A turbulence characteristic length scale for compressible flows

The current RANS models are generally established and calibrated under incompressible condition and these kinds of models could succeed in predicting many features of incompressible flows. However, these models extended to the high-speed, compressible flows are always less accurate. In the paper, a compressible von Kármán length scale is proposed for compressible flows considering the variable densities. It contains no empirical coefficients and is based on phenomenological theory. In the turbulent kinetic equation, the extra unclosed terms induced by non-constant densities are treated as dissipation terms and the equation is closed algebraically via the introduction of the von Kármán length scale. The original and the proposed von Kármán length scale lead to two different kinds of SAS (scale adaption simulation) models, KDO (turbulence kinetic energy dependent only) and CKDO (compressible KDO), respectively. Compressible mixing layer with significant compressibility is studied within standard k–?, k–ω, KDO turbulence models and their compressible versions. The compressibility effects such as the reduced mixing layer thickness, growth rate and turbulence intensity can be reproduced by CKDO. The new length scale can improve the performances of the model in predicting the mixing layer thickness, stream-wise velocity and Reynolds shear stresses when the convective Mach number is 0.8. Besides, the new length scale also leads to accurate computed growth rate when the convective Mach number ranges from 0.1 to 1.0.     

Incompressible turbulence as non-local field theory

It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.     

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.     

Intermittency in the enstrophy cascade of two-dimensional fully developed turbulence: Universal features

Intermittency (externally induced) in the two-dimensional (2D) enstrophy cascade is shown to be able to maintain a finite enstrophy along with a vorticity conservation anomaly. Intermittency mechanisms of three-dimensional (3D) energy cascade and 2D enstrophy cascade in fully developed turbulence (FDT) seem to have some universal features. The parabolic-profile approximation (PPA) for the singularity spectrum f(α) in multi-fractal model is used and extended to the appropriate microscale regimes to exhibit these features. The PPA is also shown to afford, unlike the generic multi-fractal model, an analytical calculation of probability distribution functions (PDF) of flow-variable gradients in these FDT cases and to describe intermittency corrections that complement those provided by the homogeneous-fractal model.     

On the generation and maintenance of waves and turbulence in simulations of free-surface turbulence

One of the challenges in numerical simulation of wave–turbulence interaction is the precise setup and maintenance of wave and turbulence fields. In this paper, we investigate techniques for the generation and suppression of specific surface wave modes, the generation of turbulence in an inhomogeneous physical domain with a wavy boundary-fitted grid, and the generation and maintenance of waves and turbulence during the complex wave–turbulence interaction process. We apply surface pressure to generate and suppress waves. Based on the solution of linearized Cauchy–Poisson problem, we derive three pressure expressions, which lead to a δ-function method, a time-segment method, and a gradual method. Numerical experiments show that these methods generate waves as specified and eliminate spurious waves effectively. The nonlinear wave effect is accounted for with a time-relaxation method. For turbulence generation, we extend the linear forcing method to an inhomogeneous physical domain with a curvilinear computational grid. Effects of force distribution and computational grid distortion are examined. For wave–turbulence interaction, we develop an algorithm to instantaneously identify specific progressive and standing waves. To precisely control the wave amplitude in a complex turbulent flow field, we further develop an energy controlling method. Finally, a simulation example of wave–turbulence interaction is presented. Results show that turbulence has unique features in the presence of waves. Velocity fluctuations are found to be strongly dependent on the wave phase; variations of these fluctuations are explained by the pressure–strain correlation associated with the wave-induced strain field.     

Autocorrelation function formulations and the turbulence dissipation rate: Application to dispersion models

The classical statistical diffusion theory and the binomial autocorrelation function are used to obtain a new formulation for the turbulence dissipation rate ε. The approach employs the Maclaurin series expansion of a logarithm function contained in the dispersion parameter formulation. The numerical coefficient of this new relation for ε is 100% larger than the numerical coefficient of the classical relation derived from the exponential autocorrelation function. A similar approach shows that the dispersion parameter obtained from the even exponential autocorrelation function does not result in a relation for ε and, therefore, is not suitable for application in dispersion models. In addition, a statistical comparison to experimental ground-level concentration data demonstrates that this newly derived relation for ε as well as other formulations for the turbulence dissipation rate are suitable for application in Lagrangian stochastic dispersion models. Therefore, the analysis shows that there is an uncertainty regarding the turbulence dissipation rate function form and the autocorrelation function form.     

Kolmogorov dispersion for turbulence in porous media: A conjecture

We will utilise the self-avoiding walk (SAW) mapping of the vortex line conformations in turbulence to get the Kolmogorov scale dependence of energy dispersion from SAW statistics, and the knowledge of the effects of disordered fractal geometries on the SAW statistics. These will give us the Kolmogorov energy dispersion exponent value for turbulence in porous media in terms of the size exponent for polymers in the same. We argue that the exponent value will be somewhat less than for turbulence in porous media.     

Large-eddy simulations of fluid and magnetohydrodynamic turbulence using renormalized parameters

In this paper a procedure for large-eddy simulation (LES) has been devised for fluid and magnetohydrodynamic turbulence in Fourier space using the renormalized parameters. The parameters calculated using field theory have been taken from recent papers by Verma [1,2]. We have carried out LES on 64³ grid. These results match quite well with direct numerical simulations of 128³. We show that proper choice of parameter is necessary in LES.     

