Two-dimensional (cross-shelf and depth) circulation by downwelling wind in the presence of a prograding front (with isopycnals that slope in the same direction as the topographic slope) over a continental shelf is studied using high-resolution numerical experiments. The physical process of interest is the cross-shelf circulation produced by northeasterly monsoon winds acting on the Kuroshio front over the East China Sea outer shelf and shelfbreak where upwelling is often observed. However, a general problem is posed and solved by idealized numerical and analytical models. It is shown that upwelling is produced shoreward of the front. The upwelling is maintained by (1) a surface bulge of negative vorticity at the head of the front; (2) bottom offshore convergence beneath the front; and (3) in the case of a surface front that is thin relative to water depth, also by upwelling due to the vorticity sheet under the front. The nearcoast downwelling produces intense mixing due to both upright and slant-wise convection in regions of positive potential vorticity. The analytical model shows that the size and on-shore propagating speed of the bulge are determined by the wind and its shape is governed by a nonlinear advection-dispersion equation which yields unchanging wave-form solutions. Successive bulges can detach from the front under a steady wind. Vertical circulation cells develop under the propagating bulges despite a stable stratification. These cells can have important consequences to vertical exchanges of tracers and water masses.
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