stress" was employed to describe this wave-induced thrust even though the 

 units were force per unit length and not a true stress. About the same 

 time, Lundgren (1962, 1963) discussed these same principles as a wave- 

 induced thrust and derived similar expressions which were later corrected 

 (Danish Technical University, 1969) . The term radiation stress is now 

 generally accepted for this forcing function. It has significantly helped 

 to unravel the mystery of how oblique wave attack can generate longshore 

 currents that baffled scientists and engineers up to 1970. The general 

 principles and equations associated with the radiation stress theory are 

 summarized in Chapter 3. 



The local streamline curvature of rapidly varied, free-surface flows 

 gives rise to vertical accelerations that also change the hydrostatic 

 pressure distribution assumption. In 1872, Boussinesq derived expressions 

 to account for this effect in the horizontal equations of motion for nearly 

 horizontal free-surface flows, and an additional term (or terms depending 

 upon the order of accuracy of the derivation) that permits frequency disper- 

 sion and wave propagation of permanent form. No time averaging is involved. 

 Called the "Boussinesq Theory," it offers an alternative way to introduce 

 the lateral momentum thrust due to gravity waves. 



(2) Mass Transport . Time-averaging nonlinear waveforms result 

 in a net drift velocity because particle orbits are not closed. The 

 current that results is very small and can be considered negligible in the 

 surf zone and beyond the breakers. After breaking, mass transport by 

 translation of hydraulic bores through the surf can not be neglected. 



The wave characteristics of interest are height, period, and angle 

 of crest with the shoreline. The values at the first breaker line are 

 reportedly the most significant. Surf zone transformations are discussed 

 separately. 



b. Tides . The tides create currents alongshore that are relatively 

 small except near inlets. These currents have been omitted from this 

 review. However, as mentioned by Sonu (1972), the slow water level 

 changes induced by tides change the wave breaker location, hence the surf 

 zone width, and ultimately affect the strength of wave-induced longshore 

 currents. Also rip currents were found to be stronger at low tide and 

 pulsated with a 25- to 50-second beat. The weaker rips at high tide 

 fluctuated at the swell period. 



c. Wind Surface Shear . The wind moving across the water surface 

 has a vertical velocity distribution that gives rise to a surface shear 

 stress. As a result the water surface layers move at a speed of about 

 3 percent of the mean windspeed above the boundary layer. Viscous 

 processes (both molecular and eddy type) transport this momentum down 

 into the water column. In large water bodies, Coriolis forces will cause 

 the current to deflect to the right of the wind direction (facing down- 

 wind. Northern Hemisphere) and spiral away from the wind direction 

 (Ekman motion) . These classic deepwater oceanographic concepts can be 



^DANISH TECHNICAL UNIVERSITY, ISVA, "Index to Reports," Report No. 20, 

 Dec. 1969, Lyngby, Denmark (not in bibliography). 



43 



