



C = (g/k)^/2 + 2k] u(z) exp (2kz) dz + OCu^/C^) (7) 



where u(z) is the component of current in the wave direction and deep 

 water is assumed. 



Measurements of the lengths of stationary waves in flowing water by 

 Freds^e (1974) showed some influence of the current vorticity. Jonsson, 

 Brink-Kjaer, and Thomas (Fig. 2, 1978) found that a linear current 

 profile would account for most of the deviation from the uniform 

 velocity solution. 



Sarpkaya's (1957) experiments indicate another area worthy of 

 investigation. In these, waves propagating upstream in a flume were 

 amplified, if the initial amplitude was big enough, even though the 

 current was uniform along the flume. This is an unexplained phenomenon 

 that has disturbing implications for waves entering inlets and harbors 

 against adverse flows. To date, the experimental results have not been 

 repeated though it is understood (Kemp, University College, London, 

 personal communication, 1981) that experiments in progress may be 

 suitable for verifying the results. Possible mechanisms worth 

 investigating are (a) that flow reversal occurs near the bed and a 

 thickening of the boundary layer acts to amplify the waves, and (b) the 

 waves' interaction with the mean current profile leads to different and 

 nonuniform flow conditions. 



For calculations of finite-amplitude waves on a shearing current and 



useful review, see Dalrymple (1973). Subsequent related work is in 



Dalrymple (1974a, 1974b, 1977), Dalrymple and Cox (1976), and Brevik 

 (1979). 



There have been recent developments in the study of "wind drift" 

 currents which merit notice. Craik and Leibovich (see Craik, 1977) 

 explain how surface waves can interact with the shear due to wind drift 

 and hence cause an instability which leads to a helical type of motion 

 with its axis in the direction of the current and dominant wave 

 direction. Helical motions seen in the field are known as Langmuir 

 vortices. See also Craik (1982). In the development of their theory, 

 an equation known as the Craik-Le ibovich equation is derived. This 

 equation describes the effect of Stokes drift in stretching vortex 

 lines. The vorticity of the wind shear is directed perpendicular to the 

 Stokes drift, but any deviation from that direction gives a vorticity 

 component that can be enhanced by stretching. 



These results are important for understanding "detailed" currents in 

 the ocean. This is also an area where the theoretical technique of the 

 "generalized Lagrangian mean" developed by Andrews and Mclntyre (1978 a, 

 b) can usefully be employed (e.g., see Leibovich and Paolucci, 1981). 



Z5 



