Wave Force Calculations for Stokes and Non-Stokes Waves
Authors: Lambrakos K.F. , Brannon H.R. 
Published: October 2008

ABSTRACT
A new wave particle velocity procedure permits calculation of forces from regular wave profiles of more or less arbitrary wave crest to height ratios, as well as from irregular profiles of more than one wave. The procedure uses a double Fourier series expansion for which the expansion coefficients for a given wave problem are calculated with a least-squares minimization technique. The new method has potential, because of its flexibility in the type of waves it can treat, for improving correlations of calculated and measured wave forces. Results are given of applications of the new procedure to studies of simplifications made in force calculations commonly used by industry. Studies were made of the validity in using Stokes I and other regular wave profiles to calculate forces for waves that are part of long wave records. Effects of changes in the wave height or wave crest elevation on forces are presented. Also given are results relating to the effects adjacent waves have on the force exerted by a wave of interest. Finally, a high-accuracy solution of the Stokes problem with this procedure is demonstrated.

INTRODUCTION
Offshore platform design procedures require the calculation of design wave forces from water particle velocities and accelerations, and suitable force constants l (drag and inertial coefficients). The velocities and accelerations for static platform design are calculated from single large waves (design waves) with a wave particle velocity "theory". Consequently, it is important for platform design that the velocity theory account for the essential properties of large storm waves.
The velocity procedure presented here calculates water particle velocities and accelerations for a variety of wave profiles that may alter shape with propagation. It can treat regular wave profiles (every wave in the profile is identical) and irregular wave profiles (every other wave in the profile is identical). Various wave height, wave crest, and wave period combinations are permissible. Included in the regular profiles are Stokes' waves with unique, regular wave shapes that do not change with propagation. The procedure has mathematical rigor and is not restricted to small waves.
Unique to the calculation presented here, and in contrast to other published calculations, is the ability to handle more or- less arbitrary wave crest-to-height ratios while maintaining quite accurate solutions to the governing physical equations. This capability extends to regular waves and to irregular waves as defined above. This calculation also permits evaluation of the effects of some wave shape characteristics not accurately described by published theories on wave force calculations. The nil abilities may also permit better correlation of calculated and measured wave forces--a possible application not demonstrated here.
Capability for handling complicated waves accurately grows out of the use of a double Fourier series for the velocity potential (extended velocity potential-EXVP). This series gives the flexibility required for satisfying with good accuracy all of the hydrodynamic equations for quite complex waves. Practical computing requirements restrict applications to the cases described above.