Analysis of Wave Force Data
Authors: Evans D.J. 
Published: December 2007

Wave profile and wave force data acquired in the Gulf of Mexico from several hurricanes have been analyzed to provide the drag and inertial coefficients of Morison's wave force equation. These coefficients are required to help determine design loads for offshore structures.

Introduction
The design of a structure for the marine environment is primarily dependent on the prediction of the forces generated by waves in most coastal areas. Morison et al. related these forces to the kinematic wave properties, the water particle velocity and acceleration. properties, the water particle velocity and acceleration. The equation is composed of two parts - a drag term and an inertial term - that are related to the total force by means of the drag and inertial force coefficient, C(D) and C(M), respectively. Two primary limitations associated with the Morison equation are:the poorly defined values of these hydrodynamic force poorly defined values of these hydrodynamic force coefficients for large waves andthe dependency on wave theory or theories to describe the kinematic water particle velocity and local acceleration.
A secondary consideration is the change of these wave force coefficients with changes of the kinematic flow field and changes of the pile dimensions. The drag coefficient has been shown to be a function of the Reynolds number for steady fluid flow. However, correlation of C(D) with the Reynolds number in an oscillating flow has been generally inconclusive. These problems clearly show the need for prototype field measurements of these wave properties in the high Reynolds number range. The necessity for wave profile and wave force dam for large waves to establish the desired correlation resulted, in 1954, in the instrumentation of an offshore oil platform in 30 ft of water. Wave and force data were obtained for 4 years during Wave Force Project I (1954 to 1958). Then in 1960, newer Project I (1954 to 1958). Then in 1960, newer instruments were located in 100 ft of water where additional data were obtained for 3 more years during Wave Force Project II (1960 to 1963). These projects were supported by the California Research Co., Shell Oil Co., and Humble Oil and Refining Co. Pure Oil Co. and the U. S. Navy entered the program at a later date. A complete description of the installation appears in Ref. 3. The theoretical determination of the wave particle velocity and acceleration and the fitting of the measured data by means of the correlation coefficients (C(D) and C(M)) in Morison's equation was done independently by the participants. Shell has analyzed the measured wave force data differently for each of the two wave force projects. The same wave theories were used to determine the velocity and acceleration terms from the measured wave profile data; however, the force coefficients were analyzed by different techniques, as described in the section Wave Force Coefficient Analysis. With these calibrated coefficients, Morison's equation was used to predict the individual wave forces from various large hurricane waves. The relative agreement of the predicted and observed forces is used as a measure of the degree of correctness of the Morison equation and as a measure of the confidence for the prediction of wave forces on a structure.
JPT
P. 347