finite-difference numerical model. In the model, dissipation terms are 

 included to account for bed friction and breaking. The most important 

 input data in the program are the distribution of depth and currents, 

 the period, direction and amplitude of the incident wave, the boundary 

 conditions along the sides, and data concerning dissipation. Output 

 data are wave amplitudes and directions. The computer program is 

 applied to the entrance of the Oosterschelde estuary in the southwest of 

 the Netherlands, where extensive coastal defense works are undertaken. 

 The graphs indicate that the current (typical value, 0.7 meter per 

 second) does not have a spectacular influence here. 



The author also presents solutions to the mild-slope current-wave 

 equation itself for some cases where the wave field is independent of 

 one of the horizontal coordinates. These include waves crossing an 

 undersea slope or gully, propagation along the axis of a channel bounded 

 by vertical sidewalls, and propagation along an undersea gully. The 

 agreement with measurements for the latter case is not very close. 



The main results of the report are the hyperbolic-type current-wave 

 equation (3.21), the elliptic version (3.23), and the parabolic 

 approximation (6.19) which is the basis for the numerical model. The 

 following misprints in the first two of these important equations are 

 noted: in (3.21) the sign of the term V*(aV(j)) should be minus instead 

 of plus, and in (3.23) the last term should read (Oq - Wo - k^a)$. 



Coastal Engineering Significance. The report is important both for 

 fundamental understanding and practical application. It presents the 

 first published water wave equation taking both depth and current 

 variation into account. Based upon a parabolic approximation of this 

 wave equation, a computer program is developed which allows for refrac- 

 tion-diffraction and dissipation. 



5. BRETHERTON, F.P., and GARRETT, C.J.R., "Wavetrains in Inhomogeneous 

 Moving Media," Proceedings of the Royal Society, London, England, 

 Series A, Vol. 302, No. 1471, Jan. 1968, pp. 529-554. 



Keywords. Currents, Large-Scale; Theory; Wave Action; Waves. 



Discussion. The problem of waves propagating in inhomogeneous moving 

 media is discussed. The waves are restricted to small amplitude and the 

 medium is nondissipat ive and varies only over length or time scales 

 which are much greater than the wavelength or period. Otherwise, con- 

 siderable generality is achieved. 



The discussion centers around the considerable care required to 



define energy for linearized (as distinct from linear) systems. A 



medium at rest and in equilibrium is considered first and then results 

 for a moving medium are derived. 



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