Thomas Gomez

On the validity of a nonlocal approach for MHD turbulence

The phenomenology of magnetohydrodynamic (MHD) turbulence proposed by R. H. Kraichnan, and its consequences for energy spectra and energy decay laws in the high Reynolds number self-similar regime, are first reviewed. After recalling the exact relationships for MHD derived in the spirit of the so-called “4/5” law of Kolmogorov, such laws are used to compute intermittency exponents for statistically steady MHD flows in two space dimensions. These exponents are evaluated both for the structure functions of order p built on the physical variables—velocity v and magnetic field b, or their combination, through the Elsasser variables z±=v±b—and for the flux variables Yp±(r)≡〈[δzL∓(r)(δzi±(r))2]p/3〉, where L denotes the longitudinal components of the fields. There are indications that these nonlinear fluxes scale in a manner similar to that of nonconducting fluids, whereas the physical v, b, z± fields are more intermittent than in the neutral fluid case.

Is isotropic turbulence decay governed by asymptotic behavior of large scales? An eddy-damped quasi-normal Markovian-based data assimilation study

The present paper deals with the identification of the scales and features of the initial kinetic energy spectrum that govern the decay regime of freely decaying homogeneous isotropic turbulence (HIT). To this end, a Data Assimilation (DA) study is performed, which is based on a variational optimal control problem with the eddy-damped quasi-normal Markovian (EDQNM) model whose adjoint equation is derived in the present work. The DA procedure consists in reconstructing the initial kinetic energy spectrum in order to minimize the error committed on some features of decaying turbulence with respect to a targeted EDQNM simulation. The present results show that the decay of HIT over finite time is governed by a finite range of large scales, i.e., the scales ranging from the initial to the final integral scales (or equivalently by wave numbers comprised between the initial and the final location of the peak of the energy spectrum). The important feature of the initial condition is the slope of the energy spectrum at these scales, if such a slope can be defined. This is coherent with previous findings dealing with decay of non-self-similar solutions, or with the key assumptions that underly the Comte-Bellot–Corrsin theory. A consequence is that the finite time decay of HIT is not driven by the asymptotic large-scale behavior of the energy spectrum E(k → 0, t = 0) or the velocity correlation function f(r → +∞, t = 0), or even scales such as kL ≪ 1 or L/r ≪ 1. Governing scales are such that kL(t) = O(1) for values of the integral scale L(t) observed during the finite time decay under consideration. As a matter of fact, a null sensitivity of finite time decay of turbulence with respect to the asymptotic large scale features of the initial condition is observed. Therefore, the asymptotic features of the initial condition should not be investigated defining an inverse problem based of features of turbulence decay observed over a finite time.

Reconstruction of unsteady viscous flows using data assimilation schemes

This paper investigates the use of various data assimilation (DA) approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts. Variational, ensemble Kalman filter-based and ensemble-based variational DA techniques are deployed along with a 2D compressible Navier-Stokes flow solver, which is also used to generate synthetic observations of a reference flow. The performance of these DA schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2D flow field. Moreover, different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale DA problems with up to 105 control variables. In particular, we show how an iterative procedure can be used within the framework of ensemble-based methods to deal with both non-uniform unsteady boundary conditions and initial field reconstruction. The different methodologies developed and assessed in this work give a review of what can be done with DA schemes in computational fluid dynamics (CFD) paradigm. In the same time, this work also provides useful information which can also turn out to be rational arguments in the DA scheme choice dedicated to a specific CFD application.

Large-eddy simulation of very large kinetic and magnetic Reynolds number isotropic magnetohydrodynamic turbulence using a spectral subgrid model

A spectral eddy viscosity and magnetic resistivity subgrid-scale model based on the eddy-damped quasi-normal Markovian (EDQNM) kinetic and magnetic energy transfers is used in large-eddy simulation (LES) of asymptotically large kinetic and magnetic Reynolds number magnetohydrodynamic (MHD) turbulence. The model is assessed a posteriori on three-dimensional, incompressible, isotropic, nonhelical, freely decaying MHD turbulence. Using LES initialized with spectra such that the Alfven ratio of kinetic to magnetic energy equals unity, it is shown that the kinetic energy and magnetic energy spectra exhibit k−5∕3 Kolmogorov inertial subrange scalings consistent with the EDQNM model.

Decay and growth laws in homogeneous shear turbulence

ABSTRACT Homogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow part of the pressure–strain tensor is derived for the return to isotropy process when mean velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter.

Analysis of turbulent skin friction generated in flow along a cylinder

This paper presents an extension of FIK identity [K. Fukagata et al., Phys. Fluids 14, L73 (2002)] to turbulent axial flow along a cylinder. This relation gives the contributions of both the mean flow and the turbulent fluctuating flow to the skin friction coefficient. The later contribution is then further decomposed more precisely as proposed by B. Frohnapfel, Y. Hasegawa, and N. Kasagi, “Reactive Flow Control for Skin Friction Drag Reduction based on Sensing of the Streamwise Wall-Shear Stress,” Euromech Fluid Mechanics Conference 8 (EFMC8), Bad Reichenhall, Germany, 13–16 Sept. 2010, S4-30. The Reynolds shear stress can be linked to the eigenvalues of the anisotropy tensor, the angle between the principal axis of the Reynolds stress tensor, and the mean flow direction and the turbulent kinetic energy. These eigenvalues and the alignment are important elements of the Reynolds stress profile. The present analysis is based on high-fidelity Reynolds-Stress-Model-based simulations. The results are first va...

Spiral vortices in compressible turbulent flows

We extend the spiral vortex solution of Lundgren [Phys. Fluids 25, 2193 (1982)] to compressible turbulent flows with a perfect gas. This model links the dynamical and the spectral properties of incompressible flows, providing a k−5/3 Kolmogorov energy spectrum. In so doing, a compressible spatiotemporal transformation is derived, reducing the dynamics of three-dimensional vortices, stretched by an axisymmetric incompressible strain, into a two-dimensional compressible vortex dynamics. It enables us to write the three-dimensional spectra of the incompressible and compressible square velocities in terms of, respectively, the two-dimensional spectra of the enstrophy and of the square velocity divergence, by the use of a temporal integration. Numerical results are presented from decaying direct simulations performed with 5122 grid points; initially, the rms Mach number is 0.23, with local values up to 0.9, the Reynolds number is 700, and the ratio between compressible and incompressible square velocities is 0...

Mixed-derivative skewness for high Prandtl and Reynolds numbers in homogeneous isotropic turbulence

The mixed-derivative skewness Suθ of a passive scalar field in high Reynolds and Prandtl numbers decaying homogeneous isotropic turbulence is studied numerically using eddy-damped quasi-normal Markovian closure, for Reλ ≥ 103 up to Pr = 105. A convergence of Suθ for Pr ≥ 103 is observed for any high enough Reynolds number. This asymptotic high Pr regime can be interpreted as a saturation of the mixing properties of the flow at small scales. The decay of the derivative skewnesses from high to low Reynolds numbers and the influence of large scales initial conditions are investigated as well.

Closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence

When helicity is made sign-definite by retaining only specific triadic interactions, an inverse energy cascade develops towards large scales in

Combustion instability mitigation by magnetic fields

{k}^{-5/3}