On the Formation of Rip Currents on a Plane Beach

The superposition of normally incident wave groups and an edge wave at the same frequency on a plane beach produces rip currents with a longshore spacing determined by the edge wave dispersion relationship. The model differs from Bowen in two ways. Firstly, the edge wave slowly modulates the total water depth instead of the incident wave height. Secondly, the lower infragravity frequency results in longshore scales one to two orders of magnitude larger than Bowen's model. Solutions for both tanding and progressive edge waves have been obtained. For the progressive edge wave case the location of the rip currents depends on the relative phase (θ) between the incident wave groups and the edge wave while the magnitude of the currents depends on the mean incident wave height, the modulation of the wave group and the edge wave amplitude. In the standing edge wave case the location of the rip currents is independent of the phase and, with θ = 0, the solutions are identical to the progressive edge wave case. However, as θ → п/2 the magnitude of the rip circulation decreases to zero.