scholarly journals Passive scalar decay laws in isotropic turbulence: Prandtl number effects

2015 ◽  
Vol 784 ◽  
pp. 274-303 ◽  
Author(s):  
A. Briard ◽  
T. Gomez ◽  
P. Sagaut ◽  
S. Memari
Keyword(s):  
Isotropic Turbulence ◽  
Power Laws ◽  
Passive Scalar ◽  
Initial Position ◽  
Scalar Dissipation ◽  
Integral Scale ◽  
Temporal Decay ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Reynolds

The passive scalar dynamics in a freely decaying turbulent flow is studied. The classical framework of homogeneous isotropic turbulence without forcing is considered. Both low and high Reynolds number regimes are investigated for very small and very large Prandtl numbers. The long time behaviours of integrated quantities such as the scalar variance or the scalar dissipation rate are analysed by considering that the decay follows power laws. This study addresses three major topics. First, the Comte-Bellot and Corrsin (CBC) dimensional analysis for the temporal decay exponents is extended to the case of a passive scalar when the permanence of large eddies is broken. Secondly, using numerical simulations based on an eddy-damped quasi-normal Markovian (EDQNM) model, the time evolution of integrated quantities is accurately determined for a wide range of Reynolds and Prandtl numbers. These simulations show that, whatever the values of the Reynolds and the Prandtl numbers are, the decay follows an algebraic law with an exponent very close to the value predicted by the CBC theory. Finally, the initial position of the scalar integral scale$L_{T}$has no influence on the asymptotic values of the decay exponents, and an analytical law predicting the relative positions of the kinetic and scalar spectra peaks is derived.

Experimental evidence for the theory of local isotropy

1948 ◽  
Vol 44 (4) ◽  
pp. 560-565 ◽  
Author(s):  
A. A. Townsend ◽  
Geoffrey Taylor
Keyword(s):  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Integral Scale ◽  
Local Isotropy ◽  
High Reynolds Numbers ◽  
Wide Range ◽  
Skewness Factor ◽  
High Reynolds ◽  
Image Position

Some new measurements of isotropic turbulence produced behind a biplane grid have been made at high Reynolds numbers, and these results are compared with the predictions of the theory of local isotropy developed by A. N. Kolmogoroff. The transverse double-velocity correlation has been measured at mesh Reynolds numbers up to 3·2 × 105, and the observed form agrees well with the predicted form. Measurements of the skewness factor of velocity differences over finite intervals have also been made, and the factor is nearly constant and equal to −0·38, if the interval is small compared with the integral scale. The invariance of dimensionless functions of the velocity derivatives has been confirmed for the flattening factor of ∂u/∂x, namely,which is nearly constant over a wide range of conditions. It is concluded that the theory of local isotropy is substantially correct for isotropic turbulence of high Reynolds number.

scholarly journals Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

2016 ◽  
Vol 799 ◽  
pp. 159-199 ◽  
Author(s):  
A. Briard ◽  
T. Gomez ◽  
C. Cambon
Keyword(s):  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Homogeneous Isotropic Turbulence ◽  
Scalar Flux ◽  
Anisotropic Turbulence ◽  
Theoretical Predictions ◽  
High Reynolds ◽  
Shear Driven Flows ◽  
Very High

The present work aims at developing a spectral model for a passive scalar field and its associated scalar flux in homogeneous anisotropic turbulence. This is achieved using the paradigm of eddy-damped quasi-normal Markovian (EDQNM) closure extended to anisotropic flows. In order to assess the validity of this approach, the model is compared to several detailed direct numerical simulations (DNS) and experiments of shear-driven flows and isotropic turbulence with a mean scalar gradient at moderate Reynolds numbers. This anisotropic modelling is then used to investigate the passive scalar dynamics at very high Reynolds numbers. In the framework of homogeneous isotropic turbulence submitted to a mean scalar gradient, decay and growth exponents for the cospectrum and scalar energies are obtained analytically and assessed numerically thanks to EDQNM closure. With the additional presence of a mean shear, the scaling of the scalar flux and passive scalar spectra in the inertial range are investigated and confirm recent theoretical predictions. Finally, it is found that, in shear-driven flows, the small scales of the scalar second-order moments progressively return to isotropy when the Reynolds number increases.

