The influence of river discharge on energy transport in estuaries and its implication for the equilibrium bed profile

Abstract

In this paper, we revisit the classical energy transport equation for pure tidal flows in estuaries by including the effects of residual water level and freshwater discharge. Starting from the one-dimensional mass and momentum conservations, we derive analytical expressions for energy flux and its dissipation, which can be used to explore the interaction between tide and river from an energy perspective. It has been shown that the potential energy flux is dominant over the kinetic energy flux, and the energy contribution made by tide-river interaction is negligible compared with that due to tidal flow and freshwater discharge. A critical position corresponding with zero energy flux can be identified, reflecting a balance between along-channel tidal amplitude and residual water level. Assuming the variation of system energy tends to zero, we derive the long-term equilibrium bed profile with a convex-up shape, where we identify the location of a second estuarine turbidity maximum (ETM) at a position determined by the balance between river- and tide-induced energy flux. The dynamic response of tidal propagation extent and critical position with zero energy flux are shown to adjust to reflect seasonal changes towards the formation of a bed profile that is in dynamic equilibrium. Key policy insights A new analytical method is derived to calculate energy transport and energy dissipation in river-tide estuaries. Equilibrium bed profile determined by minimum entropy production has a convex-up shape where the minimum depth coincides with the location of zero along-channel energy flux. The location of a second estuarine turbidity maximum is consistent with the location where there is a balance between river- and tide-induced energy flux.