Focused Waves on Depth-Varying Currents: The Role of Vorticity
- Magnus Beyer (Imperial College) | Chris Swan (Imperial College) | Marios Christou (Imperial College)
- Document ID
- International Society of Offshore and Polar Engineers
- The 27th International Ocean and Polar Engineering Conference, 25-30 June, San Francisco, California, USA
- Publication Date
- Document Type
- Conference Paper
- 2017. International Society of Offshore and Polar Engineers
- focused waves, depth-varying currents, wave-current interaction, Green-Naghdi theory, vorticity
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- 25 since 2007
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When waves interact with a depth-uniform current, it has been shown that the current velocity has a significant effect on the wave shape and the underlying velocity profile. If the current is sheared, for instance due to the wind acting on the water surface, the current velocity varies with depth and its shape will determine the vorticity profile. If this vorticity varies with depth, the wave will become rotational and, as a result, the classical wave theories become invalid. The present study has considered such cases, investigating the effects of both favourable and adverse depth-varying currents on the wave steepness, the wave crest height and the horizontal water particle velocity of a two-dimensional, broad- banded, nonlinear focused wave. The results are based upon a numerical, fully-nonlinear Green-Naghdi model. These novel results emphasise the importance of both the surface velocity and the surface vorticity for offshore engineering. The effect of the vorticity is to counteract the change due to surface velocity. This is particularly pronounced regarding the wave steepness and the horizontal water particle velocity.
Most of the research on wave-current interaction has considered regular waves. However, these are not representative of large waves in real sea states. Indeed, ocean waves are comprised of multiple components that differ in their phase, amplitude and direction of propagation. These waves are therefore irregular and directional. Research on the interaction of irregular waves and currents has been limited to uni-directional waves and depth-uniform or linearly-sheared currents implying that the wave motion is irrotational (Tsao, 1959). If arbitrarily sheared currents are present the flow possesses a nonuniform vorticity profile and thus becomes rotational. Because it is very difficult to account for rotationality in analytical or even numerical investigations, models in engineering design are usually limited to irrotational flows. However, sheared currents are very common in nature, as they typically arise in wind-driven sea states.
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