Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains

被引：9

作者：

Steer, James N. ^{[1
]}

McAllister, Mark L. ^{[2
]}

Borthwick, Alistair G. L. ^{[1
]}

van den Bremer, Ton S. ^{[2
]}

机构：

[1] Univ Edinburgh, Sch Engn, Kings Bldg, Edinburgh EH9 3DW, Midlothian, Scotland

[2] Univ Oxford, Dept Engn Sci, Parks Rd, Oxford OX1 3PJ, England

来源：

FLUIDS | 2019年 / 4卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

surface waves; crossing seas; modulational; Benjamin-Feir instability; coupled nonlinear Schrodinger equation (CNLSE); experiments; DEEP-WATER; ROGUE WAVES; EVOLUTION; SPECTRUM; MECHANISMS; EQUATIONS; SEA;

D O I：

10.3390/fluids4020105

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The coupled nonlinear Schrodinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schrodinger 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, theta, on MI, and reveals instabilities between 0 degrees< theta < 35 degrees, 46 degrees< theta < 143 degrees, and 145 degrees< theta < 180 degrees. 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 degrees <= theta <= 88 degrees, and strong unidirectional sideband growth was observed. This growth reduced significantly at angles beyond theta approximate to 20 degrees, reaching complete stability at theta = 30-40 degrees. We find satisfactory agreement between numerical predictions (using a time-marching CNLSE solver) and experimental measurements for all crossing angles.

引用

页数：15

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