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

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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 a... 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 a...

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