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arXiv 1006.4672physics.flu-dynnlin.PS
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调制不稳定性与毛细波turbulence

Modulation instability and capillary wave turbulence

H. Xia, M. Shats, H. Punzmann

摘要:

在实验室中研究了毛细波湍流的形成。频谱显示多个指数递减的谐波的参数激发波的非线性扩大与强迫的增加。光谱展宽导致光谱连续的发展,其尺度为$\propto f^{-2.8}$,与弱湍流理论(WTT)的预测一致。毛细管波的调制不稳定性被证明是负责从离散到宽带频谱的过渡。这种不稳定性导致谐波的频谱展宽,其相位的随机化,它将波场与壁隔离,最终允许从4波相互作用过渡到3波相互作用作为主导的非线性过程,从而创造了WTT中假设的先决条件。

英文摘要:

Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing. Spectral broadening leads to the development of the spectral continuum which scales as $\propto f^{-2.8}$, in agreement with the weak turbulence theory (WTT) prediction. Modulation instability of capillary waves is shown to be responsible for the transition from discrete to broadband spectrum. The instability leads to spectral broadening of the harmonics, randomization of their phases, it isolates the wave field from the wall, eventually allows the transition from 4- to 3-wave interactions as the dominant nonlinear process, thus creating the prerequisites assumed in WTT.

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