MODIFICATIONS TO THE NEARSHORE WAVE GUIDE 



SAND BARS 



DEPTH MINIMUM AT CREST 

 VELOCITY MINIMUM AT CREST 

 REFRACTIVE FOCUSSING ON CREST 

 RESPONSE SAME BOTH DIRECTIONS 



LONGSHORE CURRENTS 



CELERITY * V(x) 



VELOCITY MIN/MAX AT V MAXIMUM 

 REFRACTIVE FOCUSSING INTO CURRENT 

 REFRACTIVE DEFOCUSSING WITH CURRENT 



Figure 9. Modification of edge waves by longshore currents 



U(x,y,t) = [u(x,y,t), v(x,y,t) + V(x)], where x and y are the cross-shore and 

 alongshore coordinates, u and v are the edge wave velocity components, and V is 

 the mean alongshore current. It is assumed V» u,v and that depth h and V 

 are slowly varying in x alone. The linear shallow-water equations take the form 



du lr du 



— + V — 

 dt dy 



dx 



(9) 



dv dV T ,dv dr\ 



— + u — + V — = -g — '- 

 dt dx dy dy 



(10) 



^ + V(r|F + hU) = 

 dt 



(11) 



The edge wave solution assumes a wave-like form for u, v, and r\, as 



u - u (x)e y 



(12) 



v = v (x)e y 



(13) 



Chapter 2 Infragravity Wave Dynamics 



19 



