Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum?
Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum?
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振动板的弱湍流：人们能听到柯尔莫哥洛夫频谱吗？
DOI：
10.1103/physrevlett.97.025503
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发表时间：
2006
影响因子：
8.6
通讯作者：
S. Rica
中科院分区：
文献类型：
--
作者：
G. Düring;C. Josserand;S. Rica
我们研究了弹性薄板在小变形极限下的波动的长期演化，使得振动模式之间的相互作用很弱。根据弱湍流理论（过去成功地应用于等离子体，光学和流体动力学波），这种非线性波系统在很长一段时间内演化，能量从一种模式缓慢转移到另一种模式。我们推导了一个动力学方程的光谱转移的二阶矩。我们表明，这样的理论描述的方法，平衡波频谱，也代表了能量级联，通常被称为Kolmogorov-Zakharov频谱。我们进行数值模拟，证实了这种情况。
We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence (successfully applied in the past to plasma, optics, and hydrodynamic waves), this nonlinear wave system evolves at long times with a slow transfer of energy from one mode to another. We derive a kinetic equation for the spectral transfer in terms of the second order moment. We show that such a theory describes the approach to an equilibrium wave spectrum and represents also an energy cascade, often called the Kolmogorov-Zakharov spectrum. We perform numerical simulations that confirm this scenario.