The normalized turbulent dissipation rate $C_{ϵ}$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_{ϵ}$ 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 $C_{ϵ}$ 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 $C_{ϵ}$ at low Reynolds number that is observed in the simulations.

Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the eddy-damped quasi-normal Markovian model (EDQNM) and compared to results of the multifractal formalism. It is shown that both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For the multifractal formalism, this is an intermittency correction that persists at any high Reynolds number. For EDQNM, this correction is a finite Reynolds number effect, and it is shown that very high Reynolds numbers are needed for this correction to become insignificant with respect to intermittency corrections. Furthermore, the two approaches yield realistic behavior of second and third order statistics of the velocity fluctuations in the dissipative and near-dissipative ranges. Similarities and differences are highlighted, in particular, the Reynolds number dependence.

We analyse the anisotropy of homogeneous turbulence in an electrically conducting fluid submitted to a uniform magnetic field, for low magnetic Reynolds number, in the quasi-static approximation. We interpret contradictory earlier predictions between linearized theory and simulations: in the linear limit, the kinetic energy of transverse velocity components, normal to the magnetic field, decays faster than the kinetic energy of the axial component, along the magnetic field (Moffatt, J. Fluid Mech., vol. 28, 1967, p. 571); whereas many numerical studies predict a final state characterized by dominant energy of transverse velocity components. We investigate the corresponding nonlinear phenomenon using direct numerical simulation (DNS) of freely decaying turbulence, and a two-point statistical spectral closure based on the eddy-damped quasi-normal Markovian (EDQNM) model. The transition from the three-dimensional turbulent flow to a ‘two-and-a-half-dimensional’ flow (Montgomery & Turner, Phys. Fluids, vol. 25, 1982, p. 345) is a result of the combined effects of short-time linear Joule dissipation and longer time nonlinear creation of polarization anisotropy. It is this combination of linear and nonlinear effects which explains the disagreement between predictions from linearized theory and results from numerical simulations. The transition is characterized by the elongation of turbulent structures along the applied magnetic field, and by the strong anisotropy of directional two-point correlation spectra, in agreement with experimental evidence. Inertial equatorial transfers in both DNS and the model are presented to describe in detail the most important equilibrium dynamics. Spectral scalings are maintained in high-Reynolds-number turbulence attainable only with the EDQNM model, which also provides simplified modelling of the asymptotic state of quasi-static magnetohydrodynamic (MHD) 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, Bonaïtiti, 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.

Generating laboratory flows resembling atmospheric turbulence is of prime importance to study the effect of wind fluctuations on objects such as buildings, vehicles, or wind turbines. A novel driving of an active grid following a stochastic process is used to generate velocity fluctuations with correlation lengths, and, thus, integral scales, much larger than the transverse dimension of the wind tunnel. The combined action of the active grid and a modulation of the fan speed allows one to generate a flow characterized by a four-decade inertial range and an integral scale Reynolds number of $2\times {10}^7$.

Among existing subgrid scale (SGS) models for large-eddy simulation (LES), some are time reversible in the sense that the dynamics evolve backward in time after a transformation at every point in space. In practice, reversible subgrid models reduce the numerical stability of the simulations since the effect of the subgrid scales is no longer strictly dissipative. This lack of stability constitutes often a criterion to reject this kind of models. The aim of this paper is to examine whether time-reversibility can constitute a criterion that a subgrid model has to fulfill, or has not to. Thereto, we investigate by direct numerical simulation (DNS) the time dependence of the kinetic energy of the resolved scales when the velocity is reversed in all or part of the length scales of the turbulent flow. These results are compared with results from existing LES subgrid models. It is argued that the criterion of time reversibility to assess subgrid models is incompatible with the main underlying assumption of LES.