This paper describes a model for calculating water velocities and accelerations near the free surface in random directional waves. This empirical model is useful because significant errors in predicted kinematics are reduced. "Stretching" and "extrapolation" provide a lower and upper bound respectively for water velocities. The "delta-stretching" model, presented here, interpolates between these two methods and reduces the error. The model is simple to program, but does contain some of the nonlinearity of "stretching" and so requires the simulation of a velocity profile. It is, however, found to be practical for use in reasonably long time domain simulations of forces on template platforms. The model is compared to data obtained during the Fulmar Wave Crest Kinematics Experiment (FULWACK), data from the Ocean Test Structure (OTS), data from the COGNAC measurement program, data obtained by the MaTS research project, and analysis using a numerical model (KBCF). Conditioned simulations are used to calculate the model kinematics in order to eliminate some of the random variability. A short description of the conditioning method is given.


Computation of forces on offshore platforms made of slender members consists of two nearly distinct parts. The first part is the determination of water kinematics and dynamics. This describes the motion of the water due to waves and currents and the pressure gradients in the water. The second part is the determination of the forces on the platform assuming known water motions. These two aspects of the problem are separable because it is assumed that the presence of the platform has a negligible effect on the water motions. This is generally valid when the diameter of the cylinder is less than 1/8 the wave length of interest and the cylinders are widely spaced. The random directional wave (RDW) theory is desirable because it is a realistic representation of the ocean surface during a storm. This is in contrast with the regular unidirectional wave theories traditionally used for platform design. RDW is superior to regular wave models in predicting water velocities below the mean water line during storms (1, 2). And it can be modified to predict water velocities above the mean water line. The dynamic analysis of a platform necessitates the use of random waves or at least a recognition of the randomness and frequency variation of the environment. Both the increased accuracy and the need for random analysis justify the development of the RDW force model. The RDW theory is used for wave hindcasting(l) because it has been found to best describe the propagation of wave energy on the surface of the oceans. It has also been found to predict wave induced water velocities below the mean water line with reasonable accuracy (l). We show here that the theory can be modified to predict crest velocities quite well. Modified random directional wave theory is the best method to compute water motions near platforms and thence forces on platforms.

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