Analytical study of the transverse distribution of along-channel and transverse residual flows in tidal estuaries

We present an analytical model to decompose complex along-channel and transverse residual flows into components induced by individual mechanisms. The model describes the transverse distribution of residual flows in tidally dominated estuaries. Scaling and perturbation techniques are used to obtain analytical solutions for residual flows over arbitrary across-channel bed profiles. The flows are induced by horizontal density gradients, tidal rectification processes, river discharge, wind, channel curvature and the earth's rotation. These rectification processes induce residual flows that are up-estuary to the right and down-estuary to the left of an estuarine channel (looking up-estuary in the northern hemisphere). The tidal rectification processes fundamentally change the transverse structure of along-channel residual flows in many tidal estuaries, as these processes cause the flows to be internally asymmetric about the mid-axis of the channel for relatively large tidal velocities, steep channels or narrow estuaries. In addition, velocity scales are derived from the analytical solutions to estimate the relative importance of the various residual flow mechanisms from estuarine parameters. A case study of a transect across the Upper Chesapeake Bay showed that important features of the residual flow observed in that transect are reproduced and explained by the analytical model. The velocity scales were able to identify the relevant residual flow mechanisms as well. The tidal rectification processes considered here result from advection of along-channel tidal momentum by Coriolis-induced transverse tidal currents.