A quasi-Eulerian, quasi-Lagrangian view of surface-wave-induced flow in the ocean

In this study the influence of surface waves on the mean flow in an ocean of arbitrary depth is examined. The wave-induced forcing on the mean flow is obtained by integrating the Eulerian equations for mass and momentum balance from the bottom to an undulating material surface within the water column. By using the mean position of the material surface as the vertical coordinate, the authors obtain the depth dependence of the mean flow and the wave-induced forcing. Substitution of the vertical coordinate makes the model Lagrangian in the vertical direction. The model is Eulerian in the horizontal direction, allowing one to model the effects of a spatially nonuniform wave field or varying depth in a straightforward way.