Single-scale wavelet representation of turbulence dynamics: Formulation and Navier-Stokes regularity

The ‘triad interactions’, arising from the spectral resolution of the nonlinear terms in the Navier-Stokes equations, have so far not been substantially modified in the wavelet representation. In this paper, the multiscale interactions are captured by exact expressions evaluated at a single scale of the Mexican hat wavelet coefficients: the larger-scale terms as a volume integral of nearby wavelet coefficients, and the smaller-scale contributions as iterated Laplacians of the coefficient at the point of interest. As a result, the Navier-Stokes equations are expressed exactly at a single scale. This facilitates the evaluation of the dominant Hölder exponent near singularities. From the scaling properties of wavelet coefficients, it is shown that Euler dynamics would generate stronger singularities for any h<1, but that viscous dynamics would not unless h<−1 (a discontinuous case). We discuss how this conclusion could be affected by boundary conditions.     

Density-PDFs and Lagrangian statistics of highly compressible turbulence

In isothermal, highly compressible turbulent flows, density fluctuations follow a log-normal distribution. We establish a connection between these density fluctuations and the probability-density-functions (PDF) of Lagrangian tracer particles advected with the flow. Our predicted particle statistics is tested against large scale numerical simulations, which were performed with 512³ collocation points and 2 million tracer particles integrated over several dynamical times.     

交变暨静态剪切流对湍流抑制的互斥性分析

把剪切流对湍流抑制的解析理论应用于同时包含静态剪切流和周期交变剪切流的情况。所得到的结果表明：当两者单独存在时对湍流有定量上大体相同的抑制效应;当两者同时存在时对湍流的抑制效应不仅不是简单的迭加,反而在很大的区域上呈现互相削弱的趋势,特别是这种互斥性在两种剪切流强度相等时为最大。这与Maeyama等人的数值模拟结果相符合-。采用的渐近理论平均法表明导致两种剪切流在抑制湍流上不对等是由交变剪切流与它所诱发的交变相对位移之间的耦合所造成。     

Speckle photography applied to statistical analysis of turbulence

A speckle photographic technique is used for visualizing the planar distribution of the refractive deflection angles of light transmitted through the compressible turbulent flow. Both double and single (prolonged) exposure speckle photography are applied for statistical analysis of such flows. Using single (prolonged) exposure speckle photography (SPESP), instantaneous quantitative measurement of 2-D distribution of turbulence intensity in a flame is performed. Anisotropy of turbulence is visualized by a diffraction halo form and quantitatively evaluated by measuring the diffraction halo diameters. Using double exposure speckle photography (DESP), quantitative visualization of the planar distribution of the refractive deflection angles of the light transmitted through the compressible turbulent flow is done. Turbulent structures are visible in the patterns of the deflection angles isolines. The 2-D correlation functions of these deflection angles are constructed and analyzed. The 3-D density correlation functions are evaluated using the Erbeck–Merzkirch integral transformation.     

Is there screening in turbulence?

The statistical mechanics of some electric models predicts exponential decay of space correlations (screening). This suggests that one look also for screening in 2- and 3-dimensional hydrodynamic turbulence.     

Contribution to the nonlinear theory of sound and hydrodynamic turbulence of a compressible liquid

The interaction of sound with hydrodynamic turbulence has been studied in detail. The sound absorption decrement, the correlation time and length and the frequency diffusion coefficient for the acoustic wave packet are calculated. The spectral composition of the sound radiated by a unit, turbulent volume and the spectral energy density of sound in equilibrium with the turbulence are studied. The region of applicability of the kinetic equation for sound with a linear dispersion low is found.     

Statistics and structures of pressure and density in compressible isotropic turbulence

We study statistics and structures of pressure and density in the presence of large-scale shock waves in a forced compressible isotropic turbulence using high-resolution numerical simulation. The spectra for pressure and density exhibit a ?2 scaling over an operational definition of the inertial range. Both the numerical simulation and a heuristic PDF model reveal that the PDFs of pressure increment exhibit a ?2 power law region for the separation in the operational definition of inertial range, quantitatively similar to the PDF of pressure gradient, which also displays a ?2 power law region. Moreover, the statistical relation between density increment and pressure increment has been investigated through a shock-relation model. There is a positive correlation between the vorticity magnitude and pressure, which is different from the case of incompressible turbulence. We argue that this difference is due to large-scale shock waves, another type of intermittent structures in addition to vortex structures in incompressible turbulence.     

Matrix formulation of hydrodynamics and extension of ptolemaic flows to three-dimensional motions

A new matrix formulation of Lagrange hydrodynamic equations is proposed. Exact solutions of those equations are obtained in matrix form. It is found that precession of vortex lines around some fixed axis in space is a general property of the flows described by those solutions. Two types of fluid motion are studied. Flows of the first type have straight vortex lines, and their particle trajectories are windings on toroidal surfaces. The other flows have plane particle trajectories, and their vortex lines are arbitrarily shaped plane curves. All these motions are shown to be three-dimensional generalizations of plane Ptolemaic flows [1,2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, pp. 783–796, June, 1996.The authors express their gratitude to the Russian Foundation for Fundamental Research for support of these investigations under Grant No. 96-01-00585 and to INTAS Foundation for support under Grant No. 93-1373.     

Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received signal, affecting link performance.Influence of Kolmogorov and non-Kolmogorov turbulence statistics on laser communication links are analyzed for different propagation scenarios, and effects of different turbulence spectrum models on optical communication links are presented. Statistical estimates of the communication parameters such as the probability of fade (miss) exceeding a threshold dB level, the mean number of fades, and BER are derived and examples provided. The presented quantitative data suggest that the non-Kolmogorov turbulence effects on lasercom channels are more severe in many situations and need to be taken into account in wireless optical communication. Non-Kolmogorov turbulence is especially important for elevations above the boundary layer as well as for even low elevation paths over water.