Axisymmetric form of Kármán-Howarth equation and its limiting forms

Kinematics and dynamics of homogeneous axisymmetric turbulence have been derived with the assumption that the properties of the turbulence are invariant with respect to rotation about a preferred direction . In particular, the “axisymmetric" equivalent of Karman-Howarth “isotropic" equation is derived using Lindborg's representation of the two-point correlation tensors of homogeneous axisymmetric turbulence. When the more constraining assumption of isotropy is made, this equation reduces to the well-known Karman-Howarth equation. There are two interesting limiting forms of the axisymmetric Karman-Howarth equation: the axisymmetric form of the energy balance equation and the axisymmetric form of the vorticity balance equation. Received 1 July 1999 and Received in final form 9 November 1999     

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.     

Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k⁻¹ spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f (α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.     

Quasi-stationary states in a circular geometry

The quasi-stationary final states of decaying two-dimensional turbulence on a circular domain, with an initial flow field containing either no or a substantial amount of angular momentum, have been investigated numerically. The production of angular momentum is almost absent for these flows on a circular domain with a no-slip wall. Its presence or absence essentially determines the character of the quasi-stationary final state. Based on a minimum-enstrophy principle a diagram is constructed that provides insight into the development of the typical late-time flow patterns on a circular domain with a no-slip wall. The quasi-stationary final states found in the present numerical study can be understood based on the predictions from the minimum-enstrophy principle.     

Curvature Effect on Compressible Turbulent Flow over a Wavy Wall

A fully developed compressible turbulent flow in a channel with a lower wavy wall and a upper plane wall is studied using large eddy simulation. We mainly attempt to deal with the curvature effect on compressible turbulent flow over the wavy wall. Some typical quantities including the mean turbulence statistics, dilatation and baroclinic terms in the enstrophy equation, turbulent kinetic energy budgets and the near-wall turbulent structures are analysed. The results obtained in this study provide physical insight into the understanding of the effects of curvature and compressibility on wall-bounded compressible turbulent flow.     

Upper bounds on the convective heat transport in a rotating fluid layer of infinite Prandtl number: case of large Taylor numbers

By means of the Howard-Busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport in a horizontal fluid layer heated from below and rotating about a vertical axis. We consider the interval of large Taylor numbers where the intermediate layers of the optimum fields expand in the direction of the corresponding internal layers. We consider the 1 - α-solution of the arising variational problem for the cases of rigid-stress-free, stress-free, and rigid boundary conditions. For each kind of boundary condition we discuss four cases: two cases where the boundary layers are thinner than the Ekman layers of the optimum field and two cases where the boundary layers are thicker than the Ekman layers. In most cases we use an improved solution of the Euler-Lagrange equations of the variational problem for the intermediate layers of the optimum fields. This solution leads to corrections of the thicknesses of the boundary layers of the optimum fields and to lower upper bounds on the convective heat transport in comparison to the bounds obtained by Chan [J. Fluid Mech. 64, 477 (1974)] and Hunter and Riahi [J. Fluid Mech. 72, 433 (1975)]. Compared to the existing experimental data for the case of a fluid layer with rigid boundaries the corresponding upper bounds on the convective heat transport is less than two times larger than the experimental results, the corresponding upper bound on the convective heat transport, obtained by Hunter and Riahi is about 10% higher than the bound obtained in this article. When Rayleigh number and Taylor number are high enough the upper bound on the convective heat transport ceases to depend on the boundary conditions. Received 30 January 2001 and Received in final form 28 May 2001     

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.     

Numerical tests of a new molecule-dependent momentum transport equation

It is shown that a new incompressible fluid equation is obtained by inclusion of a new dimensionless coupling parameter in the momentum transport equation derived in [L. Jirkovsky, L. Bo-ot, Momentum transport equation for the fluids using projection-perturbation formalism and onset of turbulence, Physica A 352 (2005) 241-251] from the Boltzmann kinetic equation where the Boltzmann collision integral includes inelastic interactions of quantum origin among the particles of the fluid. Numerical results from the equation for the plane and circular Poiseuille flows are consistent with the observations. The numerical tests also manifest a difference in the onset of turbulence between the flat plates and the circular pipe flow systems. Although all obtained velocity profiles are flattened at the center-a feature of turbulence-the results demonstrate greater stability of the velocity profiles in the circular pipe flow.     

On one-eighth law in unforced two-dimensional turbulence

We critically revisit the various attempts to prove one-eighth law in two-dimensional (2D) turbulence and reconcile them. Herein, the one-eighth law has been proved for unforced 2D incompressible high Reynolds number turbulence. An exact expression of the time derivative of two-point second order velocity correlation function is also derived for the enstrophy cascade dominated regime.     

Controlling Flow Turbulence Using Local Pinning Feedback

Flow turbulence control in two-dimensional Navier-Stokes equation is considered. By applying local pinning control only to a single component of flow velocity field, the flow turbulence can be controlled to desirable targets. It is found that with certain number of controllers there exist an optimal control strength at which control error takes minimum value, and larger and smaller control strengths give worse control efficiency. The physical mechanism underlying these strange control results is analysed based on the interactions between different types of modes.     

