where c = (x>/k is the edge wave celerity. Rewriting Equation 2 1 in terms of 

 h'(x) gives 



dx{ dx 



n(co 2 + gh'kf) = 



(23) 



which is functionally equivalent to the classical edge wave equation but now 

 carries with it the modifications of edge wave characteristics due to mean 

 longshore currents and topography. 



Edge waves traveling into the current experience an increase in | k | and 



compress the nodal structure toward the shore. The effect is opposite for edge 

 waves progressing with the current, the magnitude of \k \ decreases and the 



nodal structure shifts offshore. This change in dispersion has interesting 

 implications for the possible effects on nearshore morphology. Without 

 currents, edge waves of identical frequency and mode traveling in opposite 

 directions would have identical, but opposite sign k . Bowen and Inman (1971) 



suggested that when these edge waves are phase-locked, the associated velocity 

 fields could generate crescentic bars. The results of Howd, Bowen, and Holman 

 (1992) imply that addition of alongshore currents would change the \k \ 



magnitudes and the associated edge wave drift velocities to a more complicated 

 pattern. This could result in more complex morphology changes, such as welded 

 bars, as proposed by Holman and Bowen (1982) for edge wave interactions of 

 different modes. 



Edge wave solutions for beaches with alongshore currents or depth profiles 

 without analytical solutions can be found by manipulating Equations 15-17 to 

 obtain two coupled first-order equations (Howd, Bowen, and Holman 1992; 

 Oltman-Shay and Howd 1993) 



(24) 



du' 

 dx 



K = 



dx 



a i 

 — u 



g 







{ a 2 ) 



, a )\ dx) 



"(i) 



( dh 



[dx 



(25) 



Howd, Bowen, and Holman (1992) solved these equations using a numerical 

 method, the Runge-Kutta method, where the initial values at the shoreline are 



TtfO) 



gP,V(0) 



(26) 



Chapter 2 Infragravity Wave Dynamics 



21 



