A closure for Lagrangian velocity gradient evolution in turbulence using recent deformation mapping of initially Gaussian fields

TL;DR

This paper introduces a new closure model for the Lagrangian velocity gradient evolution in turbulence, using Gaussian field statistics to improve physical realism and eliminate DNS tuning, showing better results at moderate Reynolds numbers.

Contribution

The paper develops the RDGF closure model that incorporates Gaussian isotropic field statistics for more realistic upstream conditions in turbulence modeling.

Findings

Improved single-time velocity gradient statistics at moderate Reynolds numbers.

Elimination of DNS-tuned coefficients in the closure model.

Enhanced physical realism over previous isotropic assumptions.

Abstract

The statistics of the velocity gradient tensor in turbulent flows are of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the velocity gradient tensor in particular. Stochastic models for the Lagrangian evolution of velocity gradients in isotropic turbulence, with closure models for the pressure Hesssian and viscous Laplacian, have been shown to reproduce important features such as non-Gaussian probability distributions, skewness and vorticity strain-rate alignments. The Recent Fluid Deformation (RFD) closure introduced the idea of mapping an isotropic Lagrangian pressure Hessian as upstream initial condition using the fluid deformation tensor. Recent work on a Gaussian fields closure, however, has shown that even Gaussian isotropic velocity fields contain significant anisotropy for the conditional pressure Hessian tensor due to the inherent velocity-pressure couplings, and that assuming an isotropic pressure Hessian as upstream condition may not be realistic. In this paper, Gaussian isotropic field statistics are used to generate more physical upstream conditions for the recent fluid deformation mapping. In this new framework, known isotropy relations can be satisfied {\it a priori} and no DNS-tuned coefficients are necessary. A detailed comparison of results from the new model, referred to as the recent deformation of Gaussian fields (RDGF) closure, with existing models and DNS shows the improvements gained, especially in various single-time statistics of the velocity gradient tensor at moderate Reynolds numbers. Application to arbitrarily high Reynolds numbers remains an open challenge for this type of model, however.