Interference of wind-driven and pressure gradient-driven flows in shallow homogeneous water bodies

This study explores the characteristics of wind-driven steady-state flows in water bodies of constant density focusing on situations in which the surface and bottom Ekman layer interfere. Under the assumption of constant eddy viscosity in conjunction with a zero-flow bottom boundary condition, such flows can be linearly decomposed into wind-driven and pressure gradient-driven flow components, each affiliated with a frictional boundary layer. The resultant interference patterns, including the creation of undercurrents, are discussed using a one-dimensional water-column model. The second part of this paper employs a three-dimensional hydrodynamic model to study interferences for an idealized large and shallow oceanic bay at low latitudes under the action of a uniform wind stress. Lee effects trigger a surface pressure field that tends to slope against the wind direction. The associated pressure gradient force creates an undercurrent in deeper portions of the bay, while unidirectional flows prevail in shallower water. It is demonstrated that such undercurrents can operate as an effective upwelling mechanism, moving sub-surface water into a bay over large distances (~100 km). Based on estimates of eddy viscosities, it is also shown that Ekman layer dynamics play a central role in the dynamics of most mid-latitude lakes. On the continental shelf of the modern ocean, inferences between the surface and bottom Ekman layers leading to undercurrents do currently only exist in shallow shelf seas at low latitudes, such as the Arafura Sea.