Experimental investigation on the evolution of the modulation instability with dissipation
Experimental investigation on the evolution of the modulation instability with dissipation
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DOI：
10.1017/jfm.2012.372
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发表时间：
2012-09
影响因子：
3.7
通讯作者：
Yuxiang Ma;G. Dong;M. Perlin;Xiaozhou Ma;G. Wang
中科院分区：
文献类型：
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作者：
Yuxiang Ma;G. Dong;M. Perlin;Xiaozhou Ma;G. Wang
本文报道了耗散对本杰明-费尔不稳定性演化影响的实验研究。在长波水槽中物理地产生了一系列具有附加边带的波列，以及不同的初始陡度、扰动幅度和频率。实验结果直接证实了Segur等人的镇定理论。(《流体力学》，第539卷，2005年，第229-271页)，即耗散可以稳定本杰明-费尔不稳定性。此外，实验还表明，耗散对调制不稳定性的影响强烈依赖于微扰频率。结果表明，对于扰动频率较高的波，耗散对边带增长率的影响比对较低扰动频率的影响更为明显。此外，基于包含线性阻尼项的Dysthe方程的数值模拟可以很好地预测实验结果，如果波列的动量积分在演化过程中是守恒的。
Abstract An experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin–Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229–271), i.e. dissipation can stabilize the Benjamin–Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe’s equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.