Coastal Engineering Significance . Although much of the presentation of 

 the book is in terms of sound waves and internal waves, it is at present 

 the best approach to understanding the interaction of water waves with 

 large-scale currents. 



35. LONGUET-HIGGINS, M.S., and STEWART, R.W., "Changes in the Form of 

 Short Gravity Waves on Long Waves and Tidal Currents," Journal of 

 Fluid Mechanics, Cambridge, England, Vol. 8, No. 4, Aug. 1960, pp. 

 565-583. 



Keywords. Currents, Tidal; Currents, Unidirectional; Dispersion Rela- 

 tion; Equations of Motion; Interactions, Short Wave-Long Wave; Interac- 

 tions, Wave-Wave; Radiation Stress; Theory; Wave Energy; Waves, Deep- 

 water. 



Discussion. This is the first paper that deals correctly with the 

 interaction between water waves and currents. (The corresponding 

 problem for sound waves was correctly treated by Blokhintzev, 1946.) 



The problem of interaction between two wave trains is treated as a 

 perturbation problem; that is, the interaction is assumed to be quad- 

 ratic in wave amplitudes. Examples considered include tidal streams and 

 standing waves. 



There is a detailed physical discussion of the results with 

 particular emphasis on the energy of the short wave motion and its 

 transfer. In particular, the term "radiation stress" is introduced for 

 the Reynolds stress of the wave motion. This leads to an equation for 

 the energy of the short-wave motion explicitly including the loss, or 

 gain, of energy transferred to or from the long-wave motion. 



Although most of the paper is in terms of wave-wave interaction, 

 the important section on radiation stress is written from the viewpoint 

 of waves on a steady current. 



Coastal Engineering Significance. The existence of energy transfer 

 between water waves and current, or longer waves, is recognized for the 

 first time in this paper. It means that it is possible for the 

 amplitudes of waves on currents to be deduced correctly. Earlier work 

 by UNNA (1942) and JOHNSON (1947) had failed to calculate amplitudes 

 correctly, though the general trend of their results is correct. 



The interaction between short waves and tides described in this 

 paper is a valuable theoretical account of a commonly observed variation 

 of wave energy which needs to be allowed for both in interpretation of 

 observations and in design. 



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