Nonlinear Fluctuating Hydrodynamics as Model for Turbulent Super-structures

由湍流自组织产生的结构，其长度和时间尺度明显大于湍流脉动场的特征尺度，可以被归类为超结构。这样的结构在促进或防止涉及工程应用或大气物理学的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积力施加在湍流上的大尺度结构和由跨尺度非线性相互作用产生的大尺度结构。这是一个有趣的问题，是否有可能用低维描述来再现基本的相互作用。过去已经观察到，在涨落流体动力学中的热涨落引起在具有强浓度梯度的层附近的标量浓度场中的所谓巨涨落。对于均匀的浓度，即单一流体材料，大规模结构的发生机制不可能相同。然而，问题出现了，是否一个简单的非平衡随机机制可以解释大规模的相关性在动量场，以及如何存在的平均梯度，体力，或边界条件影响他们的产生。目前的项目解决了这个问题，并有助于模拟的起源和动力学的湍流上层建筑。我们采用简单的随机模型的湍流波动和比较两个不同的方式满足波动耗散平衡的模型家族。一个是nLLNS（nonlinear Landau-Lifshitz Navier-Stokes equations）。虽然该模型最初是针对平衡构型提出的，但其对非平衡构型的适用性已得到证明。另一个模型是GLMEF（广义朗之万模型在欧拉参考系），这是一个变种的非线性波动流体动力学的欠阻尼朗之万方程。GLMEF允许比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作为复杂的波数依赖性耗散机制模型的资格。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)探索性模拟与施加的动量和/或密度梯度与等温状态方程。从梯度尺度和域尺度两个方面研究尺度效应。不同随机模型nLLNS和GLMEF的比较。对于后者，研究不同的核估计，从而不同的记忆效果。为非等温状态方程的前期探索。在第二个资助期内，将对随机模型在非平衡湍流场中的长程相关性方面的预测能力与湍流剪切流的实际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.