Subtidal secondary circulation induced by eddy viscosity-velocity shear covariance in a predominantly well-mixed tidal inlet

The secondary circulation in a predominantly well-mixed estuarine tidal inlet is examined with three-dimensional numerical simulations of the currents and density field in the German Bight. Simulations analyze two complete neap and spring tidal cycles, inspired by cross-section measurements in the tidal inlet, with a focus on subtidal time scales. The study scrutinizes the lateral momentum balance and quantifies the individual forces that drive the residual flow on the cross-section. Forces (per unit mass) from the covariance between eddy viscosity and tidal vertical shear (ESCO) play a role in the lateral momentum budget. During neap tide, the ESCO-driven flow is weak. Accelerations driven by advection dominate the subtidal secondary circulation, which shows an anti-clockwise rotation. During spring tide, the ESCO acceleration, together with the baroclinicity and centrifugal acceleration, drives a clockwise circulation (looking seaward). This structure counteracts the advection-induced flow, leading to the reversal of the secondary circulation. The decomposition of the lateral ESCO term contributors reveals that the difference in ESCO between neap and spring tides is attributed to the change in the vertical structure of lateral tidal currents, which are maximum near the bottom in spring tide. The findings highlight the role of the tidally varying vertical shears in the ESCO mechanism.