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： 一种新模型（D模型）被提出，用于描述在窄频带激励下可能发生的具有小和中等非线性的系统中的非线性波相互作用。 它能够在单一理论框架中再现各种非线性波现象，如间歇性和离散及连续能量谱。 级联的形成条件、级联方向、级联终止条件等。 可以根据激励参数的选择直接得出。 不需要统计假设，因为所有效应都是从不同模态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不稳定性下的侧带不对称增长，而从离散到连续能量谱的转变则产生了饱和的Phillips功率谱$\sim g^2\o^{-5}$，这是特定激励参数选择的结果。 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、对流理论等中出现的众多波系统的实验和理论研究。 dynamics, nonlinear optics, electrodynamics, convection theory, etc. 显示英文摘要

摘要： A novel model (D-model) is presented describing nonlinear wave interactions in the systems with small and moderate nonlinearity possible due to narrow frequency band excitation. It allows to reproduce in a single theoretical frame various nonlinear wave phenomena such as intermittency and discrete and continuous energy spectra. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc. can be determined as a direct outcome from the choice of excitation parameters. No statistical assumptions are needed 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 yields the saturated Phillips' power spectrum $\sim g^2\o^{-5}$, for specific choice of the excitation parameters. 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.dynamics, nonlinear optics, electrodynamics, convection theory, etc.