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 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.

An intrinsic feature of turbulent flows is an enhanced rate of mixing and kinetic energy dissipation due to the rapid generation of small-scale motions from large-scale excitation. The transfer of kinetic energy from large to small scales is commonly attributed to the stretching of vorticity by the strain-rate, but strain self-amplification also plays a role. Previous treatments of this connection are phenomenological or inexact, or cannot distinguish the contribution of vorticity stretching from that of strain self-amplification. In this paper, an exact relationship is derived which quantitatively establishes how intuitive multi-scale mechanisms such as vorticity stretching and strain self-amplification together actuate the inter-scale transfer of energy in turbulence. Numerical evidence validates this result and uses it to demonstrate that the contribution of strain self-amplification to energy transfer is higher than that of vorticity stretching, but not overwhelmingly so. * perryj@stanford.edu arXiv:1912.00293v1 [physics.flu-dyn] 1 Dec 2019

Large-eddy simulation (LES) of a wind turbine under uniform inflow is performed using an actuator line model (ALM). Predictions from four LES research codes from the wind energy community are compared. The implementation of the ALM in all codes is similar and quantities along the blades are shown to match closely for all codes. The value of the Smagorinsky coefficient in the subgrid-scale turbulence model is shown to have a negligible effect on the time-averaged loads along the blades. Conversely, the breakdown location of the wake is strongly dependent on the Smagorinsky coefficient in uniform laminar inflow. Simulations are also performed using uniform mean velocity inflow with added homogeneous isotropic turbulence from a public database. The time-averaged loads along the blade do not depend on the inflow turbulence. Moreover, and in contrast to the uniform inflow cases, the Smagorinsky coefficient has a negligible effect on the wake profiles. It is concluded that for LES of wind turbines and wind farms using ALM, careful implementation and extensive cross-verification among codes can result in highly reproducible predictions. Moreover, the characteristics of the inflow turbulence appear to be more important than the details of the subgrid-scale modeling employed in the wake, at least for LES of wind energy applications at the resolutions tested in this work.

One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ1 : λ2 : λ3 is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.

Abstract