Effect of Schmidt number on small-scale passive scalar turbulence

2003 ◽  
Vol 56 (6) ◽  
pp. 615-632 ◽  
Author(s):  
RA Antonia ◽  
P Orlandi
Keyword(s):  
Turbulent Flows ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Passive Scalars ◽  
First Case ◽  
Decaying Turbulence

Previous reviews of the behavior of passive scalars which are convected and mixed by turbulent flows have focused primarily on the case when the Prandtl number Pr, or more generally, the Schmidt number Sc is around 1. The present review considers the extra effects which arise when Sc differs from 1. It focuses mainly on information obtained from direct numerical simulations of homogeneous isotropic turbulence which either decays or is maintained in steady state. The first case is of interest since it has attracted significant theoretical attention and can be related to decaying turbulence downstream of a grid. Topics covered in the review include spectra and structure functions of the scalar, the topology and isotropy of the small-scale scalar field, as well as the correlation between the fluctuating rate of strain and the scalar dissipation rate. In each case, the emphasis is on the dependence with respect to Sc. There are as yet unexplained differences between results on forced and unforced simulations of homogeneous isotropic turbulence. There are 144 references cited in this review article.

Influence of flow topology and dilatation on scalar mixing in compressible turbulence

2016 ◽  
Vol 793 ◽  
pp. 633-655 ◽  
Author(s):  
Mohammad Danish ◽  
Sawan Suman ◽  
Sharath S. Girimaji
Keyword(s):  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Compressible Turbulence ◽  
Scalar Dissipation ◽  
Stable Node ◽  
Scalar Mixing ◽  
Flow Topology ◽  
Local Flow ◽  
Amplification Mechanism ◽  
Almost All

The kinematics of passive scalar mixing and its relation to local flow topology and dilatation in compressible turbulence are examined using direct numerical simulations (DNS) of decaying isotropic turbulence. The main objective of this work is to characterize the dependence of various evolution mechanisms of scalar dissipation on local streamline topology and normalized dilatation. The DNS results indicate that the topology has a stronger influence on the nonlinear amplification mechanism than the dilatation level of a fluid element. In its appropriately normalized form, the amplification mechanism is found to be fairly independent of the Mach and Reynolds numbers. Non-focal topologies (the so called unstable-node/saddle/saddle and stable-node/saddle/saddle) are found to be associated with more intense mixing than the focal topologies at almost all dilatation levels. Alignment tendencies (jointly conditioned upon topology and dilatation) between the scalar-gradient vector and the strain-rate eigenvectors are shown to play a key role in shaping the observed behaviour in compressible turbulence. Finally, some modelling implications of these findings are discussed.

Self-similar enstrophy divergence in a shell model of isotropic turbulence

2002 ◽  
Vol 463 ◽  
pp. 241-258 ◽  
Author(s):  
M. V. MELANDER ◽  
B. R. FABIJONAS
Keyword(s):  
Shell Model ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Continuous Functions ◽  
Inertial Range ◽  
Inviscid Limit ◽  
Integral Scale ◽  
High Reynolds ◽  
Viscous Solutions ◽  
High Wavenumbers

We focus on the early evolution of energy E and enstrophy Z when the dissipation grows in significance from negligible to important. By considering a sequence of viscous shell model solutions we find that both energy and dissipation are continuous functions of time in the inviscid limit. Inviscidly, Z takes only a finite time t* to diverge, where t* depends on initial conditions. For viscous solutions, Z peaks long after t*, but the inflection point for Z(t) provides an excellent approximation to t*. Near t*, all of our high Reynolds number solutions obey the formula ναdZ/dt = F(νβZ). Neither the function F nor the constants α and β depend on initial conditions. We use F to obtain the inviscid limit. The energy spectrum remains concave down on double logarithmic scales until t*. At t*, the spectrum becomes algebraic at high wavenumbers, i.e. E(k, t*) ∼ C0kα. Crucially, the spectral slope σ is steeper than −5/3. Thus, we conclude that the inviscid singularity at t* is not associated with the establishment of a semi-infinite Kolmogorov range. For viscous solutions, the −5/3 range builds gradually after t* starting from high wavenumbers, and Z peaks when the inertial range reaches the integral scale. Thus, the formation of the inertial range is a viscous process in our shell model.

A numerical comparison of velocity-based and strain-based Lagrangian-history turbulence approximations

1979 ◽  
Vol 91 (3) ◽  
pp. 581-597 ◽  
Author(s):  
Jackson R. Herring ◽  
Robert H. Kraichnan
Keyword(s):  
Isotropic Turbulence ◽  
Direct Interaction ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Numerical Comparison ◽  
The Difference ◽  
High Reynolds ◽  
High Wavenumbers

