A local eddy viscosity parameterization for wind-driven estuarine exchange flow, Part II: Entrainment

Structure and intensity of estuarine exchange flow depend significantly on the eddy viscosity $A_v$ profile which is dynamically linked to various forces (e.g., gravitational, tidal, wind-driven). The impact of winds on the exchange flow is complex due to its direct (local and remote changes in shear and density stratification) and indirect (modifications to $A_v$ profiles) contributions. This study aims (i) to include wind entrainment effects in the tidally averaged $A_v$ parameterization; (ii) to develop an analytical one-dimensional model for the wind driven exchange flow by using this novel parameterization and assess the tidally averaged dynamics over a relevant physical parameter-space, subdomains of which have not yet been explored numerically. This one-dimensional model is based on a balance between frictional forces and pressure gradient, calibrated with a tidally-resolving one-dimensional water-column model with second-moment closure. Structure and intensity of the resulting exchange flow profiles are analyzed with respect to three dimensionless parameters (the unsteadiness of boundary layer mixing $U_n$, scaled-directional wind stress $W$, and horizontal stratification $S_i$). While down-estuarine winds enhance the gravitational circulation, up-estuarine winds result in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow (favored by relatively strong $S_i$, weak $W$, and moderate $U_n$) that is up-estuarine at the surface with classical two-layer circulation underneath. Relative thickness of surface and bottom boundary layers affect both the intensity and the inflection depth of the exchange flow layers. Up-estuarine winds with $W\gtrsim 0.5$ yield unstable stratification and reduce the exchange flow intensity with increasing $W$.