In practice, real currents are turbulent and are rarely uniform. 

 Turbulence can be sufficiently strong to inhibit wind wave growth 

 (Skoda, 1972). The strongest nonuniformity is usually in the vertical. 

 The two most common causes are "wind drift" and "bottom friction." 



3. Effects of Vertical Variation of Current Velocity . 



There are two particularly strong effects of wave-current 

 interaction which make it important to consider the variation of current 

 with depth. One is the effect of any velocity shear at the surface on 

 the tendency of waves to break. Banner and Phillips (1974) and Phillips 

 and Banner (1974) describe this using an inviscid model. This is 

 discussed in Section II, 12. 



The other is the way in which waves In a flume have been shown 

 to modify the current velocity profile. Such experiments have been 

 described by Van Hoften and Karaki (1976), Brevik (1980), Brevik and Aas 

 (1980), Bakker and van Doom (1978, 1980), and in more detail by Kemp 

 and Simons (1982). Figure 4 shows the mean current profiles and those 

 obtained by adding the experimentally measured current and wave-induced 

 current separately. The difference seems to be best ascribed to turbu- 

 lent interactions. Note that a simple eddy viscosity would be negative 

 above the maximum of the mean velocity (assuming stress does not change 

 sign). The additional shear stress and transporting capability of 

 velocity maximum are relevant to sediment transport (Section III, 3). 



Velocity profiles established by bottom friction and by surface wind 

 stress have attracted most attention. Numerous papers either derive 

 dispersion relations for various simplifications of the profiles or find 

 results numerically. Peregrine (Section IV, 1976) and Jonsson (Section 

 3.2.7, 1978b) review the subject, and a number of features are 

 noteworthy. 



Since water waves are surface waves, they are particularly sensitive 

 to the velocity in the surface layers. In wind wave flumes the velocity 

 profile due to the wind needs to be taken into account in studying wind 

 waves; e.g., Lilly (in an appendix to Hidy and Plate, 1966) calculates a 

 correction to the dispersion equation, Shemdin (1972) gives more 

 detailed numerical and experimental comparisons including the air 

 motion, and Plant and Wright (1980) find that including other effects 

 such as finite-amplitude effects does not improve comparison with 

 experiment. 



A sensitivity to surface drift also shows up when wave fields are 

 used to measure surface currents, as is possible by analyzing the 

 Doppler shift in the scattering of high-frequency radio waves. 

 Scattering by water waves of differing wavelengths leads to different 

 values of the "current." Stewart and Joy (1974) give a useful 

 approximate formula for the current so obtained. The phase velocity 

 (after minor correction of their formula) is 



23 



