Refraction of gravity waves by weak current gradients

When deep water surface waves cross an area with variable current, refracti on takes place. If the group velocity of the waves is much larger than the current velocity we show that the curvature of a ray, kappa, is given by th e simple formula kappa = zeta/nu (g). Here zeta is the vertical component o f the current vorticity and nu (g) is the group velocity.