Time-dependent transport on the continental shelf driven by steady winds

The horizontal transport on a linearly sloping continental shelf forced by time-independent wind stress is studied here in the Lagrangian framework using the adiabaticity principle, in which a potential is constructed for the cross-shelf dynamics. The dynamics is separated into fast oscillations about the potential's minimum and slow changes in the location of the minimum itself. The resulting analysis and accompanying numerical solutions show that the wind-driven transport consists of nonlinear inertial oscillations and slow net transport. As in traditional Ekman theory, the net transport is directed at 90 ° to the right (in the northern hemisphere) of the applied wind stress, although on the shelf the cross-shore transport is time dependent. Analytic solutions yield explicit expressions for mass conservation that imply convergence of net off-shore directed transports and divergence of net on-shore directed transports prior to reaching the shoreline.