T\(x,t) = aJ {s/4^) cos (co t) (7) 



where J is the zeroth order Bessel function. Leaky waves, like edge waves, are 

 standing in the cross-shore but do not attenuate with distance offshore. Thus, 

 they theoretically have an infinite number of nodes and antinodes extending out 

 to deep water. These waves have a cross-shore structure similar in appearance to 

 edge waves, particularly close to shore (Figure 4). High mode edge waves have 

 many nodes and antinodes and can be indistinguishable from leaky waves in surf 

 zone measurements. 



Measurements of nearshore infragravity waves are for the purpose of 

 identifying modes made with alongshore-aligned arrays of current meters. 

 Huntley, Guza, and Thornton (1981) were the first to clearly identify edge wave 

 modes using an alongshore array of current meters. Alongshore wave number- 

 frequency (k -f) spectra are particularly useful for partitioning wave variance 



into the contributions from incident, edge, leaky, and shear waves (Oltman-Shay 

 and Guza 1987; Oltman-Shay and Howd 1993; Howd, Oltman-Shay, and 

 Holman 1991). The complex cross-shore standing structure of infragravity 

 waves makes cross-shore wave number-frequency (k x -f) spectra, that would be 

 observed from a cross-shore array, of little use for resolving high-mode edge and 

 leaky waves. An Iterative Maximum Likelihood Estimator (IMLE) (Pawka 

 1982, 1983) method of analyzing cross- and longshore component current data 

 from along-shore aligned arrays has been shown highly successful at estimating 

 k-f spectra (e.g., Oltman-Shay and Guza 1987). 



Typical k-f spectra from the Oltman-Shay and Guza (1987) analysis of 

 longshore-aligned array data from the Nearshore Sediment Transport Study 

 (NSTS) field site at Torrey Pines is shown in Figure 5. The k -f spectra of 



longshore component of flow are significantly better at resolving low mode edge 

 waves, each mode showing up as a 'ridge' of high variance over a predictable 

 frequency range. Cross-shore component velocity is dominated by high mode 

 edge waves or leaky waves. 



Oltman-Shay and Guza (1987) studied 15 days of data from two beaches. 

 They found longshore current component energy was observed to consist of 70 

 to 90 percent low-mode (n < 2) edge waves. Cross-shore currents were found to 

 contain low-mode edge waves which accounted for about 20 percent of the wave 

 energy, but the k y -f (u) spectra also contained other low wave number energy 



from unresolvable combinations of high-mode edge waves and/or leaky waves. 

 The observation of high modes in the A: -f{u) spectra does not contradict the 



dominance of low-modes in the k -f (v) spectra because high-mode and leaky 



waves have their largest velocity components in the cross-shore direction. 



Chapter 2 Infragravity Wave Dynamics 