The abridged Langrangian-history direct-interaction (ALHDI) approximation (Kraichnan 1966) and the strain-based abridged Lagrangian-history direct-interaction (SBALHDI) approximation (Kraichnan & Herring 1978) are integrated numerically for isotropic turbulence in two and three dimensions and compared with data. At moderate Reynolds numbers in three dimensions, comparison with the computer simulations by Orszag & Patterson (1972) shows that the ALHDI gives numerically excessive energy transfer in the dissipation range while the SBALHDI approximation displays satisfactory accuracy in all ranges. In two dimensions, both approximations are in reasonable agreement with the simulations of Herring et al. (1974), the ALHDI approximation showing the better accuracy of the two at low wavenumbers. At high wavenumbers the SBALHDI approximation again transfers less energy than the ALHDI approximation but the effect is less marked than in three dimensions and the two curves straddle the data. High Reynolds number integrations of both approximations in three dimensions agree well with the tidal-channel inertial- and dissipationrange data of Grant, Stewart & Moilliet (1962), the SBALHDI approximation yielding a somewhat larger value of Kolmogorov's constant than the ALHDI approximation. The origin of the difference in straining efficiency between the two approximations at high wavenumbers and of the dependence of this difference on dimensionality is exhibited by application to the stretching of small scales of a convected passive scalar field. In three dimensions the SBALHDI approximation gives markedly larger values of the constant in Batchelor's (1959) k−1 spectrum range than the ALHDI approximation and is in better agreement with experiment. The SBALHDI values of Batchelor's constant satisfy Gibson's (1968) lower bound while the ALHDI values do not.

Direct Numerical Simulation of Mixing of a Passive in Decaying Turbulence

1999 ◽  
Author(s):  
P. Deb ◽  
Pradip Majumdar
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Step Method ◽  
Fractional Step Method ◽  
Mixing Processes ◽  
Turbulent Reactive Flows ◽  
Decaying Turbulence

Abstract Research on turbulent mixing processes is of great interest to those working on turbulent-reactive flows. In this paper, a detailed study has been performed for the evolution of scalar fields of different initial integral scales in decaying, homogeneous and isotropic turbulence using DNS technique. Passive scalar mixing in a cubical decaying, homogeneous, isotropic turbulence field is considered. The three-dimensional incompressible Navier-Stokes equations together with scalar equation are solved using Fractional Step Method. The convective and diffusive terms in governing equations are discretised by Compact Finite Difference Scheme. The 32 × 32 × 32 uniform staggered grids are used. The present simulation is performed at Taylor Reynolds number of 28.83. In this paper, the evolution of scalar RMS and scalar dissipation rate for different integral length scales has been presented. The initial velocity vector and Probability Density Function (PDF) of scalar at different eddy turn over time have also been presented.

Velocity, scalar and transfer spectra in numerical turbulence

1990 ◽  
Vol 211 ◽  
pp. 309-332 ◽  
Author(s):  
Robert M. Kerr
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Exponential Tails ◽  
Grid Points ◽  
Prandtl Numbers ◽  
Dimensional Simulation ◽  
Velocity Spectra ◽  
Kolmogorov Constant

Velocity and passive-scalar spectra for turbulent fields generated by a forced three-dimensional simulation with 1283 grid points and Taylor-microscale Reynolds numbers up to 83 are shown to have convective and diffusive spectral regimes. One-and three-dimensional spectra are compared with experiment and theory. If normalized by the Kolmogorov dissipation scales and scalar dissipation, velocity spectra and scalar spectra for given Prandtl numbers collapse to single curves in the dissipation regime with exponential tails. If multiplied by k⅗ the velocity spectra show an anomalously high Kolmogorov constant that is consistent with low Reynolds number experiments. When normalized by the Batchelor scales, the scalar spectra show a universal dissipation regime that is independent of Prandtl numbers from 0.1 to 1.0. The time development of velocity spectra is illustrated by energy-transfer spectra in which distinct pulses propagate to high wavenumbers.

The integral scale in homogeneous isotropic turbulence

2002 ◽  
Vol 459 ◽  
pp. 429-443 ◽  
Author(s):  
HONGLU WANG ◽  
WILLIAM K. GEORGE
Keyword(s):  
Isotropic Turbulence ◽  
Power Laws ◽  
Spectral Model ◽  
Homogeneous Isotropic Turbulence ◽  
Integral Scale ◽  
Integral Scales ◽  
Order Of Magnitude ◽  
Decaying Turbulence ◽  
Statistical Sample ◽  
Almost All

A simple spectral model is used to examine what is required to determine the energy and integral scale in homogeneous isotropic turbulence. The problem is that these are determined in part by the largest scales of the turbulence which are either not simulated at all by DNS or experiments, or cannot be estimated because of an insufficient statistical sample. The absence of scales an order of magnitude below the peak in the energy spectrum is shown to affect the determination significantly. Since this energy peak shifts to lower wavenumbers as the flow evolves, the problem becomes progressively worse during decay. It is suggested that almost all reported integral scales for isotropic decaying turbulence are questionable, and that the power laws fitted to them are seriously in error. Approximate correction using the spectral model shows that recent DNS data which decay as u2 ∝ tn with constant n, are also consistent with L ∝ t1/2.

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