A Simple Analytical Model of Periodic Coastal Upwelling

An existing reduced-gravity model that reproduces the response of the coastal sea to alongshore wind forcing at subinertial frequencies is extended by allowing for cross-shore wind forcing and by considering superinertial frequencies. The obtained explicit solution shows that the wind-driven currents are predominantly controlled by friction and the Coriolis force at subinertial frequencies and by friction and local acceleration at superinertial frequencies. The effect of the coast is manifested by coastal-trapped variability at subinertial frequencies and baroclinic inertia–gravity waves propagating away from the coast at superinertial frequencies. The pycnocline oscillates at the coast not only at subinertial but also at superinertial frequencies, with the alongshore wind contributing more to the former and the cross-shore wind influencing more the latter. The oscillations are most pronounced when the periodic wind forcing is resonantly coupled to the local inertial oscillations (but only if the wind is not rotating counter to the inertial currents) and at near-zero frequencies (but not when the wind is purely cross-shore). These theoretical findings are related to recent observations of diurnal temperature oscillations in the near-shore water column.