height and steepness and increases breaking. An artist's impression of 

 a similar phenomenon is Turner's (1_775-1851) "The Junction of the Thames 

 and the Medway" (National Gallery' of Art, Washington, D.C.). A radar 

 picture of the Columbia River Entrance in The Quarterly CERCular 

 Information Bulletin, January 1980, displays similar refraction by tidal 

 currents . 



Navigators have made other use of wave-current interaction. 

 Polynesian canoeists allowed for currents and identified their existence 

 by the change in shape of the waves (Lewis, 1972, pp. 100-115). Modern 

 nautical experience with waves interacting with currents is reported by 

 Coles (1975), including examples from the Gulf Stream (pp. 102, 214, 

 216-218) and English Channel (pp. 116, 119, 121, 122, 147, 168, 169, and 

 Plate 14). 



Wave-current interaction can have important effects on shoreline 

 position or stability of shore protection. In design for shore 

 maintenance, it is accepted practice to hindcast wave characteristics 

 for deep water and refract these waves into shore without consideration 

 of the currents that the waves may cross in reaching shore. These 

 currents have the potential to change the height and direction of the 

 waves actually reaching shore, and thus the magnitude and possibly 

 direction of longshore transport. Changes in height will also affect 

 the design weight of armor stone used for shore protection. 



These effects are to be expected especially where shoreline 

 irregularities, such as projecting headlands or tidal inlets, constrict 

 the flow, or produce large semipermanent eddies. At the present, there 

 is no generally accepted agreement whether such currents render a beach 

 more, or less, exposed to the incident wave. 



II. EFFECTS OF CURRENTS ON WAVES 



1. Scales. 



In interpreting, analyzing and modeling wave-current interactions, 

 it is useful to have a clear appreciation of the relative magnitude of 

 time and length scales for both the waves and the currents. For 

 example, many mathematical techniques and physical concepts are of value 

 only if the scale of the currents is much larger than that of the 

 waves. The dispersion relation is such an example. The most obvious 

 time and length scales of waves are their period, T, and wavelength, L. 

 Thus a large-scale current might be one which varies very little, say, 

 no more than a few percent over a distance of one wavelength or over a 

 time of one wave period. Experience in other fields suggests that in 

 some examples, the shorter length and time scales of the inverse wave 

 number, k~^, where k = 27t/L, and inverse radian frequency, w~ , where w 

 = 2tt/T, can sometimes be used. 



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