Nonlinear Fluctuating Hydrodynamics as Model for Turbulent Super-structures

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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.