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

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.