New Sedov-Type Solution of Isotropic Turbulence

The starting point lies in the results obtained by Sedov （1944） for isotropic turbulence with a self-preserving hypothesis. A careful consideration of the mathematical structure of the Karman-Howarth equation leads to an exact analysis of all cases possible and to all admissible solutions of the problem. I study this interesting problem from a new point of view. New solutions are obtained. Based on these exact solutions, some physical significant consequences of recent advances in the theory of self-preserved homogeneous statistical solution of the Navier-Stokes equations are presented.     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Towards lowering dissipation bounds for turbulent flows

We examine the background flow variational principle for calculating bounds on the energy dissipation rate in turbulent shear flow, and suggest to select this principle's test functions such that they comply with the small-scale smoothness of real turbulent velocity fields. A self-consistent algorithm implementing this requirement then yields an upper bound on the dimensionless dissipation coefficient which shows a weak power-law decrease at high Reynolds numbers, instead of approaching a nonzero constant, as it did in previous estimates. Received 26 October 1998     

Large scale correlations for energy injection mechanisms in swirling turbulent flows

We report an experimental study of large scale correlations in the power injected in turbulent swirling flows generated in the gap between two coaxial rotating disks. We measure the pressure fluctuations on the blades of one disk, as well as the pressure drop between the leading and the trailing edges of the rotating blades, i.e. the local drag force. Measurements at different positions on one blade and on two successive blades display a correlation length much larger than the ones usually expected in turbulent flows. The time lag for which the correlation between two points is maximum, strongly depends on the global flow configuration. These results help us to understand the statistical properties of the injected power fluctuations in turbulent swirling flows. Received 2 September 1999     

A multi-scale simulation method for high Reynolds number wall-bounded turbulent flows

We present an assessment and enhancement of the hybrid two-level large-eddy simulation method (A.G. Gungor and S. Menon, A new two-scale model for large eddy simulation of wall-bounded flows, Prog. Aerosp. Sci. 46 (2010), pp. 28–45), a multi-scale formulation for simulation of high Reynolds number wall-bounded turbulent flows. The assessment of the method is performed by examining role of static and dynamic blending functions used to perform hybridisation of two-level simulation (K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows, J. Comput. Phys. 220 (2006), pp. 290–311; K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows. Part 2: Non-homogeneous flows, J. Comput. Phys. 222 (2007), pp. 673–701) and large-eddy simulation methods. The sensitivity of first- and second-order turbulence statistics to the type of blending functions is investigated by simulating a fully developed turbulent flow in a channel at a friction Reynolds number Re_τ = 395 and comparing the results with those obtained using a direct numerical simulation. The first-order statistics do not show any significant differences for different blending functions, but the second-order statistics show some minor differences. The dynamic evaluation of the hybrid region and the blending function is necessary for non-equilibrium and complex flows where use of a static blending function can lead to inaccurate results. We propose two criteria for the dynamic evaluation; first evaluates extent of the hybrid region based on the subgrid turbulent kinetic energy and the second estimates the blending function based on a characteristic length scale. The computational efficiency of the method is enhanced by incorporating a hybrid programming paradigm where a standard domain decomposition by the message-passing-interface library is combined with the open multi-processing based parallelisation. A further enhancement of the method is achieved by incorporating a closure model for the unclosed hybrid terms in the governing equations, which appear due to hybridisation of two-level- and large-eddy-simulation methods. The model is based on an order of magnitude approximation and a preliminary assessment of the model shows improvement of turbulence statistics when used to simulate turbulent flow in a periodic channel. The assessment and improvements to the multi-scale method make it more suitable for simulation of practical wall-bounded turbulent flows at higher Reynolds number than a conventional large-eddy simulation. This is demonstrated by simulating two representative cases; turbulent flow at high Reynolds number in a periodic channel and flow over a bump placed on the lower surface of a channel, where a relatively coarser computational grid is found to be sufficient for reasonably accurate results.     