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     

Flame growth and wrinkling in a turbulent flow

High-speed planar laser-induced fluorescence (PLIF) and 3-D large eddy simulations (LES) are used to study turbulent flame kernel growth, wrinkling and the formation of separated flame pockets in methane/air mixtures. Turbulence was effected by a set of rotary fans situated in a cylindrical enclosure. Flame wrinkling was followed on sequential 2-D OH images captured at kHz repetition rates. Under stoichiometric conditions and low turbulence levels the flame kernel remains singly connected and close to spherical in shape. By increasing turbulence or reducing the stoichiometry of the mixture the formation of separated pockets could be observed and studied. The mechanisms behind these phenomena are investigated qualitatively by LES of a level-set G-equation describing the flame surface propagation in turbulent flows. Received: 12 April 2000 / Revised version: 26 June 2000 / Published online: 5 October 2000     

Supersonic Turbulent Boundary Layer： DNS and RANS

We assess the performance of a few turbulence models for Reynolds averaged Navier-Stokes （RANS） simulation of supersonic boundary layers, compared to the direct numerical simulations （DNS） of supersonic flat-plate turbulent boundary layers, carried out by Gao et al. [Chin. Phys. Lett. 22（2005）1709] and Huang et al. [Sci. Chin. 48 （2005） 614], as well as some available experimental data. The assessment is made for two test cases, with incoming Mach numbers and Reynolds numbers M = 2.25, Re = 365, 000//in, and M = 4.5, Re = 1.7 × 10^7/m, respectively. It is found that in the first case the prediction of RANS models agrees well with the DNS and the experimental data, while for the second case the agreement of the DNS models with experiment is less satisfactory. The compressibility effect on the RANS models is discussed.     

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.     

Multi-fractal formulation of compressible fully developed turbulence: Parabolic-profile approximation for the singularity spectrum

A parabolic-profile approximation (PPA) for the singularity spectrum D (h) in the multi-fractal model for compressible fully developed turbulence (FDT) is considered and is then extrapolated to the Kolmogorov microscale regime. The generalization of Kolmogorov’s “4/5th law” relating the third-order velocity structure function to the mean energy dissipation rate ε to compressible FDT is considered. The PPA is also shown to afford, unlike the generic multi-fractal model, an analytical calculation of probability distribution function (PDF) of velocity gradients and to describe intermittency corrections for this PDF that complement those provided by homogeneous-fractal model.     

Vortex Turbulence due to the Interplay of Filament Tension and Rotational Anisotropy

The mechanism of scroll wave turbulence is investigated in excitable media with rotational anisotropy. We adopt the Barkley model with heterogeneity in the diffusion constants. Through comparative numerical studies, we demonstrate the vortex turbulence results from the rotational anisotropy＇s cooperation with negative filament tension or competition with positive filament tension. The presence of rotational anisotropy can enlarge the parameter region leading to negative-tension induced wave turbulence in isotropic media.     

Minimum state for high Reynolds and Péclet number turbulent flows

Direct numerical simulations (DNS) or experiments for the very high Reynolds (Re) and Péclet (Pe) number flows commonly exceed the resolution possible even when use is made of the most advanced computer capability or most sophisticated diagnostics and physical capabilities of advanced laboratory facilities. In practice use is made of statistical flow data bases developed at the highest Re and Pe levels achievable within the currently available facility limitations. In addition, there is presently no metric to indicate whether and how much of the fully resolved physics of the flow of interest has been captured within the facilities available. In this Letter the authors develop the necessary metric criteria for homogeneous, isotropic and shear layer flows. It is based on establishing a smaller subset of the total range of dynamic scale interactions that will still faithfully reproduce all of the essential, significant, influences of the larger range of scale interactions. The work identifies a minimum significant Re and Pe level that must be obtained by DNS or experiment in order to capture all of the significant dynamic influences in data which is then scaleable to flows of interest. Hereafter this is called the minimum state. Determination of the minimum state is based on finding a minimum scale separation for the energy-containing scales of the flow and scalar fields sufficient to prevent contamination by interaction with the (non-universal) velocity dissipation and scalar diffusivity inertial range scale limits.     

Convective heat transport in a fluid layer of infinite Prandtl number: upper bounds for the case of rigid lower boundary and stress-free upper boundary

We present the theory of the multi--solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport is obtained. The highest bound is between the bounds for the case of a fluid layer with two rigid boundaries and for the case of a fluid layer with two stress-free boundaries. As an additional result of the presented theory we obtain small corrections of the boundary layer thicknesses of the optimum fields for the case of fluid layer with two rigid boundaries. These corrections lead to systematically lower upper bounds on the convective heat transport in comparison to the bounds obtained in [5]. Received 29 September 1999