Continental shelf wave generation due to surface stress anomalies in the wake of offshore wind farms

For isolated oceanic structures above sea level in synoptic-scale wind fields, shielding causes a wind wake with reduced wind intensity on the lee side of the structure. This generates a wind-stress curl that may act as a source term for continental shelf waves (CSWs) propagating around the structure, if the bottom is sloping. We investigate CSW propagation in the case where the structure (a wind farm or an island) is circular and the depth over the shelf slope increases exponentially with radial distance. For free waves, the wave number, and hence the frequency, is quantized. We demonstrate that for circular banks with narrow continental margins, the resulting eigenfrequencies are close to those obtained for a straight shelf. Modelling the stress in the wind wake as a solitary pulse that moves along a straight shelf, we find, in the absence of friction, a forced solution that increases linearly in time when the pulse moves with the same speed as the free wave speed. For strong winds over longer periods of time, the along-shore wave velocity in the case of resonance may be of the order $m/s$ for topographic parameters characteristic of the Taiwan Bank. Velocities of this magnitude could potentially cause harmful erosion as well as affect the ecosystem on the bank slopes.