Lagrangian characteristics of continental shelf flows forced by periodic wind stress

Abstract. The coastal ocean may experience periods of fluctuating along-shelf wind direction, causing shifts between upwelling and downwelling conditions with responses that 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 along-shelf) primitive equation numerical model to study shelf flows in the presence of periodic, zero-mean wind stress forcing. The model bathymetry and initial stratification is typical of the broad, shallow shelf off Duck, NC 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. Eulerian mean velocities, in contrast, have almost no dependence on initial phase. In an experiment with sinusoidal wind stress forcing of maximum amplitude 0.1Nm and period of 6 days, the mean Lagrangian across-shelf displacements are largest in the surface and bottom boundary layers. Parcels that originate near the coast in the top 15m experience complicated across-shelf and vertical motion that does not display a clear pattern. Offshore of this region in the top 10m a rotating cell feature exists with offshore displacement near the surface and onshore displacement below. A mapping technique is used to help identify the qualitative characteristics of the Lagrangian motion and to clarify the long time nature of the parcel displacements. The complexity of the Lagrangian motion in a region near the coast and the existence of a clear boundary separating this region from a more regular surface cell feature offshore are quantified by a calculation from the map of the largest Lyapunov exponent.