  This paper considers steady surface waves `riding' a Beltrami flow (a
three-dimensional flow with parallel velocity and vorticity fields). It is
demonstrated that the hydrodynamic problem can be formulated as two equations
for two scalar functions of the horizontal spatial coordinates, namely the
elevation $\eta$ of the free surface and the potential $\Phi$ defining the
gradient part (in the sense of the Hodge-Weyl decomposition) of the horizontal
component of the tangential fluid velocity there. These equations are written
in terms of a nonlocal operator $H(\eta)$ mapping $\Phi$ to the normal fluid
velocity at the free surface, and are shown to arise from a variational
principle. In the irrotational limit the equations reduce to the
Zakharov-Craig-Sulem formulation of the classical three-dimensional steady
water-wave problem, while $H(\eta)$ reduces to the familiar Dirichlet-Neumann
operator.
