Wave Forces: Data Analysis and Engineering Calculation Methods
Authors: Aagaard P.M. , Dean R.G. 
Published: October 2008

ABSTRACT
This paper presents a methods calculating ocean wave forces on offshore drilling structures. The methods is based upon data from two full-scale wave force measurement installations in the oceans and a mathematic model representing hydrodynamic forces on submerged bodies in unsteady flow (Morison, et al., 1950) and the kinematic flow field of highly non-linear waves (Dean,1950). The method is considered applicable to a broad range of wave conditions commonly encountered in offshore structure design. Several comparisons show that the method represents measured forces satisfactorily for engineering design.

INTRODUCTION
An extensive body of knowledge is developing in the area of ocean wave forces on cylinders excellent summaries appear in References 1 and 2; important contributions of mathematical models used in wave force calculations are described in References 3, 4 and 5; and wave force measurement installations are described in Reference 6 and 7. Form theoretical and experimental work has come a variety of wave force calculation methods for use in engineering; one such example is presented in Reference 8. Most published methods are based on the analysis of relatively few waves of low to moderate height and mathematical models that involve major simplifications in the representation of real ocean waves. There was a need, therefore, to improve the mathematical model and to use information from larger waves.
Forces from large waves were measured in the Gulf of Mexico, and a mathematical model developed by Dean (9) was shown to be a substantial improvement over other available models. Using the Dean model and data from large amplitude measured waves, the method reported here was developed in the Standard Oil Company of California for use in design of offshore structures. The presentation follows the four steps used in development:Selection of a mathematical model.Analysis of measured wave forces to develop required empirical coefficients.Implementation of a method for wave force calculation.Evaluation of the method against measured data.

SELECTION OF A MATHEMATICAL MODEL
The mathematical model used in the wave force calculation method was picked to be compatible with currently used platform design criteria and structure design procedures. The model described herein is compatible with specification of design wave conditions in term of a single wave; the calculated forces are used in a space-frame loading program to calculated the loads on a complete structure (10).
This deterministic, single-wave approach would appear to be in conflict with the observation that the sea is nondeterministic and can only be described statistically; however, the deterministic approach was chosen because:Natural periods of structures considered when the method was developed were much shorter than the period range of significant wave; hence, wave loads could be treated ad static loads.Nonlinear wave theories could be used for calculating the single wave, whereas time series representations used in the statistical models were not developed to the point where nonlinear wae characteristics could be modeled.Use of a single wave was consistent with established Company procedures for design wave selection and structure loading.