标题： 弱非线性波系统中窄频带激励下的能量传输 显示英文标题

标题： Energy transport in weakly nonlinear wave systems with narrow frequency band excitation

摘要： 一种新的离散模型（D模型）被提出，用于描述在窄频带激励下具有小和中等非线性的系统中的非线性波相互作用。它在一个统一的理论框架中集成了两种模式之间的能量传输机制，即间歇性和能量级联，并给出了哪种机制将发生的条件。给出了级联形成的条件、级联方向、级联终止的条件等，并且这些条件强烈依赖于激励参数的选择。可以计算级联的能量谱，从而得到离散和连续的能量谱。该模型不需要统计假设，因为所有效应都是从不同模式的相互作用中得出的。在给出的例子中——具有色散函数$\o^2=g\,k$和小非线性的表面水波——D模型预测了Benjamin-Feir不稳定性侧波的不对称增长，而当激励参数正确选择时，从离散到连续能量谱的转变会产生饱和的Phillips功率谱$\sim g^2\o^{-5}$。D模型可以应用于流体力学、非线性光学、电动力学、等离子体、对流理论等众多波系统的研究。 显示英文摘要

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 $\o^2=g\,k$ 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 $\sim g^2\o^{-5}$. 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.