Infragravity Wave Generation Mechanisms 



Two fundamental mechanisms have been proposed for the generation 

 (forcing) of infragravity waves. The first is second-order bound wave generation 

 by wave groups in intermediate water depths. Longuet-Higgins and Stewart 

 (1962) showed theoretically that grouped- forced long waves could be generated 

 by variations in radiation stress, which is a time-varying mean momentum flux 

 induced by the wind waves. The second leading theory considers a forcing of 

 low-frequency waves by a variation in the breakpoint location, which gives rise 

 to a time variation in setup producing free long waves. Based on field 

 observations (e.g., List 1992), it is reasonable to assume that both mechanisms 

 have a role in the production of low-frequency motions in the nearshore region. 



Longuet-Higgins and Stewart (1962) showed theoretically that grouped- 

 forced waves could be generated by variations in radiation stress (5^(0)- This 

 group forced long wave can be described by 



1,(1) = -- 



P 



sjfi 



gh - cl 



(8) 



where 



r)(t) is the low-frequency surface elevation 



p is the water density 



h is water depth 



c g is the group velocity 



Radiation stress forces a lowering of the mean water level under high waves in 

 the group and a corresponding rise under low waves. Thus, the bound wave is 

 180 deg out of phase from the incident wind-wave group envelope. When the 

 incident waves break, Longuet-Higgins and Stewart (1962) proposed that the 

 bound wave is released as a free wave to either propagate seaward from the 

 breakpoint or reflect off the shoreline and travel seaward. 



The magnitudes of bound waves are reasonably well-predicted in 

 intermediate to deep water by the bound long- wave (BLW) model (Sand 1982). 

 However, in intermediate to shallow depths the prediction of infragravity energy 

 becomes significantly more complicated because of the significant presence of 

 free edge waves and because multiple generation mechanisms can be locally 

 active (Herbers et al. 1995; Herbers, Elgar, Guza 1995). In addition to forced 

 bound waves, break point forced waves may contribute a significant fraction of 

 the total infragravity energy. Also, resonant amplifications of trapped edge 

 waves that often dominate the nearshore infragravity variance are difficult to 

 model over typical beaches, where the topography and current field can be 

 complex. Furthermore, the transformation of bound waves as they propagate 



1 4 Chapter 2 Infragravity Wave Dynamics 



