ORCID
- Borthwick, Alistair: 0000-0001-6053-7764
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.
DOI
10.3390/fluids4020105
Publication Date
2019-06-04
Publication Title
Fluids
Volume
4
Issue
2
Organisational Unit
School of Engineering, Computing and Mathematics
First Page
105
Last Page
105
Recommended Citation
Steer, J. N., McAllister, M., Borthwick, A., & van, d. (2019) 'Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains', Fluids, 4(2), pp. 105-105. Available at: https://doi.org/10.3390/fluids4020105