Nonperturbative renormalization group approach to turbulence

We suggest a new, renormalization group (RG) based, nonperturbative method for treating the intermittency problem of fully developed turbulence which also includes the effects of a finite boundary of the turbulent flow. The key idea is not to try to construct an elimination procedure based on some assumed statistical distribution, but to make an ansatz for possible RG transformations and to pose constraints upon those, which guarantee the invariance of the nonlinear term in the Navier-Stokes equation, the invariance of the energy dissipation, and other basic properties of the velocity field. The role of length scales is taken to be inverse to that in the theory of critical phenomena; thus possible intermittency corrections are connected with the outer length scale. Depending on the specific type of flow, we find different sets of admissible transformations with distinct scaling behaviour: for the often considered infinite, isotropic, and homogeneous system K41 scaling is enforced, but for the more realistic plane Couette geometry no restrictions on intermittency exponents were obtained so far. Received: 28 December 1997 / Accepted: 6 August 1998     

Intermittency in a turbulent low temperature gaseous helium jet

We analyse experimental velocity measurements on the axis of a low temperature gaseous helium jet. From independent increments arguments, we reproduce the behaviour of structure functions. We show where this approach fails and how the intermittency phenomenon is a small correction. The physical arguments under the multiplicative cascade models for this intermittency imply an acceleration of this cascade close to the dissipative range, which we are able to evidence. This acceleration could be responsible of the apparent Extended Self Similarity between structure functions of various orders. Received 13 October 1999 and Received in final form 19 May 2000     

Turbulence over arrays of obstacles in low temperature helium gas

Turbulence produced in low temperature helium gas flowing over arrays of rectangular- and triangular-shaped blunt obstacles is investigated experimentally. The set-up allows both low fluctuation rates (down to 8%), and high microscale Reynolds numbers, (up to 1 150). The forced Kolmogorov equation is found to apply accurately. Similar to another flow configuration (counter rotating flow case [1]), the analysis of the flatness factor evolution with the Reynolds number reveals a transitional behavior around 650. Received 26 August 1999 and Received in final form 28 August 2000     

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.     

Persistency of material element deformation in isotropic flows and growth rate of lines and surfaces

We explore the consequence of isotropy on the growth of material lines and surfaces in complex flows. We show that the key parameter is the persistency , defined as the product of a typical stretching rate to its associated coherence time . In particular, we derive the dependence of the net growth rate of both lines and surfaces on . Their growth rates increase strongly with increasing persistencies for small , and then saturate for . Making use of measurements of Girimaji and Pope [1], we estimate the persistency to be of order 1 in isotropic turbulence. We then comment on the evolution of the shape of an initially spherical material blob. While its length increases, one of its tranverse dimension increases slowly and the other one decreases. This quasi-two-dimensional deformation leads a final ribbon-shape. Received 10 November 1999 and Received in final form 14 August 2000     

A statistical estimator of turbulence intermittency in physical and numerical experiments

The velocity increments statistic in various turbulent flows is analysed through the hypothesis that different scales are linked by a multiplicative process, of which multiplier is infinitely divisible. This generalisation of the Kolmogorov-Obukhov theory is compatible with the finite Reynolds number value of real flows, thus ensuring safe extrapolation to the infinite Reynolds limit. It exhibits a estimator universally depending on the Reynolds number of the flow, with the same law either for Direct Numerical Simulations or experiments, both for transverse and longitudinal increments. As an application of this result, the inverse dependence is used to define an unbiased value for a Large Eddy Simulation from the resolved scales velocity statistics. However, the exact shape of the multiplicative process, though independent of the Reynolds number for a given experimental setup, is found to depend significantly on this setup and on the nature of the increment, longitudinal or transverse. The asymmetry of longitudinal velocity increments probability density functions exhibits similarly a dependence with the experimental setup, but also systematically depends on the Reynolds number. Received 7 January 2000 and Received in final form 17 March 2000     

