  In 1895, Korteweg and de Vries (KdV), derived their celebrated equation
describing the motion of waves of long wavelength in shallow water. In doing so
they made a number of quite reasonable assumptions, incompressibility of the
water and irrotational fluid. The resulting equation, the celebrated KdV
equation, has been shown to be a very reasonable description of real water
waves. However there are other phenomena which have an impact on the shape of
the wave, that of vorticity and viscosity. This paper examines how a constant
vorticity affects the shape of waves in electrohydrodynamics. For constant
vorticity, the vertical component of the velocity obeys a Laplace equation and
also has the usual lower boundary condition. In making the vertical component
of the velocity take central stage, the Burns condition can be thus bypassed.
