A more general case of the nonlinear difference frequency interaction between two waves is that between two, closely-spaced spectral components within an incident band spectral peak. The difference frequency interaction then forces low frequency flows known as infragravity waves (0.005-0.05 Hz). The linear manifestation of two similar frequencies is wave groups. The nonlinear result in intermediate and deep water is a phase-locked, forced depression of sea level beneath the large waves in the group [ Longuet-Higgins and Stewart, 1964]. In shallow water, this mechanism can directly directly transfer energy to free infragravity waves.
Because the nearshore acts as a wave guide, nearshore wave motions can act as leaky modes, that escape the nearshore wave guide to the deep ocean, or trapped waves called edge waves, that are refractively contained within the wave guide. In addition to the Longuet-Higgins and Stewart mechanism above, models for leaky mode generation have been proposed by Symonds et al. [1982], based on fluctuations in surf zone width in a modulating wave field, and by Watson and Peregrine [1992], based on the propagation of a modulating bore field within the surf zone. If the difference wavenumber of the interaction includes a longshore component, edge waves can be generated either by the same nonlinearities in the shoaling region [ Gallagher, 1971], and/or at the region of the modulating break point [ Shaffer, 1990].
Earlier estimates of the relative importance of infragravity waves were quite variable, from the original value of roughly 10% of the wave height for just outside the surf zone [ Munk, 1949] to 99% of the runup on a very dissipative Oregon beach [ Holman and Bowen, 1984]. However, there has been abundant evidence supporting predicted shallow water kinematics of these motions [e.g. Guza and Thornton, 1985] and supporting the common existence of edge waves on natural beaches [e.g. Oltman-Shay and Guza, 1987].
Over the last five years, rapidly increasing amounts of available
data have allowed progress. Howd et al. [1991] were able to synthesize
the extensive data sets from experiments at Duck, North Carolina, with
four other experiments on beaches of widely varying geometries. They
found that infragravity wave heights scaled with offshore wave height,
with ratios varying from roughly 0.2 to 0.6, depending on the
non-dimensional beach steepness (the Irribaren number, 
, where 
is the beach slope and
the offshore wave steepness).
In deeper waters where forced waves were expected to dominate, the opposite has been found true. In analysis of several data sets spanning one to two years, it has been found that the directly forced (phase-locked) component of the infragravity wave field accounted for only 0.1-30% of the observed field [ Elgar, et al., 1992; Okihiro, et al., 1992; Herbers, et al., in press], with the larger percentages associated with higher incident waves. The dynamics of this forced component were shown to obey theory [ Hasselmann, 1962]. The physics of the (large) remaining free wave component are of obvious interest in current research.
In shallower water, Howd et al. [1992] introduced an interesting, new idea by analyzing the kinematics of edge waves propogating with and against strong longshore currents. Since shear of a longshore current can act to refract longshore-propagating waves, a formal equivalence could be set up between bathymetric and current-shear refraction. Kinematic predictions were well supported by data from Duck experiments.