4 Results 



1-D Wave-Current Interaction 



The dispersion relationship for waves and currents traveling in the same 

 direction or directly opposing each other is (Jonsson 1990, and others): 



io - kU = yjgk tzxihkd (2) 



where o) is angular frequency, k is wave number, f/is current velocity, g is gravita- 

 tional acceleration, and d is water depth. The wave period (7= 27t/(o) is assumed to 

 remain constant as the wave propagates from still water onto the current. For the 

 situation where f/ = 0, Equation 2 reverts to the standard dispersion equation. 

 Wave blocking (stopping of waves by an opposing current) occurs for relatively 

 strong ebb currents for which there is no solution for Equation 2 (\U\>(gT)/(% tt) in 

 deep water and \U\>(gd)'^ in shallow water/ The strong current prevents the wave 

 from propagating through the channel, and the wave energy is reflected or dissipated 

 by breaking. 



Using k calculated from Equation 2, the wavelength is given by: 



2tc 

 k 



L = — (3) 



In shallow water. Equation 2 reduces to: 



and Equation 3 becomes: 

 L=(U ^^)t (5) 



Chapter 4 Results 15 



