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Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains

1
School of Engineering, The University of Edinburgh, King’s Buildings, Edinburgh EH9 3DW, UK
2
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 105; https://doi.org/10.3390/fluids4020105
Received: 3 April 2019 / Revised: 24 May 2019 / Accepted: 30 May 2019 / Published: 4 June 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Abstract

The coupled nonlinear Schrödinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schrödinger wave equation, is characterized (to first order) by an exponential growth of sideband components and the formation of distinct wave pulses, often containing extreme waves. Linear stability analysis of the CNLSE shows the effect of crossing angle, θ , on MI, and reveals instabilities between 0 < θ < 35 , 46 < θ < 143 , and 145 < θ < 180 . Herein, the modulational stability of crossing wavetrains seeded with symmetrical sidebands is determined experimentally from tests in a circular wave basin. Experiments were carried out at 12 crossing angles between 0 θ 88 , and strong unidirectional sideband growth was observed. This growth reduced significantly at angles beyond θ 20 , reaching complete stability at θ = 30–40 . We find satisfactory agreement between numerical predictions (using a time-marching CNLSE solver) and experimental measurements for all crossing angles. View Full-Text
Keywords: surface waves; crossing seas; modulational/Benjamin-Feir instability; coupled nonlinear Schrödinger equation (CNLSE); experiments surface waves; crossing seas; modulational/Benjamin-Feir instability; coupled nonlinear Schrödinger equation (CNLSE); experiments
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MDPI and ACS Style

Steer, J.N.; McAllister, M.L.; Borthwick, A.G.L.; van den Bremer, T.S. Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains. Fluids 2019, 4, 105.

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