of open-work piers and steel platforms, offshore pile-supported plat- 

 forms, and steel risers for drilling rigs or oil production platforms. 



Hogben (Fig. 1, 1976) describes the force regime in which some off- 

 shore structures may be found for steep, deepwater waves. The larger 

 structures are in a wave diffraction regime in the absence of currents. 

 In the presence of currents, both incident and reflected waves are 

 refracted, and perhaps diffracted, by the current variations caused by 

 the structure. This is very much like the problem of a moving ship 

 meeting waves. For a proper analysis full account should be taken of 

 all solutions of the dispersion equation described in Section II, 2. 

 This has only recently been achieved to any extent in the ship 

 hydrodynamics field by Newman and Sclavounos (1980). However, in most 

 circumstances, solutions C and D of Figure 2 (the shortest wavelength 

 solutions) may be neglected. 



There are a number of approximations, many known to be inconsistent, 

 used in the field of naval architecture and ocean engineering which 

 might be adapted to coastal engineering problems. A measure of the 

 difficulty of dealing with the wave forces on a moving structure is 

 indicated by the number of papers on the forces due to waves on ships at 

 "zero forward speed." A review of this large and active field is not 

 considered appropriate, but much of the work can be found in the Journal 

 of Ship Research, Proceedings of Naval Hydrodynamics Symposia, and 

 Transactions of the Royal Institution of Naval Architects. 



For smaller cylindrical structures, class (b) , present engineering 



practice is to use Morison's formula for the force on each element of a 

 structure: 



f = J5pCqDu|u| + pCj^A (du/dt) (28) 



where 



f = force per unit length of cylinder 



D = mass density of water 

 Cq = drag coefficient 



D = cylinder diameter 



u = instantaneous velocity of the water in the absence of the 

 cylinder 

 Cjjj = inertia coefficient 



A = cross- sect ional area of the cylinder 



The first term in equation (28) is a drag force per unit length and the 

 second term is an inertial force due to the water's acceleration. More 



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