Transient Tidal Circulation and Momentum Balances at a Shallow Inlet

Abstract

An analysis of transient momentum balances is carried out to elucidate circulation, dynamics, and exchange mechanisms at shallow barotropic tidal inlets. Circulation is computed using a depth-integrated, fully nonlinear, time-stepping, finite-element model with variably spaced grids having horizontal resolution down to 50 m. Velocity and elevation fields from the model are used to directly evaluate the contribution of each term in the momentum equations to the overall momentum balance. A transformation of the x?y momentum terms into an s?n coordinate system is used to simplify the interpretation of the dynamics and provide vivid illustrations of the forces and resulting accelerations in the flow. The analysis is conducted for an idealized inlet and contrasted with a highly detailed model of Beaufort Inlet, North Carolina. Results show that momentum balances in the immediate vicinity of these inlets vary significantly in time and space and oscillate between two dynamical states. Near maximum ebb or flood, the alongstream momentum balances are dominated by advective acceleration, pressure gradient, and bottom friction. Cross-stream balances are dominated by centrifugal acceleration and pressure gradients. Near slack, balances more closely follow linear wave dynamics, with local accelerations balancing pressure gradients, and (to a lesser degree) Coriolis. Comparisons between the idealized inlet and Beaufort Inlet show broad similarities in these momentum balances. However, natural inlet geometry and bottom topography, as well as the tidal transmission characteristics of the sounds behind Beaufort Inlet produce strong asymmetries. Moreover, momentum balances are highly localized, often with subkilometer length scales. The dynamics are used to explain the physical mechanisms for inlet exchange. In particular, the results indicate that the cross-stream dynamics generate a ?wall? along the length of an inlet during the stronger phases of the tide. The wall is established by opposing cross-inlet pressure gradients and centrifugal forces, and it poses a significant barrier to cross-inlet exchange during the stronger phases of the tide but is absent near slack.