response of the mean level to wave groups can be much larger, but it is 

 pointed out that it is a resonant response which would need time to 

 build up. The effects of wave dissipation and breaking are shown to 

 lead to "setup." 



These ideas are compared with observations of reflected long waves 

 from swell (Tucker, 1950). They give the sign of elevation in the long 

 waves (depression rather than elevation) but the variation with incident 

 wave amplitude is unconvincing. 



Coastal Engineering Significance. This paper presents the first 

 theoretical analysis and identification of wave setup and setdown. It 

 is of great significance in providing the theoretical basis for the 

 study of wave-induced currents and is still an appropriate starting 

 point for their study. 



38. LONGUET-HIGGINS, M.S., and STEWART, R.W., "Radiation Stresses in 

 Water Waves; a Physical Discussion, with Applications," Deep-Sea 

 Research, Oxford, England, Vol. 11, No. 4, Aug. 1964, pp. 529-562. 



Keywords. Averaged Equations; Current Refraction; Currents, Large- 

 Scale; Currents, Opposing; Currents, Shearing; Group Velocity; Inter- 

 actions, Wave-Wave; Radiation Stress; Setdown; Setup; Surf Beat; Theory; 

 Wave Groups. 



Discussion . The results of LONGUET-HIGGINS and STEWART (1960, 1961, 

 1962) are brought together in this paper, which omits many of their 

 mathematical details and yet presents a plausible physical argument. 



The initial section gives a very detailed account of all three 

 components of radiation stress 8^^^^, s^^^ , s for a sinusoidal traveling 

 gravity wave. Standing waves and capillary-gravity waves are then 

 considered in slightly less detail. 



Applications that are described are (a) wave setup on a beach, 

 which includes some observational data, (b) the setdown under groups of 

 waves in deep water, (c) wave groups in shallow water and their rele- 

 vance to "surf beat," (d) the interaction of waves and steady currents 

 including irrotational plane strains, laterally converging currents and 

 shear flows, (e) nonlinear interactions between waves of disparate 

 lengths, and (f) the damping of gravity waves by capillary waves. 



Coastal Engineering Significance. This paper is intended for non- 

 theoreticians interested in the physical applications of the results 

 described in more detail in earlier papers (LONGUET-HIGGINS and 

 STEWART, 1960, 1961, 1962). Coastal engineers may prefer to have that 

 detail; however, this paper does present some further extension of their 

 work. It was of great value in extending knowledge of their basic 

 advances . 



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