Jean-Pierre Bertoglio

Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified as v T =(C s δ) 2 (| S |—|〈 S 〉|): the magnitude of the mean shear |〈 S 〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor | S |; C S is the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Re τ = 395 and Re τ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.

Spectral imbalance and the normalized dissipation rate of turbulence

The normalized turbulent dissipation rate Cϵ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of Cϵ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of Cϵ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of Cϵ at low Reynolds number that is observed in the simulations.

Dynamics of spectrally truncated inviscid turbulence

The evolution of the turbulent energy spectrum for the inviscid spectrally truncated Euler equations is studied by closure calculations. The observed behavior is similar to the one found in direct numerical simulations [Cichowlas, Bonaititi, Debbasch, and Brachet, Phys. Rev. Lett. 95, 264502 (2005)]. A Kolmogorov spectral range and an equipartition range are observed simultaneously. Between these two ranges a “quasi-dissipative” zone is present in the kinetic energy spectrum. The time evolution of the wave number that marks the beginning of the equipartition range is analyzed and it is shown that spectral nonlocal interactions are governing this evolution.

Optimal estimation for large-eddy simulation of turbulence and application to the analysis of subgrid models

The tools of optimal estimation are applied to the study of subgrid models for Large-Eddy Simulation of turbulence. The concept of optimal estimator is introduced and its properties are analyzed in the context of applications to a priori tests of subgrid models. Attention is focused on the Cook and Riley model in the case of a scalar field in isotropic turbulence. Using DNS data, the relevance of the beta assumption is estimated by computing (i) generalized optimal estimators and (ii) the error brought by this assumption alone. Optimal estimators are computed for the subgrid variance using various sets of variables and various techniques (histograms and neural networks). It is shown that optimal estimators allow a thorough exploration of models. Neural networks are proved to be relevant and very efficient in this framework, and further usages are suggested.

Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient

In this paper, the eddy-damped quasi-normal Markovian closure is used to study the behavior of the scalar flux spectrum in isotropic turbulence as the Reynolds number Reλ varies in a range between 30 and 107. The different contributions to the evolution equation of the scalar flux spectrum are studied. One-dimensional spectra are in good agreement with direct numerical simulation (DNS) and experiments at moderate Reλ. The closure shows that at high Reynolds numbers, a K−7∕3 scaling is found for the scalar flux spectrum, in agreement with Lumley’s prediction [Phys. Fluids 10, 855 (1967)], but enormous Reλ are needed before it can be clearly observed. In the range of wind tunnel experiments, the spectral exponent for the scalar flux is closer to −2 in agreement with existing measurements [Mydlarski and Warhaft, J. Fluid Mech. 358, 135 (1998)]. The results for the molecular dissipation of scalar flux are in agreement with the DNS results of Overholt and Pope [Phys. Fluids A 8, 3128 (1996)]. The large Reλ beh...

The decay of turbulence in a bounded domain

The decay of turbulence in a bounded domain without mean velocity is investigated. Direct and large-eddy simulations, as well as the eddy-damped quasi-normal Markovian closure, are used. The effect of the finite geometry of the domain is accounted for by introducing a low-wavenumber cut-off into the energy spectrum of isotropic turbulence. It is found that, once the saturation of the turbulent energy-containing length scale has occurred, the rms vorticity decays following a power law with a −3/2 exponent, in agreement with the helium superfluid experiment of Skrbek and Stalp (Skrbek L and Stalp S R 2000 Phys. Fluids 12 1997–2019). The decay exponent for the turbulent kinetic energy is found to be −2, also in agreement with Skrbek and Stalp. Using scalings deduced from a simple analysis, all data can be collapsed into single curves for both the fixed scale turbulent regime and the final viscous period of decay. A spectral model for inhomogeneous turbulence is finally applied to the decay of turbulence betw...

On the behavior of the velocity-scalar cross correlation spectrum in the inertial range

The velocity-scalar cross spectrum (or scalar flux spectrum) is generally presumed to have a K−7/3 wavenumber dependence in the inertial range, in agreement with the dimensional analysis proposed by Lumley [Phys. Fluids 10, 855 (1967)]. Such a behavior is, however, clearly not observed in experiments in which spectra closer to K−2 (or even less steep) are generally found. It is shown in the paper that dimensional analysis is compatible with a K−2 scaling if a spectral flux of the velocity-scalar cross correlation is introduced. An analysis of the different terms in the equation of the scalar flux spectrum shows that two nonlinear contributions can be identified: a transfer term and the pressure contribution. Direct numerical simulations and large eddy simulation calculations are performed to obtain spectral information about the scalar flux spectrum and to analyze some key properties of the associated nonlinear transfer and pressure terms.

Two-point closures for weakly compressible turbulence

The aim of the present paper is to address the problem of homogeneous isotropic compressible turbulence within the framework of two-point statistical closures. In order to simplify the description, weak compressibility assumptions are first introduced in the equations governing the fluctuating field: the fluid is supposed to be barotropic and nonlinear terms involving density fluctuations are neglected. The equations for the two-point two-time correlations are written. They are closed by extending the direct interaction approximation to (weakly) compressible fields. This work is then used as a ground to derive an extension of the eddy damped quasi-normal Markovian closure that accounts for compressibility effects. Both closures reflect the existence of acoustic waves and the complex nature of nonlinear interactions between modes. The EDQNM model is solved numerically for the case of an isotropic turbulent field maintained statistically stationary by injecting energy in the large scales. At low Mach number...

Inertial range scaling of scalar flux spectra in uniformly sheared turbulence

A model based on two-point closure theory of turbulence is proposed and applied to study the Reynolds number dependency of the scalar flux spectra in homogeneous shear flow with a cross-stream uniform scalar gradient. For the cross-stream scalar flux, in the inertial range the spectral behavior agrees with classical predictions and measurements. The streamwise scalar flux is found to be in good agreement with the results of atmospheric measurements. However, both the model results and the atmospheric measurements disagree with classical predictions. A detailed analysis of the different terms in the evolution equation for the streamwise scalar flux spectrum shows that nonlinear contributions are governing the inertial subrange of this spectrum and that these contributions are relatively more important than for the cross-stream flux. A new expression for the scalar flux spectra is proposed. It allows us to unify the description of the components in one single expression, leading to a classical K−7∕3 inertia...

The rapid–slow decomposition of the subgrid flux in inhomogeneous scalar turbulence

In large eddy simulation of turbulent flow, because of the spatial filter, inhomogeneity and anisotropy affect the subgrid stress via the mean flow gradient. A method of evaluating the mean effects is to split the subgrid stress tensor into ‘rapid’ and ‘slow’ parts. This decomposition was introduced by Shao et al. (L. Shao, S. Sarkar, and C. Pantano, On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows, Phys. Fluids 11 (1999), pp. 1229–1248) and applied to a priori tests of existing subgrid models in the case of a turbulent mixing layer. In the present work, the decomposition is extended to the case of a passive scalar in inhomogeneous turbulence. The contributions of rapid and slow subgrid scalar flux, both in the equations of scalar energy and scalar flux, are analyzed. A priori numerical tests are performed in the turbulent Couette flow with a mean scalar gradient. Results are then used to evaluate the performances of different popular subgrid scalar models. It is shown that the existing models can not well simulate the slow part and need to be improved in future works.