Stratification and the vertical structure of wave-driven cross-shelf circulation over the inner shelf

Surface waves are increasingly being recognized as a significant driver of transport over the inner shelf, offshore of the surf zone. When waves are present over the inner shelf, observations reveal an offshore-directed Eulerian transport that balances the depth-integrated onshore transport due to Stokes drift. The goal of this study is to investigate the vertical structure of the wave-driven cross-shelf circulation under different conditions. New analysis of observations from the Martha’s Vineyard inner shelf characterizes velocity profiles during wave events based on observed stratification. Numerical modeling builds on previous work by accounting for lateral variations in the flow and the dependence of turbulent mixing on shear and stratification, as well as the Earth's rotation. These complex physics are examined in idealized scenarios using the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system. When lateral variations are neglected, a surface-intensified Eulerian flow that mirrors the Stokes drift profile only forms when the model is initialized with stratification that suppresses turbulent mixing. Introducing stratification in a two-dimensional case leads to convectively-driven mixing near the surf zone boundary, but stratification over the inner shelf is maintained due to lateral advection of density gradients. A non-dimensional number based on initial stratification and wave characteristics is used to explain variation in the vertical structure of cross-shelf velocity. This dynamical framework is consistent with a tendency for weaker vertical shear in observed cross-shelf velocity profiles at the 12-m isobath when the water column is unstratified, and will be tested further with additional observations at other sites.