details on present practice may be found In Hallam, Heaf, and Wootton 

 (1978). When the waves and currents have different directions, the 

 scalar coefficients in equation (28) may not be appropriate. 



Lacking experiments measuring forces in the presence of waves and 

 currents, it is of some value to note discussion of Morison's formula in 

 closely related flows. Shaw (1979) is a valuable collection of papers 

 on this topic, among which Pearcey (1979) gives a good survey of the 

 problems that arise in estimating forces on cylinders. The book by 

 Sarpkaya and Isaacson (1981) should also be consulted. 



For cylinders in waves, Morison's formula gives the right order of 

 magnitude for forces, but for detailed comparisons Cp and Cj^ must be 

 allowed to vary with the Keulegan-Carpenter number, the Reynolds number, 

 and the ratio of roughness to cylinder diameter. The Keulegan-Carpenter 

 number ("max^/'^ where u^^^^ is the amplitude of the oscillating velocity) 

 is a measure of the water particle displacement divided by cylinder 

 diameter. When this number is in the range 6 to 20, drag and inertia 

 terms are of approximately equal importance, increasing the uncertainty 

 in using Morison's equation (eq. 28). Sarpkaya's (1976) results are 

 often used, but papers in Shaw (1979) give results that differ by 10 to 

 20 percent. It is clear that more experiments over physically 

 representative ranges of parameters are needed. 



There is also a transverse oscillating force, not predicted by 

 Morison's formula. Usually this is not important on free-standing 

 members unless resonance is a possibility. For pipelines laid against 

 the bottom, one-sided transverse lift forces may be significant when 

 currents are added, but the requirement to design for drag and bottom 

 erosion usually insures stability against transverse forces in this 

 case. Other phenomena to be considered are the interaction between 

 eddies shed from different members of the structure, and the effects of 

 sidewalls on experiments. In wave-current experiments, eddies that 

 move perpendicular to the flow direction are confined by the channel 

 walls and may give misleading results when they interact with test 

 members. 



Cylinders oscillating in a current have been compared with 

 cylinders subject to combined wave and current motion. Such experiments 

 are described by Ottesen Hansen, Jacobsen, and Lundgren (1979), Verley 

 and Moe (1979), and Matten, et al. (1979). In particular, Matten, et 

 al. (1979) report very substantial changes in drag and lift coefficients 

 depending on whether or not their cylinder had end plates to inhibit 

 three-dimensional flow. Oscillating cylinders differ physically in some 

 ways from cylinders in waves, since the pressure fields are different 

 due to the different acceleration field relative to the cylinders (see 

 Batchelor, 1967, p. 409). These differences must be considered before 

 applying the results in engineering design. 



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