Ekman motion in shallow open sea in the presence of time-harmonic variation of water depth

The time variation of the wind-induced flow in a homogeneous unbounded sea region has been analytically investigated. The time-dependent Ekman solution in a homogeneous, shallow open sea has been further extended by taking into account the time variation in water depth which might be caused by either tidal motion or change in the mixed layer thickness. The solution approach taken in this study is based on the Galerkin-eigenfunction method originally developed by Heaps [1972. On the numerical solution of three-dimensional hydrodynamical equations for tides and storm surges. Memoires de la Societe Royale des Sciences de Liege Serie 6(2), 143–180]. A series of calculations have been made with emphasis on the influence of the time variation in water depth upon the build-up of Ekman spirals in the presence of oscillatory variations in water depth. It has been found that two oscillations contribute to the wind drift current, the inertial oscillation and the depth-variation-induced oscillation; the inertial oscillation decays with time, but the depth-variation-induced oscillation remains undamped despite the presence of bottom friction. The presence of time-harmonic variation produces peculiar forms of hodograph with a curled or circular pattern according to the angular frequency of the water depth variation.