one is negative. This means that the development of the unstable waves is due to the baroclinic instability. However, the dependence of the growth rate on the bottom slope that it increases with the slope is caused by the barotropic energy,conversion among the sloping bottom cases except for the flat case. That is, the energy transfer from EKE to MKE (the negative viscosity effect) decreases with the slope except for the flat case, which causes the increase in the net growth rate with the slope. This indicates that the barotropic energy conversion rather than the baroclinic one is crucial to the dependence of the growth rate on the bottom slope. The flat bottom case shows a somewhat different dependence from the sloping cases. It is possibly affected by the coastal wall on the shelf because the unstable waves develop near it in this case while they do on the slope in the sloping cases.
Finally, we examined the effect of the bottom slope on the efficiency of the transport of dense water. Figure 5 shows the increased (or decreased) amount of total water density in 8 days after the onset of the eddies. As seen in this figure, the offshore transport of dense water in this duration is the most effective in the gentle slope case with s = 5 × 10-3, where the significant positive peak appears on the lower slope region (x〜21.5km). In the other cases, the transport becomes less effective whether the bottom slope increases or decreases. These result are qualitatively explained by the above-mentioned two effects of the bottom slope operating oppositely, the enhancement of the instability of flow and the prevention of the downslope eddy movement by the topographic effect. The less effective transport is due to the slow growth rate in the flat bottom case, while due to the prevention of the eddy movement by the topographic effect in the steep slope cases. As a result, the most effective transport is realized in the gentle slope case with s =5 × 10-3.
4. SUMMARY
We have investigated the effects of the bottom slope on the response of the density current, using a three-dimensional nonhydrostatic numerical model. The results are summarized as follows
The sloping bottom has two effects operating oppositely on the descending process of dense water. One is the enhancement of the instability of flow to promote the development of the eddies, which leads to the effective downslope transport of dense water. The other is the prevention of the smooth downslope movement of the eddies, which leads to the less effective transport of dense water. Therefore, the eddies develops slowly on the gentle sloping bottom such as a continental shelf, but once fully developed, they move offshoreward smoothly to transport dense water effectively (e.g. Gawarkiewicz and Chapman,1995). On the other hand, the eddies develops rapidly on the steep sloping bottom such as a continental slope, but they don't descend smoothly so that most of dense water is confined in the upper slope region (e.g. Jiang and Garwood,1995).
REFERENCE
Gawarkiewicz, G. and D. C. Chapman, 1995: A numerical study of dense water formation and transport on a shallow, sloping continental shelf, J.Geophys.Res., 100, 4489-4507.
Jiang, L. and R. W. Garwood, 1995: A numerical study of three-dimensional dense bottom plumes on a Southern Ocean continental slope, J.Geophys.Res., 100, 18471-18488.
