OPTICAL TURBULENCE - WEAK TURBULENCE, CONDENSATES AND COLLAPSING FILAMENTS IN THE NONLINEAR SCHRODINGER-EQUATION
OPTICAL TURBULENCE - WEAK TURBULENCE, CONDENSATES AND COLLAPSING FILAMENTS IN THE NONLINEAR SCHRODINGER-EQUATION
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DOI：
10.1016/0167-2789(92)90090-a
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发表时间：
1992-06-15
影响因子：
4
通讯作者：
ZAKHAROV, VE
中科院分区：
文献类型：
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作者：
DYACHENKO, S;NEWELL, AC;ZAKHAROV, VE
非线性薛定谔 (NLS) 方程 i-psi(t) + del2-psi + alpha\psi\(s)psi = 0 是一个规范且通用的方程，在连续介质力学、等离子体物理和光学中具有重要意义。本文认为，在临界情况 sd = 4（其中 d 是维度，s 是非线性阶数）下观察到的大部分解行为可以用弱湍流理论与凝结和塌陷形成的组合来理解。结果是在 NLS 所属的一类哈密顿系统的广泛背景下得出的，以便读者可以了解对于实现各种平衡谱、热力学、纯柯尔莫哥洛夫及其组合的重要成分。我们还提出了与时间相关的自相似解，描述了系统向这些平衡状态的弛豫。我们表明，在单个塌陷事件中损失的粒子数量实际上与阻尼无关。我们对完整控制方程的数值模拟首次证明了弱湍流近似的有效性。我们还提出了一种应该得到广泛应用的间歇机制。它是由强非线性塌缩事件引起的，这些塌缩事件是由朝向波数空间中的原点的粒子流成核的。这些高度组织的事件导致粒子数向高波数级联，并引起间歇性和违反许多关于统计信息丢失和大小尺度统计独立性的常见柯尔莫哥洛夫假设的行为。我们在结论中讨论了这些想法与流体动力湍流的相关性。
The nonlinear Schrodinger (NLS) equation i-psi(t) + del2-psi + alpha\psi\(s)psi = 0 is a canonical and universal equation which is of major importance in continuum mechanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension and s is the order of nonlinearity, can be understood in terms of a combination of weak turbulence theory and condensate and collapse formation. The results are derived in the broad context of a class of Hamiltonian systems of which NLS is a member, so that the reader can gain a perspective on the ingredients important for the realization of the various equilibrium spectra, thermodynamic, pure Kolmogorov and combinations thereof. We also present time-dependent, self-similar solutions which describe the relaxation of the system towards these equilibrium states. We show that the number of particles lost in an individual collapse event is virtually independent of damping. Our numerical simulation of the full governing equations is the first to show the validity of the weak turbulence approximation. We also present a mechanism for intermittency which should have widespread application. It is caused by strongly nonlinear collapse events which are nucleated by a flow of particles towards the origin in wavenumber space. These highly organized events result in a cascade of particle number towards high wavenumbers and give rise to an intermittency and a behavior which violates many of the usual Kolmogorov assumptions about the loss of statistical information and the statistical independence of large and small scales. We discuss the relevance of these ideas to hydrodynamic turbulence in the conclusion.