Nonlinear Fluctuating Hydrodynamics as Model for Turbulent Super-structures

长度和时间尺度明显大于湍流脉动场特征的湍流中的自组织结构可归类为超结构。在涉及的工程应用中或在大气物理中，这种结构在促进或防止混合方面可能具有深远的影响。人们可以区分由边界条件或体力施加在湍流上的大尺度结构，以及跨尺度的非线性相互作用产生的大尺度结构。一个有趣的问题是，是否有可能进行低维描述，以再现本质上的相互作用。过去已经观察到，在具有强浓度梯度的层附近的标量浓度场中，涨落流体动力学中的热涨落会引起所谓的巨型涨落。对于均匀浓度，即单一的流体材料，大尺度构造的发生机制不可能是相同的。然而，问题出现了，一个简单的非平衡随机机制是否能解释动量场中的大尺度关联，以及平均梯度、体力或边界条件的存在如何影响它们的产生。目前的项目解决了这个问题，并有助于对涡旋上部结构的起源和动力学进行建模。我们使用简单的随机湍流模型，并比较了满足涨落-耗散平衡的不同方式的两个模型族。一个是nLLNS(非线性Landau-Lifshitz Navier-Stokes方程)。虽然这个模型最初是为平衡构型而提出的，但它对非平衡构型的适用性已被证明。另一种模型是欧拉坐标系中的广义朗之万模型，它是由欠阻尼朗之万方程导出的非线性脉动流体力学的变体。GLMEF允许产生比nLLNS更复杂的非平衡效应。第一个资助期的计划有两个主要部分：(A)GLMEF作为一个复杂的、与波数有关的消散机制的模型的资格。用于大规模并行计算的GLMEF和nLLNS代码的三维实现和性能优化。(B)用等温状态方程进行外加动量和/或密度梯度的探索性模拟。从梯度尺度和领域尺度考察尺度效应。不同随机模型nLLNS和GLMEF的比较。对于后者，研究了不同的核估计，从而研究了不同的记忆效应。对于前人对非等温物态方程的探索。在第二个资助期，随机模式在非平衡湍流场中的长期相关性方面的预测能力将与实际的湍流剪切流的直接数值模拟进行比较。

Structures arising from self-organization in turbulence with length and time scales significantly larger than those characteristic for the turbulent fluctuation field can be classified as superstructures. Such structures may have far-reaching effects in promoting or preventing mixing in engineering applications involving, or in atmospheric physics. One may differentiate between large-scale structures enforced on a turbulent flow by boundary conditions or body forces, and large-scale structures that arise from nonlinear interactions across scales. It is an interesting question whether a lower-dimensional description is possible that reproduces the essential interactions. It has been observed in the past that thermal fluctuations in fluctuating hydrodynamics give rise to so-called giant fluctuations in a scalar-concentration field near a layer with a strong concen-tration gradient. With uniform concentration, i.e. a single fluid material, the mechanism for the occurrence of large-scale structures cannot be the same. Nevertheless, the question arises, whether a simple non-equilibrium stochastic mechanism can explain large-scale correlations in the momentum field, and how the presence of mean gradients, body forces, or boundary conditions affects their generation. The current project addresses this question and contributes to modeling the origin and dynamics of turbu-lent superstructures. We employ simple stochastic models for turbulent fluctuations and compare two model families with different ways of satisfying a fluctuation-dissipation balance. One is nLLNS (nonlinear Landau-Lifshitz Navier-Stokes equations). Although this model originally has been proposed for equilibrium configurations its applicability to non-equilibrium has been demonstrated. The other model is GLMEF (generalized Langevin model in Eulerian reference frame) which is a variant of nonlinear fluctuating hydrodynamics derived from the underdamped Langevin equation. GLMEF allows for more complex non-equilibrium effects than nLLNS. The plan for the 1st funding period has two main parts: (A) Qualification of GLMEF as model for a complex, wave-number dependent dissipation mechanism. Three-dimensional implementations and performance optimization of GLMEF and nLLNS codes for large-scale parallel computing. (B) Explorative simulations with imposed momentum and / or density gradient with an isothermal equation of state. Investigation of scale-effects in terms of gradient scales and domain scales. Comparison of the different stochastic models nLLNS and GLMEF. For the latter, investigation of different kernel esti-mators and thus different memory effects. For the former exploration of non-isothermal equation of state. In a 2nd funding period the predictive capability of the stochastic models in terms of long-range correlations in a non-equilibrium turbulence field will be compared with actual direct numerical simulations of turbulent shear flows.