Long waves induced by short‐wave groups over a sloping bottom

Abstract

The cross‐shore propagation of group‐bound long waves is investigated. A detailed laboratory data set from Boers [1996] is analyzed using primarily the cross‐correlation function for a sequence of closely spaced cross‐shore locations, thus visualizing the propagation of the short‐wave envelope and attendant low‐frequency motion in detail. The results confirm the previously observed lag of the forced subharmonics behind the short‐wave envelope that increases with decreasing water depth. The forced subharmonics are found to be released and reflected at the shoreline and to propagate in offshore direction as free waves. A theoretical, linear model for the forced wave evolution accurate to first order in the relative bottom slope is presented; it predicts a bottom‐slope induced, spatially varying phase shift between the short‐wave envelope and forced waves which is in good agreement with the observations. The phase shift has dynamical consequences since it allows energy transfer between the short‐wave groups and the forced low‐frequency response.