窄频带激励下弱非线性波系统的能量输运
Energy transport in weakly nonlinear wave systems with narrow frequency band excitation
摘要：
提出了一种新的离散模型（D-模型），用于描述窄带激励下中小非线性系统中的非线性波相互作用。它在一个单一的理论框架中集成了两种模式之间的能量传输机制，即不稳定性和能量级联，并给出了发生这种机制的条件。给出了形成级联的条件、级联方向、级联终止的条件等，这些条件强烈依赖于激励参数的选择。可以计算级联的能谱，产生离散和连续的能谱。该模型不需要统计假设，因为所有效应都来自不同模式的相互作用。在给出的例子中--具有色散函数$ø^2=g\,k$和小非线性的表面水波--D模型预测Benjamin-Feir不稳定性边带的不对称增长，而从离散到连续能谱的过渡适当选择的激发参数产生饱和的Phillips功率谱$\sim g^2ø^{-5}$。D模型可用于流体力学、非线性光学、电动力学、等离子体、对流理论等领域中出现的众多波系的实验和理论研究。
英文摘要：
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely intermittency and energy cascade and gives conditions when which regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc. are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed yielding discrete and continuous energy spectra. The model does not need statistical assumptions as all effects are derived from the interaction of distinct modes. In the example given -- surface water waves with dispersion function $ø^2=g\,k$ and small nonlinearity -- D-model predicts asymmetrical growth of side-bands for Benjamin-Feir instability while transition from discrete to continuous energy spectrum excitation parameters properly chosen yields the saturated Phillips' power spectrum $\sim g^2ø^{-5}$. D-model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.
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