In order to model pressure and viscous terms in the equation for the Lagrangian dynamics of the velocity gradient tensor in turbulent flows, Chevillard & Meneveau (Phys. Rev. Lett. 97, 174501, 2006) introduced the Recent Fluid Deformation closure. Using matrix exponentials, the closure allows to overcome the unphysical finite-time blow-up of the well-known Restricted Euler model. However, it also requires the specification of a decorrelation time scale of the velocity gradient along the Lagrangian evolution, and when the latter is chosen too short (or, equivalently, the Reynolds number is too high), the model leads to unphysical statistics. In the present paper, we explore the limitations of this closure by means of numerical experiments and analytical considerations. We also study the possible effects of using time-correlated stochastic forcing instead of the previously employed white-noise forcing. Numerical experiments show that reducing the correlation time scale specified in the closure and in the forcing does not lead to a commensurate reduction of the autocorrelation time scale of the predicted evolution of the velocity gradient tensor. This observed inconsistency could explain the unrealistic predictions at increasing Reynolds numbers.We perform a series expansion of the matrix exponentials in powers of the decorrelation time scale, and we compare the full original model with a linearized version. The latter is not able to extend the limits of applicability of the former but allows the model to be cast in terms of a damping term whose sign gives additional information about the stability of the model as function of the second invariant of the velocity gradient tensor.
On the importance of stochasticity in closures of turbulence
University of Rome “Tor Vergata”, Italy（罗马托尔维加塔大学）；LTCI, Télécom Paris, IP Paris, France（巴黎理工学院电信学院）；Inria and École Polytechnique, IP Paris, France（法国国家信息与自动化研究所与巴黎综合理工学院）；Dept. of Applied Mathematics & Statistics, The Johns Hopkins University, Baltimore, MD, USA（约翰斯·霍普金斯大学）；Instituto de Matemática Pura e Aplicada – IMPA, Rio de Janeiro, Brazil（巴西纯粹与应用数学研究所）
A posteriori closure of turbulence models: are symmetries preserved?
University of Rome "Tor Vergata"（罗马托尔维加塔大学）；Télécom Paris, IP Paris（巴黎电信学院，巴黎理工学院）；Inria and École Polytechnique, IP Paris（法国国家信息与自动化研究所与巴黎综合理工学院，巴黎理工学院）
The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers…
The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian Fluid Mech. $\mathbf{10}$, 291 (1982)] is used to predict the behaviour of the above quantities analytically.
Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation
协方差函数的时间排序过程，如前一篇论文（K。Kiyani和W. D. McComb Phys.Rev.E70，066303（2004））的方法进行了扩展，并用于表明与Kraichnan-Wyld扰动级数相关的二阶响应函数可以由局部（波数）能量平衡确定。这些时间排序程序也允许两次制定减少到时间无关的形式，通过指数近似，它被验证的响应方程没有红外发散在无限雷诺数。最后，单次马尔可夫封闭方程（在前面的论文中所述）的推导和证明是兼容的Kolmogorov分布，而不需要引入一个特设常数。
Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. T…