Scaling in large Prandtl number turbulent thermal convection

We study the scaling properties of heat transfer Nu in turbulent thermal convection at large Prandtl number Pr using a quasi-linear theory. We show that two regimes arise, depending on the Reynolds number Re. At low Reynolds number, NuPr ^-1/2 and Re are a function of RaPr ^-3/2. At large Reynolds number NuPr ^1/3 and RePr are function only of RaPr ^2/3 (within logarithmic corrections). In practice, since Nu is always close to Ra ^1/3, this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Reynolds number. This difference may solve an existing controversy between measurements in SF₆ (large Re) and in alcohol/water (lower Re). We link these regimes with a possible global bifurcation in the turbulent mean flow. We further show how a scaling theory could be used to describe these two regimes through a single universal function. This function presents a bimodal character for intermediate range of Reynolds number. We explain this bimodality in term of two dissipation regimes, one in which fluctuation dominate, and one in which mean flow dominates. Altogether, our results provide a six parameters fit of the curve Nu(Ra, Pr) which may be used to describe all measurements at Pr≥0.7. Received 27 February 2002 / Received in final form 29 May 2002 Published online 31 July 2002     

Angle-of-arrival variance’s dependence on the aperture size for indoor convective turbulence

We analyze the angle-of-arrival variance of an expanded and collimated laser beam once it has traveled through an indoor convective turbulence. A continuous position detector is set at the focus of a lens collecting the laser beam. The effect of the different turbulent scales, between the inner and the outer scales, is studied by changing the diameter of a circular pupil before the collector lens. The experimental optical setup follows the design introduced by Masciadri and Vernin [Appl. Opt., 36(6) (1997) 1320]. Tilt data measurements are studied using the fractional Brownian motion model for the turbulent wave-front phase introduced in a previous paper [Pérez et al., J. Opt. Soc. Am. A 21(10) (2004) 1962]. The Hurst exponents associated to different strengths of turbulence are obtained from the here proposed D^2H−2 dependence.     

Stabilized finite element method for incompressible flows with high Reynolds number

In the following paper, we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3D time-dependent incompressible Navier–Stokes equations. The proposed method starts by the use of a finite element variational multiscale (VMS) method, which consists in here of a decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. This choice of decomposition is shown to be favorable for simulating flows at high Reynolds number. We explore the behaviour and accuracy of the proposed approximation on three test cases. First, the lid-driven square cavity at Reynolds number up to 50,000 is compared with the highly resolved numerical simulations and second, the lid-driven cubic cavity up to Re = 12,000 is compared with the experimental data. Finally, we study the flow over a 2D backward-facing step at Re = 42,000. Results show that the present implementation is able to exhibit good stability and accuracy properties for high Reynolds number flows with unstructured meshes.     

Levels of complexity in turbulent time series for weakly and high Reynolds number

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold’s number in inertial range. Further, we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents.     

A restricted nonlinear large eddy simulation model for high Reynolds number flows

Recent numerical studies of the restricted nonlinear (RNL) model have demonstrated its ability to reproduce important features of wall turbulence despite a severe reduction in the number of degrees of freedom. In these prior studies, the RNL model included full resolution of the viscous term. In this work, we extend the RNL model to arbitrarily high Reynolds numbers by developing a RNL large eddy simulation (LES) framework along with a method to systematically identify an appropriate streamwise wavenumber support based on spectral properties of wall turbulence. This method leads to a band-limited RNL–LES system which is successful in reproducing some of the most important statistical features captured in previous low to moderate Reynolds number simulations, e.g. the mean velocity and second-order moment profiles. The RNL–LES framework offers a new approach to understanding the connection between coherent structures and the momentum transfer mechanisms of wall turbulence at arbitrarily high Reynolds numbers, where resolution of the viscous terms can become computationally expensive even with the relatively low computational complexity afforded through the dynamical restriction of the RNL model.     

Lagrangian and Eulerian velocity intermittency

Usual turbulence experiments, based on the Taylor hypothesis, differ from true Eulerian measurements. This is the origin of the apparent discrepancy between a recent two point correlation analysis and the multiplicative cascade picture. Indeed, both Eulerian and Lagrangian observations perfectly agree with this picture. Received 19 June 2002 / Received in final form 29 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: bcastain@ens-lyon.fr