Laboratory simulation and numerical modelling of the kinematics of oceanic internal waves

Abstract

Internal waves are known to occur in most ocean areas, especially the deep ocean where stable stratification is often found. While engineering operations have hitherto largely been confined to well-mixed shallow seas (such as the North Sea). new petroleum discoveries have prompted a move into areas (e.g. west of Shetland) where internal waves are more likely to be a problem. The implications of internal waves for safety in offshore operations have been raised by Osborne, Burch and Scarlett (1978) and by Bole, Ebbesmeyer and Romea (1994). The presence of internal waves in sea areas of current interest to the UK offshore industry has been confirmed by Sherwin (1991). While many aspects of internal wave behaviour have been extensively studied (e.g., Thorpe, 1975), very few measurements of detailed wave kinematics have been performed. Using an advanced flow measurement technique, this study provides measurements of internal wave kinematics in the laboratory and comparisons with non-linear wave theory.

The extensive literature on internal waves is reviewed from the viewpoint of offshore engineering. Then, extending the Stokes expansion presented by Thorpe (1968), a nonlinear model for internal waves in a continuously stratified fluid, suitable for numerical solution, is derived. The long wave theory of Benjamin (1966) is also discussed. The experimental facilities are described, and the velocity measurement technique (Particle' Image Velocimetry) is discussed in the context of stratified flow measurement. Errors in the measurements are discussed, and an upper bound of about 9% is found to apply to the bulk of the flow, with larger errors (up to 17%) in the interface. The results of the experiments are presented alongside comparisons with the numerical predictions. The im plications of the results for offshore engineering are discussed with special reference to loading effects.

It is concluded that second order Stokes theory is able to predict the velocities in large amplitude short internal waves within around 16% on an'rage, although in t he extremes the measured velocities can be up to 40% above predictions. The kinematics of large amplitude long waves are underpredicted by linear theory to a factor of up to :2 for the horizontal components. and 4 for the vertical components. These disparities warrant the liSP of more advanced nwthods of prediction in engineering applications.