Decay of homogeneous turbulence in three-range models

New models, with energy spectra which consist of three power-law ranges, are suggested to describe the free evolution of homogeneous and isotropic high-Reynolds-number turbulence. By selecting a single number, a characteristic of the energy spectrum in the model, very good agreement with experiments has been achieved for two independently measured parameters. Also, verifiable dependences of turbulence decay features on characteristics of the turbulence generation process are suggested.     

Coherence and large fluctuations of helicity in homogeneous turbulence

The build up of coherent large amplitude helicity fluctuations is detected in numerical experiments on 3-D homogeneous turbulence.     

Decay and growth laws in homogeneous shear turbulence

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.     

Decay of turbulence in pipe flow

A novel experiment has been devised which provides direct evidence for critical point behavior in the longstanding problem of the transition to turbulence in a pipe. The novelty lies in the quenching of turbulence by reducing the Reynolds number and observing the decay of disordered motion. Divergence of the time scales implies underlying deterministic dynamics which are analogous to those found in boundary crises in dynamical systems. A modulated wave packet emerges from the long term transients and this coherent state provides evidence for connections with recent theoretical developments.     

Decay of scalar turbulence revisited

We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions where mixing is less efficient. We examine two situations. The first is of a spatially homogeneous stationary turbulent flow with both viscous and inertial scales present. It is shown that at large times scalar fluctuations decay algebraically in time at all spatial scales. The second example explains chaotic stationary flow in a disk/pipe. The boundary region of the flow controls the long-time decay, which is algebraic at some transient times, but becomes exponential, with the decay rate dependent on the scalar diffusion coefficient, at longer times.     

Magnetic helicity tensor for an anisotropic turbulence

The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magnetic helicity is calculated as well. It is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnetic helicity. It is demonstrated that the tensor of the magnetic part of the alpha effect for weakly inhomogeneous turbulence is determined only by the isotropic part of the magnetic helicity tensor.     

Pressure spectrum in homogeneous turbulence

The pressure spectrum in homogeneous steady turbulence is studied using direct numerical simulation with resolution up to 1024(3) and the Reynolds number R(lambda) between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant K = 1.65+/-0.05 followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately P(k) = B(p)epsilon;(4/3)k(-7/3) with B(p) = 8.0+/-0.5, and followed by a bump of nearly k(-5/3) at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.     

Developing homogeneous isotropic turbulence

We investigate the self-similar evolution of the transient energy spectrum, which precedes the establishment of the Kolmogorov spectrum in homogeneous isotropic turbulence in three dimensions using the EDQNM closure model. The transient evolution exhibits self-similarity of the second kind and has a non-trivial dynamical scaling exponent, which results in the transient spectrum having a scaling that is steeper than the Kolmogorov k^−5/3 spectrum. Attempts to detect a similar phenomenon in DNS data are inconclusive, owing to the limited range of scales available.     

Large-scale structure of isotropic homogeneous turbulence

It is shown that the longitudinal correlation functionf is asymptotically proportional tor ^?3 asr→∞ and the energy spectrum function is asymptotically proportional toκ ² asκ→0 if and only if 0<〈(f u d ³ x)·u〉<∞. Moreover, the latter finiteness condition is shown to be essentially equivalent to 〈(fy·ud ³ x)²〉<∞ for nonstochasticyεL ²(R₃). Confirmed by recent experimental measurements, the larger dependencef ∝r ^?3 is concomitant with anO(r ^?6)=O(f ²) fall-off of the viscous force term in the Kármán-Howarth equation.     

Phase space structure in ideal homogeneous turbulence

The phase spaces of finite Fourier representations of ideal, incompressible, homogeneous fluid and magneto-fluid turbulence are discussed. Helical invariance allows the definition of set-theoretic characteristic functions which partition the various ensemble phase spaces into disjoint components. This explicit disjointness explains the previously observed nonergodicity in ideal, incompressible, homogeneous turbulence.     

Decay of pure quantum turbulence in superfluid 3He-B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.     

Single point velocity distributions in homogeneous isotropic turbulence

The starting point for this paper lies in the results obtained by Tatsumi (2004) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi (2004) leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view, and obtains a new complete set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier--Stokes equations are presented. The comparison with former theory was also made. The origin of non--Gaussian character could be deduced from the above exact solutions.     

Numerical investigation of self-similar unstably stratified homogeneous turbulence

New numerical results concerning unstably stratified homogeneous turbulence are presented. The system of equations considered gives the dynamics of homogeneous incompressible binary mixtures submitted to a gravity field in the low Atwood number limit (Boussinesq approximation). It allows to gain insight into several characteristics relevant to buoyancy driven turbulent mixing, such as unsteadiness and anisotropy. In this work, the dependency of the asymptotic self-similar states on different dissipation processes is extensively explored. The resulting states are shown to agree with recent theoretical predictions based on a large scale dynamics analysis.     

Dynamics and structure of unstably stratified homogeneous turbulence

We characterise the properties of unstably stratified homogeneous turbulence by means of high-resolution direct numerical simulations and a two-point statistical spectral model based on a quasi-normal closure proposed by Burlot et al. Both approaches agree very well regarding the evolution of one- and two-point turbulent statistics, showing that the model is valid at even higher Reynolds numbers than previously considered. From a parametric study with different initial conditions, we confirm that the energy distribution at large scale influences strongly the late time dynamics of the flow. In particular, we assess the existence of backscatter transfer of energy, and evaluate its role in the growth rate of several turbulent quantities. Moreover, thanks to the statistical model, we analyse the scale-by-scale anisotropy of the flow through the decomposition of turbulent spectra in terms of directional anisotropy and polarisation anisotropy, for a refined characterisation of the structure of the flow which is strongly anisotropic in the large scales. This also allows us to study how isotropy is restored in the inertial scales.     

Modification of Spalart-Allmaras model with consideration of turbulence energy backscatter using velocity helicity

The correlation between the velocity helicity and the energy backscatter is proved in a DNS case of 256³-grid homogeneous isotropic decaying turbulence. The helicity is then proposed to be employed to improve turbulence models and SGS models. Then Spalart-Allmaras turbulence model (SA) is modified with the helicity to take account of the energy backscatter, which is significant in the region of corner separation in compressors. By comparing the numerical results with experiments, it can be concluded that the modification for SA model with helicity can appropriately represent the energy backscatter, and greatly improves the predictive accuracy for simulating the corner separation flow in compressors.