Nonlinear internal waves and induced currents in a two-layer fluid

Across the world’s oceans, variations in sea water temperature and salinity stratify the water column. In many locations an interfacial layer, known as the pycnocline, forms where temperature and density vary strongly with depth. The pycnocline supports internal waves which propagate horizontally and play a deciding role in processes such as climate change and nutrient cycles. Internal solitary waves are a particular form of internal waves that are localised and can travel large distances without significant change of form or magnitude. While continuously stratified flows have infinitely many modes, most observations are of the first baroclinic mode, which displace isopycnals in one direction only and can either be waves of elevation, or depression. In this work, we study the simplest physical system supporting these waves: a two-layer fluid confined between two solid walls. Various mathematical models, ranging from the weakly nonlinear to the strongly nonlinear regime, are examined in detail. A comparative study of their solitary-wave solutions and main characteristics is performed. We then explore ways weakly nonlinear models can be improved to better approximate the solutions within the strongly nonlinear regime, well described by the socalled Miyata-Choi-Camassa (MCC) model. Large amplitude internal waves are known to exert substantial loads on deep-water structures. We use the different models to predict the wave-induced currents in water column. Once the velocity field in the water column is known, the Morison’s formula is then applied to find the horizontal force exerted on thin cylinder piles. We have identified a spurious flow reversal predicted by some weakly nonlinear models, when relatively large amplitude waves are considered. In addition, our numerical results show that the internal wave force is considerably underestimated if the traditional KdV theory is used. Therefore, a better understanding of the effects caused by large amplitude internal solitary waves is needed for the design of future deepwater offshore production facilities.