Leaky waves 



7. The complement to the edge wave is the leaky wave which escapes to 

 deep water upon reflection at the shoreline. (It should be noted here that 

 "deep water" and "shallow water" are relative terms. Surface gravity waves at 

 these low frequencies have wavelengths longer than wind waves. Therefore, 

 shallow water extends farther offshore for these waves.) The difference 

 between leaky and edge waves is that the edge wave travels only in shallow 

 water, concentrating its energy toward the shoreline, whereas the leaky wave 

 will eventually travel far enough from shore to be effective in deep water, no 

 longer refracting and lost forever from the nearshore. 



8. These two wave types differ in the geometry of their approach to the 

 shoreline. Leaky waves can approach from deep or shallow water, whereas edge 

 waves must be shallow-water generated (if the nearshore has plane-parallel 

 bathymetry). These differences can best be understood by following the prop- 

 agation path of a single leaky wave. A wave that is generated in deep water 

 will approach shallow water, refracting to a more normal angle of incidence, 

 reflect, and travel offshore. As it travels offshore, the wave will follow 

 the mirrored path of its approach path and therefore will not turn enough to 

 again approach the shoreline, but instead will escape to deep water. So, by 

 this argument, if the wave is generated in deep water, it will return to deep 

 water. Thus, edge waves can be shallow-water generated only, whereas leaky 

 waves can be shallow- or deep-water generated. 



9. Freely propagating (unbounded) infragravity waves are not without 

 mathematical foundation; they are the solutions to the homogeneous (unforced) 

 equations of motion. Stokes (1846) actually noted the edge wave solution to 

 the equations of motion but considered it one of those mathematical curiosi- 

 ties without any physical relevance (Lamb 1932). Eckart (1951), following up 

 on the physical description of Isaacs, Williams, and Eckart (1951), found the 

 edge wave solutions for the linear shallow-water equations on a plane-parallel 

 beach. Soon afterwards, Ursell (1952) found edge wave solutions on a plane 

 beach using the full linear equations of motion. A mathematical description 

 for edge waves can be written as follows: 



n(x,y,t) - a<t>(x) cos (ky - at) (1) 



