Infragravity energy in the surf zone

Field measurements of onshore and longshore velocities in the surf zone have been obtained on Martinique Beach, Nova Scotia, for the purpose of investigating the dynamics of the infragravity band (0.0030.03 Hz) of the spectra. A total of 35 data runs were obtained during a 1-week period. Of particular interest is the response of the infragravity energy to the changing incident waves, which increased considerably in size during the latter haft of the week due to an approaching hurricane. It is shown theoretically, using equilibrium arguments, that the infragravity amplitude should vary approximately linearly with incident wave amplitude. This is supported from the field data if signifier wave height is used as a measure of incident amplitude. The incident band of spectra observed by instruments in the surf zone is limited by breaking. Thus the infragravity band appears to dominate these spectra during storms. The analysis is carried out in terms of a spectral transformation, the spectrum which would be observed at an offshore instrument if the shoreline amplitude spectrum were white with unit spectral energy density. For onshore velocity the transformation predicts the observed spectral structure in the infragravity band, showing that the structure did not represent any true frequency selection. The match of theory and data also implies that the onshore motions are free waves, forced near resonance. The longshore spectra are red and show no structure which would be associated with free waves. This is consistent with the theoretical prediction that many edge wave modes, including high modes, would be forced given the broad directional spread of the storm waves. It is noted that further field experiments would be simpler on the Pacific coast where the typical, narrow-band, incident swell should force only a few, low, edge wave modes, a more accommodating situation to observe and analyze. The term 'infragravity' has been used to indicate motions with time scales of about 30-300 s, usually associated with the surf zone. Munk [1949] was the first to observe infragravity energy by using a tsunami recorder, basically a stilling well which filtered out the higher frequency components of the spectrum. He called the phenomenon 'surf beat' to reflect the observed association of these low frequency motions with the beat in the incident waves. The term infragravity energy is perhaps preferable to indicate that it is the low frequency motion that is being referred to, not the simple beating of two, firstorder incident waves (which has no spectral representation at the beat frequency and does not necessarily provide the forcing at infragravity frequencies). Theoretical studies of infragravity dynamics have evolved along two lines. The earlier theories were two dimensional, with no longshore dependence [Munk, 1949; Tucker, 1950; Longuet-Higgins and Stewart, 1964; Suhayda, 1974]. Associated with incident groups (defined by Bowen and Guza [1978] as the amplitude modulation in the incoming wave train) is a second-order, forced correction to mean sea level, progressing shoreward with the group. This forced wave is then released as a seaward-propagating free wave when the incident waves break [Longuet. Higgins and Stewart, 1964]. The summation of the inward and outward propagating components should give a standing component to the wave pattern. This mechanism does not allow for longshore periodicity, and the response is limited since the interaction is not resonant. More recently, three -dimensional theories have been developed in which longshore modulation in the incident wave field is also considered. Gallagher [1971] was the first to discuss this case, showing that, under certain conditions, the incident wave groups could force edge waves. Longshore periodicity was thus introduced into the problem and, since the