Mass transport in three-dimensional water waves

A spectral scheme is developed to study the mass transport in three-dimensional water waves where the steady flow is assumed to be periodic in two horizontal directions. The velocity-vorticity formulation is adopted for the numerical solution, and boundary conditions for the vorticity are derived to enforce the no-slip conditions. The numerical scheme is used to calculate the mass transport under two intersecting wave trains; the resulting flow is reminiscent of the Langmuir circulation patterns. The scheme is then applied to study the steady flow in a three-dimensional standing wave.