Discussion. Fluid forces on cylinders just below water level are 

 evaluated for the combined occurrence of random waves and current. The 

 waves are deepwater, zero mean, stationary random waves. The current is 

 steady and uniform in depth. Morison's formula is used to predict 

 forces . 



The emphasis is on fatigue failure, as measured by the probability 

 density function of the peaks of the forces induced in the structure. 

 The paper examines how this probability density function is affected by 

 currents and wave-current interactions. The approach is statistical, 

 with evaluation of specific cases clearly presented in plotted form. 



The analysis identifies a statistical quantity as a measure of the 

 potential fatigue damage. This quantity is a rate of change of the 

 expected value of the peak forces above a threshhold with respect to the 

 change in threshhold. 



The effect of assuming a Gaussian distribution of forces (rather 

 than a distribution of forces resulting from Gaussian waves) is 

 examined. From the examples shown, it is clear that the Gaussian force 

 assumption significantly underestimates the initial forces. The 

 examples also show that the wave-current interaction serves to reduce 

 critical forces when the current and waves move in the same direction, 

 and significantly affects the force in the wave trough when the current 

 is opposite the wave direction. 



Coastal Engineering Significance . The assumption of a Gaussian 

 distribution of forces is shown to underestimate the forces most 

 critical in inducing fatigue failure. The presence of wave-current 

 interactions significantly changes the critical forces, usually reducing 

 them. 



57. UNNA, P.J.H., "Waves and Tidal Streams," Nature, London, England, 

 Vol. 149, No. 3773, Feb. 1942, pp. 219-220. 



Keywords . Currents, Tidal; Historical Interest; Phase Velocity. 



Discussion . This is the first paper to consider the change of phase 

 velocity (and hence of frequency) as waves propagate over varying cur- 

 rents. It follows an earlier brief note (Unna, 1941) in which the 

 author considered the contraction and expansion of the water as a cause 

 of the steepening of short waves at the crest of long waves. 



The change in linear phase velocity for currents parallel to the 

 direction of wave propagation is given correctly. 



The implications for waves entering an estuary are discussed, and 

 it is indicated that there is likely to be a bunching of wave energy at 

 the end of the flood which agrees with experiences recorded by Bristol 

 Channel pilots. 



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