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