Barotropic response in a lake to wind-forcing

Abstract

Abstract.We report results gained with a three-dimensional, semi-implicit, semi-spectral model of the shallow water equations on the rotating Earth that allowed one to compute the wind-induced motion in lakes. The barotropic response to unidirectional, uniform winds, Heaviside in time, is determined in a rectangular basin with constant depth, and in Lake Constance, for different values and vertical distributions of the vertical eddy viscosities. It is computationally demonstrated that both the transitory oscillating, as well as the steady state current distribution, depends strongly upon the absolute value and vertical shape of the vertical eddy viscosity. In particular, the excitation and attenuation in time of the inertial waves, the structure of the Ekman spiral, the thickness of the Ekman layer, and the exact distribution and magnitude of the upwelling and downwelling zones are all significantly affected by the eddy viscosities. Observations indicate that the eddy viscosities must be sufficiently small so that the oscillatory behaviour can be adequately modelled.Comparison of the measured current-time series at depth in one position of Lake Constance with those computed on the basis of the measured wind demonstrates fair agreement, including the rotation-induced inertial oscillation.

Hydrodynamic modelling and characterisation of a shallow fluvial lake: a study on the Superior Lake of Mantua

“…The upper boundary of the model is provided by a fixed horizontal surface at the control elevation of the lake: this is a reasonable assumption, since the free surface variations due to wind setup, head losses and pull effect near the outlets are much smaller than the grid vertical resolution (Wang et al, 2001). Therefore, more computationally expensive techniques which allow to track the moving boundary, such as Volumes of Fluids (VOF), are not needed here.…”

Measurements and three-dimensional simulations of flow in a shallow reservoir subject to small-scale wind field inhomogeneities induced by sheltering

“…The 3D mesh for a water surface level of 91.4 msl consists of 49833 nodes and 40560 elements, its spatial resolution ranges between 20 and 50 m horizontally and corresponds to one sixth of the local water depth in the vertical direction. Vertical movements of the water surface are considered to be small and therefore neglected in the computations ("rigid lid assumption", e. g. Wang et al, 2001).…”

Effects of spatial wind inhomogeneity and turbulence anisotropy on circulation in an elongated basin: A simplified analytical solution

“…The effect of Coriolis acceleration due to earth rotation is neglected and the turbulence stresses are closed within the framework of a Fickian diffusive model (e.g. [39]). For sake of simplicity, spatial variations of the eddy diffusivity tensor are neglected, and turbulence anisotropy is considered only between the horizontal and the vertical direction, where stratification is important.…”

“…Contour plot of the circulation number x given by(39) in the a-/ w plane for a single layer with no-slip bottom boundary condition and for the first lateral mode of wind forcing ðn ¼ 1Þ. The tendency towards horizontal/vertical circulation is highlighted.…”

“…Contour plot of the circulation number x given by(39) for the epilimnion of a two-layer system, for the first lateral mode of wind forcing ðn ¼ 1Þ:x is plotted in the aE-/ w plane in the case of large jT , Eq (36)…”