Discussion. Measured swell at Perranporth, Cornwall, has a regular 

 fluctuation in wave period of about 10 percent. It is suggested that 

 this is due to interaction with the tidal streams as the waves traverse 

 the Continental Shelf. 



A theory describing the propagation of waves on a time-varying 

 current is derived which provides an expression for the time variation 

 of the period. 



A theoretical expression is evaluated for swell traveling from the 

 South Atlantic by determining its refraction over the Continental Shelf, 

 including the effects of hourly changes in the tidal currents and depth 

 encountered by the waves. The results do not agree in detail with all 

 the observations but are of the right order of magnitude. 



Coastal Engineering Significance. This paper is one of few papers which 

 consider waves on real unsteady currents. For this reason, it is of 

 present technical importance despite its relatively early publication 

 date. The phenomenon observed at Perranporth is potentially present at 

 the mouth of many large estuaries such as at San Francisco near the 

 Golden Gate. 



3. BIESEL, F., "Etude theorique de la houle en eau courante" 

 (Theoretical Study of Waves on Running Wat3r), La Houille Blanche, 

 Grenoble, France, Vol. 5, No. Special A, May 1950, pp. 279-285. 



Keywords. Critical Current Velocity; Currents, Unidirectional; 

 Currents, Vertical Shear; Dispersion Relation; Historical Interest; 

 Theory; Waves, Stationary. 



Discussion. This is an early systematic study of the effect of vertical 

 shear in a current on wave motion. It is a theoretical paper which 

 considers small-amplitude waves propagating with or against the current, 

 but it presents mathematical results in relevant physical contexts. In 

 particular, three conditions of practical importance are emphasized: 

 waves propagating up an estuary, wind waves on canals, and stationary 

 waves . 



The analysis considers those waves which can be made to appear 

 stationary by a suitable choice of reference frame. The problem is 

 formulated in terms of a stream function and an arbitrary current pro- 

 file. It reduces to an ordinary differential equation when sinusoidal 

 waves are assumed, although the wave phase velocity is an unknown in the 

 coefficients of the equation. Analytical solutions are found when a 

 simple linear velocity profile is inserted. 



The author goes further than Thompson (1949), who had obtained a 

 dispersion relation, by indicating how to find wavelength, wave phase 

 speed, or both, when the current, depth, and one wave property 



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