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

Abstract

[1] 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.

Local Concentration of Slowly Varying Wave and Current Fields Around the Abruptly Changing Bottom Slopes Along the Shore

“…All these procedures were then applied to the time-series data of surface water fluctuations along the cross-shore line A shown in Figure 2 and also the alongshore line on the seawall. As seen in the figure, phase shift decreases as the wave propagate toward the shore along the line A and this feature surely corresponds to the similar experimental results (e.g., Janssen andBattjes, 2003, andSeki andMizuguchi, 2008). On the seawall, on the other hand, the phase of envelope and the low-frequency surface water fluctuations match with each other.…”

Infragravity waves over topography : generation, dissipation, and reflection

“…Re [B] between infragravity and higher frequency waves are consistent with the known evolution from φ = −180 [Elgar and Guza, 1985, Janssen et al, 2003.…”

Wave modelling – The state of the art

“…In general triad interactions transfer energy from the incident wave components to higher-(e.g., harmonic) and lower-(e.g., infra-gravity) frequency components (see, e.g., Freilich and Guza, 1984;Elgar and Guza, 1985;Agnon et al, 1993;Kaihatu and Kirby, 1995;Agnon and Sheremet, 1997;Herbers and Burton, 1997;Ruessink, 1998;Kaihatu, 2001;Sheremet et al, 2003;Janssen et al, 2003, and many others). These interactions not only broaden the frequency spectrum in shallow water, but also phase-couple the spectral components, causing the characteristic steepening and pitching forward of nearbreaking wave crests.…”