Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin’s model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.     

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

We implement a lattice Boltzmann method (LBM) for decaying homogeneous isotropic turbulence based on an analogous Galerkin filter and focus on the fundamental statistical isotropic property. This regularized method is constructed based on orthogonal Hermite polynomial space. For decaying homogeneous isotropic turbulence, this regularized method can simulate the isotropic property very well. Numerical studies demonstrate that the novel regularized LBM is a promising approximation of turbulent fluid flows, which paves the way for coupling various turbulent models with LBM.     

Dependence of decaying homogeneous isotropic turbulence on inflow conditions

A careful data analysis of far downstream turbulent flows generated by conventional and multiscale grids shows that these decaying flows are very clearly different from both Saffman and Loitsyansky turbulence. The analysis also shows that there are marked differences between the far downstream turbulence behaviours generated by different types of grid. There is an inflow condition dependence on both the normalised energy dissipation and the conserved large-scale invariant.     

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.     

Prandtl number effects in decaying homogeneous isotropic turbulence with a mean scalar gradient

Decaying homogeneous isotropic turbulence with an imposed mean scalar gradient is investigated numerically, thanks to a specific eddy-damped quasi-normal Markovian closure developed recently for passive scalar mixing in homogeneous anisotropic turbulence (BGC). The present modelling is compared successfully with recent direct numerical simulations and other models, for both very large and small Prandtl numbers. First, scalings for the cospectrum and scalar variance spectrum in the inertial range are recovered analytically and numerically. Then, at large Reynolds numbers, the decay and growth laws for the scalar variance and mixed velocity–scalar correlations, respectively, derived in BGC, are shown numerically to remain valid when the Prandtl number strongly departs from unity. Afterwards, the normalised correlation ρ_wθ is found to decrease in magnitude at a fixed Reynolds number when Pr either increases or decreases, in agreement with earlier predictions. Finally, the small scales return to isotropy of the scalar second-order moments is found to depend not only on the Reynolds number, but also on the Prandtl number.     

Manifestations of drag reduction by polymer additives in decaying, homogeneous, isotropic turbulence

The existence of drag reduction by polymer additives, well established for wall-bounded turbulent flows, is controversial in homogeneous, isotropic turbulence. To settle this controversy, we carry out a high-resolution direct numerical simulation of decaying, homogeneous, isotropic turbulence with polymer additives. Our study reveals clear manifestations of drag-reduction-type phenomena: On the addition of polymers to the turbulent fluid, we obtain a reduction in the energy-dissipation rate, a significant modification of the fluid energy spectrum especially in the deep-dissipation range, a suppression of small-scale intermittency, and a decrease in small-scale vorticity filaments.     

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.     

Depression of nonlinearity in decaying isotropic MHD turbulence

Spectral method simulations show that undriven magnetohydrodynamic turbulence spontaneously generates coherent spatial correlations of several types, associated with local Beltrami fields, directional alignment of velocity and magnetic fields, and antialignment of magnetic and fluid acceleration components. These correlations suppress nonlinearity to levels lower than what is obtained from Gaussian fields, and occur in spatial patches. We suggest that this rapid relaxation leads to non-Gaussian statistics and spatial intermittency.     

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.     

An infinity of possible invariants for decaying homogeneous turbulence

The von Kárman-Howarth equation implies an infinity of invariants corresponding to an infinity of different asymptotic behaviours of the double and triple velocity correlation functions at infinite separations. Given an asymptotic behaviour at infinity for which the Birkhoff-Saffman invariant is not infinite, there are either none, or only one or only two finite invariants. If there are two, one of them is the Loitsyansky invariant and the decay of large eddies cannot be self-similar. We examine the consequences of this infinity of invariants on a particular family of exact solutions of the von Kárman-Howarth equation.     

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence (DHIT) of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase "strain generation resistance" and "vorticity generation resistance", i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.     

On the scaling of three-dimensional homogeneous and isotropic turbulence

In this paper we investigate the scaling properties of three-dimensional isotropic and homogeneous turbulence. We analyze a new form of scaling (extended self-similarity) recently introduced in the literature. We found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low Reynolds number and it extends over a much wider range of scales with respect to the inertial range.     

Some recent advances in the theory of homogeneous isotropic turbulence

We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on the new insights that have been gained from recent numerical studies of the three-dimensional Navier Stokes equation and simpler shell models for turbulence. In particular, we examine the status of multiscaling corrections to Kolmogorov scaling, extended self similarity, generalized extended self similarity, and non-Gaussian probability distributions for velocity differences and related quantities. We recount our recent proposal of a wave-vector-space version of generalized extended self similarity and show how it allows us to explore an intriguing and apparently universal crossover from inertial- to dissipation-range asymptotics.     

Investigation of anomalous very fast decay regimes in homogeneous isotropic turbulence

The emergence of anomalous fast decay regimes in homogeneous isotropic turbulence (HIT) decay is investigated via both theoretical analysis and eddy-damped quasi-normal Markovian simulations. The work provides new insight about a fundamental issue playing a role in HIT decay, namely the influence of non-standard shapes of the energy spectrum, in particular in the large energetic scale region. A detailed analysis of the kinetic energy spectrum E(k) and the non-linear energy transfer T(k) shows that anomalous decay regimes are associated with the relaxation of initial energy spectra which exhibit a bump at energetic scales. This feature induces an increase in the energy cascade rate, toward solutions with a smooth shape at the spectrum peak. Present results match observations reported in wind-tunnel experiments dealing with turbulence decay in the wake of grids and bluff bodies, including scaling laws for the dissipation parameter C_?. They also indicate that the ratio between the initial eddy turnover time and the advection time determines of how fast anomalous regimes relax toward classical turbulence free-decay. This parameter should be used for consistent data comparison and it opens perspectives for the control of multiscale effects in industrial applications.     

Abnormal nearly homogeneous radiation by slit-grooves structure

Ultra-short high-intensity light pulses were utilized to induce the optical birefringence in a polyimide material possessing the azo-dye covalently bonded to the main chain. The obtained results showed that a two-photon absorption process was involved in a creation of the sample birefringence which, to the best of our knowledge, was not previously reported for polyimide materials. The growths and decays of birefringence were examined as functions of the pulse intensities. No damage to the material during the illumination process was detected in a wide range of optical powers applied. High birefringence level of the order of 0.005 was measured.     

Differential integral equation for the spectrum of isotropic homogeneous turbulence

The double and triple velocity correlations for isotropic homogeneous turbulence are constructed and used in v. Kármán-Howarth differential equation for isotropic correlations; it is reduced to a differential integral equation for the spectrum of turbulence; it contains only one dependent function (5.2). The equation of energy, which follows from the above equation, can be reduced toHeisenberg's type of equation for the spectrum of turbulence (5.6). Eddies of the same order of magnitudeinteract; they partly generate partly destroy votricity. Small eddies (large wave numbersk)act on large eddies by mainly destroying them.