Water waves interacting with arbitrary shear currents in 3 dimensions

When both surface waves and currents are present at the same time near the water surface, the two cannot be considered individually, because waves and currents can strongly affect one another. This is a typical situation: for instance, the wind sets the sea surface in motion, and tides create strong currents near the coast. The interaction of waves and currents is a critical factor for the mixing of warmer and colder waters beneath the ocean surface, a crucial process in the climate's development. Technology in the maritime sector, whether concerning ships and vessels or other offshore installations, must invariably be designed to cope with forces from waves and currents. The project seeks to expand our understanding of how water waves are affected by a current which varies with depth; a shear current. Despite being an old problem, our understanding of waves with a shear current below them is limited and comes almost exclusively from simplified, two-dimensional models which can only describe waves moving exactly along the current or exactly counter to it. Of course, real situations are three-dimensional. Recently the project manager made progress on the real, 3D situation, and the project will build on that success. We propose to devise methods for studying waves in the presence of a shear current which can take any form, and the effect of these on ship economy and safety, and the transportation of water, nutrients and energy in coastal waters.

Potensielle virkninger er mange. Vi har vist teoretisk at drivstofforbruket til et skip under visse realistiske forhold (f.eks i elvedeltaer) kan avvike mye fra prediksjoner med standard teori. Teorien er testet i laboratoriet der effektene som er forutsett ble observert for første gang. Dermed har vi vist at skjærstrømning er viktig for bølgekrefter i kystsonen, som bør endre analyse og praksis i sektoren. De numeriske metodene som ble utviklet har bred anvendelse, og det forventes at metoder tas inn i operasjonelle hav- og bølgemodeller. Spesielt har prosjektet utviklet "Rolls Royce-en" innen numerisk beregning av bølgedispersjon på vilkårlige strømninger. Prosjektet har herigjennom bidratt til en ny og sterkt forbedret metode for å måle strømning under overflaten ved å se på bølgemønstre ovenfra. Måling av strømning med fly eller droner har store fordeler sammenlignet med dagens metoder, som er langsomme og måler et enkelt punkt der den nye metoden dekker et helt område.

Water waves and currents are primary factors in a vast array of applications in the maritime field, such as shipping, coastline management, aquaculture and offshore structures to name a few. Crucially, the interaction between waves and currents is important, and is believed to be a key reason for the development of dangerous rogue (or giant/freak) waves. Nevertheless, wave-current interactions remain relatively unexplored for currents with a velocity variation in the vertical direction (so-called shear currents), for which virtually all our knowledge is from two-dimensional models. The first progress for the 3D system of a vertically sheared current meeting a wave at an arbitrary angle (which is the realistic scenario) was made recently by the project manager (Ellingsen 2014a) when it was realised that a solution to the equations of motion exists for a wave of low steepness when the current varies linearly with depth. This new theory provides an opportunity for a theory which allows the understanding of waves on general shear currents actually encountered in applications, because it enables analytical treatment by approximating the actual current profile with a number of linear sections. Already for the simplest case, important 3D effects have been observed (Ellingsen 2014a), and at present no theory exists for the general 3D problem, making this research an important and somewhat pioneering enterprise. The project also seeks to extend the work to second order in wave steepness in order to study the onset of non-linearity, with application to rogue waves. Wave current interactions are seen as a key factor in the formation of highly destructive giant ocean waves (Kharif & Pelinovsky 2003), and identifying conditions of increased rogue wave probability is crucial safety concern, a problem which was recently demonstrated to be significantly affected by the shear of the velocity profile (Nwogu 2009).