A Modeling Study of Lagrangian and Eulerian Shelf Flows due to Periodic Wind Forcing

The circulation of fluid on the continental shelf is greatly influenced by the wind stress magnitude and direction. Many shelf regions experience periods of fluctuating alongshelf winds, causing shifts between upwelling and downwelling conditions. The upwelling and downwelling responses are not symmetric. We seek to understand these asymmetries and their implications on the Eulerian and Lagrangian flows. We use a two-dimensional (variations across-shelf and with depth; uniformity alongshelf) primitive equation numerical model to study shelf flows in the presence of periodic, zero-mean wind forcing. The model bathymetry and initial stratification is typical of a broad, shallow shelf during summer. After an initial, transient adjustment, the response of the Eulerian fields is nearly periodic. Despite the symmetric wind stress forcing, there exist both mean Eulerian and Lagrangian flows. The mean Lagrangian displacement of parcels on the shelf depends both on their initial location and on the initial phase of the forcing. The use of mean parcel positions during a cycle for calculating displacements helps to remove the dependence on phase. In an experiment with sinusoidal wind stress forcing of 1 dyne cm^-}{2 maximum amplitude and 6 day period, the mean Lagrangian displacements were largest in the surface and bottom boundary layers. Parcels initialized near the bottom within 50 km of the coast can be displaced to the surface at the coastal boundary over several periods. Parcels initially in the upper 10 m within 25 km of the coast form large, irregular orbits, yet remain within this region. Parcels initialized in the middle of the water column offshore of about 15 km form almost closed orbits after one period and migrate slowly downward over many periods. Eulerian mean velocities, in contrast, have no dependence on initial phase. The Eulerian across-shelf mean velocity field shows 2 cm s^-}{1 onshore flow in the bottom layer from the coast to 30 km offshore and in the top layer from 10 km to 20 km offshore. Offshore flow of this magnitude is found both onshore of and below the surface region of onshore flow. Corresponding to regions of onshore flow are upward vertical velocities of 1 {\times} 10^-}{3 cm s^-}{1 with similar downward velocities in regions of offshore flow.