Analytical study of lateral-circulation-induced exchange flow in tidally dominated well-mixed estuaries

- An analytical model for lateral circulation in well-mixed tidal estuaries is proposed.
- Small horizontal Kelvin number indicates importance of differential advection.
- Large horizontal Kelvin number indicates importance of the earth's rotation.
- The pattern of lateral-advection-induced flow is related to horizontal Kelvin number.
- Lateral-advection-induced flow generally reinforces gravitational circulation.

In straight estuary channels, differential advection and the Coriolis force are the major driving mechanisms for lateral circulation. An analytical model was developed to explore the roles of the two mechanisms in the dynamics of tidally dominated well-mixed estuaries. The model provided a nondimensional parameter, Keh, a type of Kelvin number (considered as horizontal Kelvin number) to elucidate the relative importance of the two mechanisms. Differential advection is effective under small Keh, while the Coriolis force is effective under larger Keh. The critical value of Keh has an order of magnitude of 0.1 in well-mixed estuaries. Lateral circulations generate residual currents through the lateral advection term in the along-estuary momentum equation. When differential advection is effective, the lateral-advection-induced flow has a laterally sheared structure with the landward flow in the channel and seaward flows over shoals. When the Coriolis force is effective, it has a laterally sheared structure with the landward flow in the left part of the cross-section and the seaward flow in the right (facing ocean). When the two mechanisms are equally important, it has an asymmetric laterally sheared structure with a stronger seaward flow over the right shoal. Those lateral structures indicate that the lateral-circulation-induced flow generally reinforces the estuarine gravitational circulation.