论文标题
随机强迫汉堡的动态多标准
Dynamic multiscaling in stochastically forced Burgers turbulence
论文作者
论文摘要
我们对湍流非平衡的动态多标准进行了详细的研究，但统计稳定，随机迫使一维汉堡方程的状态。我们介绍了$ \ textIt {Interval倒塌时间} $ $τ_ {\ rm col} $的概念，这是长度$ \ ell $的时间所花费的时间，由一对拉格朗日示踪剂划分，以震惊。通过计算$τ_ {\ rm col} $的订单-P $时刻的动态缩放指数，我们表明（a）有$ \ textit {不是一个，而是一个特征性的时间尺度} $} $ and（b）$τ_ {\ rm col} $的概率分布功能。我们的研究基于（a）一个理论框架，使我们能够分析地获得动态 - 培训指数，（b）广泛的直接数值模拟，以及（c）（c）（c）（a）和（b）的结果仔细比较。我们讨论了对尺寸的可能概括，以$ d> 1 $，用于随机强迫汉堡方程，以及其他可压缩的流动，表现出湍流。
We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of $\textit{interval collapse times}$ $τ_{\rm col}$, the time taken for an interval of length $\ell$, demarcated by a pair of Lagrangian tracers, to collapse at a shock. By calculating the dynamic scaling exponent of the order-$p$ moment of $τ_{\rm col}$, we show that (a) there is $\textit{not one but an infinity of characteristic time scales}$ and (b) the probability distribution function of $τ_{\rm col}$ is non-Gaussian and has a power-law tail. Our study is based on (a) a theoretical framework that allows us to obtain dynamic-multiscaling exponents analytically, (b) extensive direct numerical simulations, and (c) a careful comparison of the results of (a) and (b). We discuss possible generalizations of our work to dimensions $d >1 $, for the stochastically forced Burgers equation, and to other compressible flows that exhibit turbulence with shocks.
