diffraction, subject to the assumption that there are no large changes 

 in wave direction. Dissipation terms are included to account for bottom 

 friction and breaking. The program has been applied to the entrance of 

 an estuary in the Netherlands, and is said to be capable of covering 

 areas a few hundred wavelengths across. Required input includes bathym- 

 etry and currents; height, period, and direction of incident wave; data 

 concerning dissipation; and certain boundary conditions and computa- 

 tional options. The output includes wave height, phase, and direction. 



The Danish Hydraulic Institute's "short wave" program is a second 

 possibility, but there is still no experience regarding its use in wave 

 current situations. This program uses the long wave Boussinesq equa- 

 tions to describe the water motion. These equations include the non- 

 linear shallow-water terms, plus dispersive terms which permit descrip- 

 tion of somewhat shorter waves than simple long wave equations. These 

 equations could be used for harbor studies with partial reflection at 

 boundaries. Terms partially accounting for bottom friction and breaking 

 can be included. Although wave and current motions are not separated in 

 the computation, it would be relatively straightforward to separate them 

 in solutions so that pictures of mean current and wave height could be 

 extracted. If a sea surface with dimensions greater than a few tens of 

 wavelengths is to be studied, considerable computer resources would be 

 required with present-day technique. 



At the time of writing, computational and theoretical developments 

 in wave refraction mean that the state-of-the-art is changing rapidly. 

 The engineer seeking to calculate wave-current refraction may choose 

 between a ray theory approach, using a parabolic equation, or more 

 direct solution of the equations. Ray theory is well established for 

 depth refraction, but inclusion of currents is not a simple modification 

 to most existing programs (e.g., see Skovgaard and Jonsson, 1976; Chris- 

 toffersen and Jonsson, 1980; Christof fersen, 1982). Parabolic methods 

 can be useful in just those cases where ray theory is poor: sparse 

 coverage by rays, multiple crossing of adjacent rays. However, apart 

 from the Dutch work mentioned above, there is no experience in the use 

 of parabolic equations for water-wave refraction. The pace of develop- 

 ment is such that an individual wishing to compute wave-current refrac- 

 tion should make an effort to find up-to-date information. 



2. Forces on Structures in Waves and Currents . 



Structures can be divided into two classes based on relative size: 



(a) those that are larger than about one-fifth of the wavelength and 



(b) those that are smaller than one-fifth of the wavelength. The factor 

 one-fifth is a frequently adopted value, e.g., Hogben (1976). Examples 

 of the larger class (a) include: submerged oil storage and ballast 

 tanks, semisubmersibles, large drill ships, and large offshore break- 

 waters. Examples of the smaller class (b) include: structural members 



58 



