Analysis of Wave Force Data
Authors: Evans D.J. 
Published: October 2008

ABSTRACT
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 on offshore structures. An analysis of profile and force data from waves in shallow water gave drag and inertial coefficient modal values of 0.5 and 1.2 respectively, using nonlinear wave theories. Data acquired in 100 feet of water gave slightly larger drag coefficient (0.58) and a considerably larger inertial coefficient (1.76).

INTRODUCTION
The design of a structure in the marine environment is primarily dependent on the prediction of the forces generated by waves in most coastal areas. Morison et al. (1950) related these forces to the kinematic waves properties, the water particle velocity and acceleration. The equation is composed of two parts; a drag term and an inertial term which are related to the total force by means of the drag and inertial force coefficient, Co and CM, respectively. Two primary limitations associated with the Morison equation are:the numerous values of these hydrodynamic force coefficients for large waves andthe dependency on the wave theory of theories to describe the kinematic water particle velocity and 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 (Schlichting, 1955). However, correlation of CD 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 data for large waves to establish the desired correlation resulted in the instrumentation of an offshore oil platform in 30 feet of water in 1954. Wave and force data were obtained for four years during Wave Force Project I (1954 – 1958). Newer instruments were then located in 1960 in 100 feet of water where additional data were obtained for three more years during Wave Force Project II (1960–1963). During the first project, wave profile and force data were recorded from hurricanes Flossy(1956), Audrey(1957), and Ella(1958) and tropical storms Bertha (1957) and Esther(1957). During the second project, waves were records from hurricanes Donna (1960), Ethel (1960), Carla(1961) and waves in excess of 15 feet at the installation site. These projects were supported by the California Research Company, Shell Oil Company and Humble Oil and Refining Company, Pure Oil Company and U.S. Navy entered the program at a later date.
The theoretical determination of the wave particle velocity and acceleration and the fitting of the measured data by means of the correlation coefficients (CD and CM) 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.