Methods for Calculating Forces Produced by Irregular Waves
Authors: Wheeler J.D. 
Published: October 2008

Abstract
This paper describes and evaluates a new methods for calculating wave forces on offshore structure. The methods is based on an extension of Airy theory for two-dimensional waves and uses a linear filtering technique to calculate wave forces as a function of time for wave profiles of arbitrary shape and length. Thus, it is especially suited to evaluating the forces exerted on offshore structure by a sequence of irregular storm waves. The accuracy of the method is checked by comparison with measured hurricane-wave forces.

I Introduction
Interest in wave-force predictions has been increasing in recent years with the increasing worldwide investment in offshore operations and the movement into deeper water. The larger structure requires in deeper water increase the need for rapid and accurate wave-force predictions.
This paper presents a method for computing forces from an ocean-wave profiles by a linear filtering technique and compares those forces with measurement. The linear filter employed is developed from a modification of small-amplitude wave theory suggested by wave-tank studies and used to calculate water velocities and accelerations. The linear filtering method permits use of a wave train of any length and ant degree of irregularity in design and dynamic studies of offshore structure. Further, the change of the wave profile shape with time (dispersion) can be allowed for.
Introduction of velocities and acceleration calculated with the linear filter into an equation proposed by Morisson et al.6 permits calculation of wave forces. Forde coefficients required in Morrison's equation were determined by fitting calculated forces to observed hurricane wave force measurements. Consequently, the force coefficients should be used only with the calculation procedures presented in this paper; further, their application has been limited to calculation of forces on members similar in size and surface properties to the test member used to obtain the measured forces.
The force predictions are compared with force measurements made in about 400 waves at various heights along a 44-inch diameter piling in 99 feet of water during Hurricane Carla in 1961. The procedures gives acceptable prediction of maximum forces at all height above bottom. Force profiles in the four largest measured waves are reproduces with reasonable fidelity, and the peak forces in these largest waves are closely reproduced.
Additional force measurements made in shallow water (34 feet) are not referred to in this paper. The wave theory used is less applicable in shallow water, leading to fitting result having considerable scatter.
The force measurement indicate that wave forces fall off sharply near the water surface. Reproduction of the actual flow regime near the wave surface requires further modification of any wave theory. This additional modification is not discussed in this paper.

II. Procedure Used to Predict Wave Forces.

A. Force Equation
The horizontal force per foot of vertical pilling length is calculated as a function of time (t) and height (z) above the ocean bottom as:(Mathematical Equation)(Available in full paper)
Eq. (1), proposed by Morrison et al.6, represents the total force as a sum of drag and inertial forces.