Wave-Current Loading on a Shallow Water Caisson
Authors: Kriebel D.L. , Berek E.P. , Chakrabarti S.K. , Waters J.K. 
Published: October 2008

Abstract
Results of laboratory model tests are used to assess the accuracy of the API RP2A method of predicting wave-current loading on a shallow water production caisson in extreme random waves. Model tests were conducted using a 1-to-20 scale model of a 36 inch diameter caisson in a 50 foot water depth. Tests were conducted in extreme (breaking) random waves both with and without in-line currents. Based on analysis of 138 extreme waves, it was found that predicted in-line fluid velocities were 6% larger than measured values on average, while predicted in-line wave forces and moments were 10% and 15% larger than measured values on average. Unfortunately, not all predictions were overly-conservative as several large breaking waves produced measured forces and moments 1.5 to 2.2 times larger than predicted. For these and other breaking waves, measured wave loads were strongly effected by dynamic amplification effects due to ringing of the structure following wave impact.

Introduction
The 20th edition of the American Petroleum Institute RP2A (Ref. 1) contains, for the first time, a recommended method for computing the kinematics and loading of waves propagating on a steady mean current. While numerous theories have been proposed for wave-current interaction, the API suggests use of the simple "superposition principle" in which wave and current kinematics are computed separately and then added together for use in the Morison equation. This is a simplification of the actual wave-current interaction and, as a result, it is of interest to examine the accuracy and potential bias of the method for extreme design conditions.
In the API procedure, as also outlined in Ref. 2, wave kinematics are computed in a coordinate system moving at the steady current speed using an apparent wave period that accounts for the Doppler shift in wave frequencies. Once the wave kinematics are determined, the combined wave-current velocities in the fixed reference frame are approximated by direct superposition of the wave kinematics onto the steady current. The combined wave-current fluid velocities are then used in the traditional Morison equation to estimate wave loading.
In the open literature, few comprehensive verifications of the API wave-current loading procedure have been published. In laboratory tests, Allender and Petrauskas3 found that maximum wave forces were over-estimated for conditions with no current and under-estimated for conditions with currents. In contras[, Heidemarr and Weaver4 compared measured and predicted wave forces on three instrumented ocean platforms and found little bias in the API procedure, although the ratio of measured to predicted forces varied between about 0.5 and 2,0.
While the API RP2A provides a recommended procedure for dealing with currents, it does not contain a recommended practice for predicting loads due to breaking waves. Several laboratory studies, e.g. Ref. 5, have suggested (hat wave forces of breaking waves are larger than those of no breaking waves of comparable height and period. In the offshore industry, however, it is usually assumed that the effects of breaking are adequately treated by computing wave kinematics with a highly nonlinear wave theory and by applying standard values of force coefficients.