Affiliation:
1. Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
Abstract
The evolution of steep waves in the open ocean is nonlinear. In narrow-banded but directionally spread seas, this nonlinearity does not produce significant extra elevation but does lead to a large change in the shape of the wave group, causing, relative to linear evolution, contraction in the mean wave direction and lateral expansion. We use the nonlinear Schrödinger equation (NLSE) to derive an approximate analytical relationship for these changes in group shape. This shows excellent agreement with the numerical results both for the NLSE and for the full water wave equations. We also consider the application of scaling laws from the NLSE in terms of wave steepness and bandwidth to solutions of the full water wave equations. We investigate these numerically. While some aspects of water wave evolution do not scale, the major changes that a wave group undergoes as it evolves scale very well.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference42 articles.
1. Adcock T. A. A.. 2009 Aspects of wave dynamics and statistics on the open ocean. DPhil thesis UK:University of Oxford.
2. Estimating ocean wave directional spreading from an Eulerian surface elevation time history
3. Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model
4. Energy input amplifies the non-linear dynamics of deep water wave groups;Adcock T. A. A.;Int. J. Offshore Polar Eng.,2011
5. The focusing of uni-directional Gaussian wave-groups in finite depth: an approximate NLSE based approach;Adcock T. A. A.;In Proc. 29th Int. Conf. Ocean, Offshore and Arctic Engineering (OMAE), Shanghai, China, 6–11 June 2010,2010
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