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The viscosity of water induces a vorticity near the free surface boundary.The resulting rotational component of the fluid velocity vector greatlycomplicates the water wave system. Several approaches to close this system havebeen proposed. Our analysis compares three common sets of model equations. Thefirst set has a rotational kinematic boundary condition at the surface. In thesecond set, a gauge choice for the velocity vector is made that cancels therotational contribution in the kinematic boundary condition, at the cost ofrotational velocity in the bulk and a rotational pressure. The third setcircumvents the problem by introducing two domains: the irrotational bulk andthe vortical boundary layer. This comparison puts forward the link betweenrotational pressure on the surface and vorticity in the boundary layer,addresses the existence of nonlinear vorticity terms, and shows whereapproximations have been used in the models. Furthermore, we examine theconservation of mass for the three systems, and how this can be compared to theirrotational case.

Reconciling different formulations of viscous water waves and their mass conservation