Wind spatial variability and topographic wave frequency

The association of topographic waves with wind action has been documented in several natural lakes throughout the world. However, the influence of the wind's spatial variability (wind stress curl) on the frequency of topographic waves has only been partially investigated. Here the role of wind stress curl on the frequency of topographic waves in an idealized elliptic paraboloid basin has been studied both analytically and numerically. It is shown that the analytical solution is the sum of an elliptic rotation determined by the wind stress curl and two counterrotating circulation cells, which propagate cyclonically after the wind ceases. Furthermore, it is shown that cyclonic elliptical rotation (associated with positive wind stress curl) increases the rotation frequency of the double-gyre pattern while anticyclonic elliptical rotation (associated with negative wind stress curl) decreases the oscillatory mode frequency. It is also shown that bottom friction has some effect on the structure of the double-gyre pattern but hardly affects the oscillatory frequency. Numerical solutions of the depth-integrated nonlinear shallow-water equations confirmed that the frequency of the topographic wave increases (decreases) when forcing the model with cyclonic (anticyclonic) wind curl.