Steady Wind-Driven Currents in a Large Lake with Depth-Dependent Eddy Viscosity

Abstract

The theory of steady wind-driven currents in shallow water is extended to the case of a spatially variable eddy viscosity of the form ν=ν0eaz, where ν0 and a are constants and z is the vertical coordinate measured upward from the free surface. The theory is first applied to the case of a pure drift current in water of constant depth, and a good fit with observed data is obtained. Subsequently, the theory is applied to a simplified model basin (representing Lake Ontario). Results are given for a uniform surface wind stress for different values of the parameters ν0 and a, and compared with results for a constant eddy viscosity. Although the vertically-integrated mass flux is fairly insensitive, the three-dimensional current pattern is fairly sensitive to the variations in the eddy viscosity. The results for the exponential eddy viscosity show deeper coastal “jets” as well as a weak central current not found in the case of a constant eddy viscosity. The pattern of return flow is changed, and there are significant differences in the pattern of upwelling and downwelling. The results point out the importance of more accurate representations of turbulent momentum transport in lake modeling.