Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents
Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents
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恒涡流表面重力波色散与调制不稳定性实验研究
DOI：
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发表时间：
2019
影响因子：
3.7
通讯作者：
T. V. D. Bremer
中科院分区：
文献类型：
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作者：
James N. Steer;A. Borthwick;D. Stagonas;E. Buldakov;T. V. D. Bremer
本文通过实验研究了弱非线性波在相对的线性垂直剪切电流剖面上的色散和稳定性。测量结果与Thomas等人推导的单向$(1 ext{D}+1)$定涡度非线性Schrödinger方程（vor-NLSE）的预测结果进行了比较。液体，第24卷，no。[j] .农业科学学报，2012,32(7)。当实验室参考系中电流的大小为负（即与波的传播方向相反）并且随着深度而减小时，剪切率在相反的电流中为负，这在自然界中是最常见的。与具有相同表面速度的均匀电流相比，负切变具有增加波长和增强稳定性的作用。在规则低陡度波的实验中，研究了剪切率为$0$到$-0.87~ ext{s}^{-1}$的5个反向电流剖面上波长与频率的色散关系。对于所有的电流剖面，线性恒定涡度色散关系预测的波数在与切变速率和表面流速估计相关的95%置信区间内。剪切对调制不稳定性的影响是通过在剪切率在$0$和$-0.48~ ext{s}^{-1}$之间的反向电流剖面上播种带有谱边带的载波的频谱演变来确定的。在重复实验中，我们一致发现vo -NLSE的数值解可以在两个标准差范围内预测边带的增长，比其均匀电流NLSE对应的结果要好得多。同样地，实验波包络的放大也可以用vor-NLSE的数值解很好地预测，而均匀电流NLSE的数值解则明显高估。
This paper examines experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional $(1 ext{D}+1)$ constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from $0$ to $-0.87~ ext{s}^{-1}$. For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the $95,\%$ confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between $0$ and $-0.48~ ext{s}^{-1}$. Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE.