When the vertical turbulent coefficient is constant, the model is called Ekman model. We place emphasis on its mode of response, and find out that its mode of response is not related to the magnitude of sea surface wind stress and value of the turbulent coefficient. When the water depth is finite, if t<h²/3 (t, h are nondimensional time and water depth), the features for finite water depth are very similar to those for infinite water depth. In this artical, we also dealt with the case for the varied vertical turbulent coefficient and the infinite depth. In this case the nondimensional response time can be scaled empirically by the sea surface wind speed. After comparing with the observational data, we conclude that the varied vertical turbulent coefficient model is more reasonable than the Ekman model.

Although the variation of the wind field is neglected, our results are helpful for understanding the temporal response process of the sea to the surface wind stress. Otherwise, our results can applied to the decay process when the surface wind disappears.