Wave refraction in ocean currents

Abstract Reflection of surface gravity waves in major ocean currents is investigated by applying the geometrical optics approximation to deep water waves in steady nonuniform currents. Assuming the group speed c ′ g relative to the current is much greater than the current speed, the radius of curvature R of the wave rays is given by R = c ′ g / ξ , where ξ is the vertical component of the vorticity of the current. The magnitude of R decreases with decreasing group speed (increasing frequency) relative to the current and with increasing vorticity. The sign of R is given by the sign of ξ, and the radius of curvature is positive (negative) if the ray is concave to the left (right) when looking in the direction of energy propagation. Applications to the ocean indicate that both the trapping of surface waves in currents and the total reflection of waves by currents should be possible under the appropriate conditions. Some observations of swell propagating across the Pacific are not inconsistent with a wave-current refraction mechanism.