Generation of exchange flows in estuaries by tidal and gravitational eddy viscosity-shear covariance (ESCO)

We present a systematic analysis of generation mechanisms for exchange flows in partially stratified estuaries using water column (1DV) and width-averaged (2DV) numerical models. We focus on exchange flows generated by eddy viscosity-shear covariance (ESCO). We identify two distinctly different physical mechanisms. The first, tidal ESCO circulation, results from interactions between the barotropic tide and temporal variations of the eddy viscosity. While this flow is mostly generated by direct interactions between the tide and eddy viscosity variations at the main tidal frequency, a similarly important contribution can be attributed to indirect interactions. These are more complex interactions involving eddy viscosity variations at other frequencies than the main tidal frequency (e.g., M4). The second mechanism is called gravitational ESCO circulation. This results from an amplification of the gravitational circulation through indirect interactions between the gravitational circulation and temporal variations of the eddy viscosity at any time scale. Tidal and gravitational ESCO circulations are generated by different mechanisms and have a different dependency on the phase and frequency of eddy viscosity variations and the density gradient. The relative contributions of gravitational circulation and tidal and gravitational ESCO circulation to the exchange flow are typically 1/3 each in tidally energetic well-mixed or partially stratified estuaries. The results are generalized using an idealized width-averaged model of the Scheldt River estuary. This model confirms the results of the water column model and additionally shows that temporal variations of turbulence not captured in the water column model have a significant effect on the exchange flow.