High wavenumber spectrum of a passive scalar in isotropic turbulence

1986 ◽  
Vol 29 (5) ◽  
pp. 1734 ◽  
Author(s):  
A. F. Bennett
Keyword(s):  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Wavenumber Spectrum

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.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

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.

scholarly journals Dependence of the non-stationary form of Yaglom’s equation on the Schmidt number

2002 ◽  
Vol 451 ◽  
pp. 99-108 ◽  
Author(s):  
P. ORLANDI ◽  
R. A. ANTONIA
Keyword(s):  
Dynamic Equation ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Second Order ◽  
Order Moment ◽  
Length Scale ◽  
Stationary Form

The dynamic equation for the second-order moment of a passive scalar increment is investigated in the context of DNS data for decaying isotropic turbulence at several values of the Schmidt number Sc, between 0.07 and 7. When the terms of the equation are normalized using Kolmogorov and Batchelor scales, approximate independence from Sc is achieved at sufficiently small r/ηB (r is the separation across which the increment is estimated and ηB is the Batchelor length scale). The results imply approximate independence of the mixed velocity-scalar derivative skewness from Sc and underline the importance of the non-stationarity. At small r/ηB, the contribution from the non-stationarity increases as Sc increases.

A consequence of the zero fourth cumulant approximation

1962 ◽  
Vol 13 (3) ◽  
pp. 369-382 ◽  
Author(s):  
Edward E. O'Brien ◽  
George C. Francis
Keyword(s):  
Energy Spectrum ◽  
Numerical Computation ◽  
Root Mean Square ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Passive Scalar ◽  
Turbulent Energy ◽  
Length Scale ◽  
Mean Square ◽  
Stationary Turbulence

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.

Diffusion of weak magnetic fields by isotropic turbulence

1976 ◽  
Vol 75 (4) ◽  
pp. 657-676 ◽  
Author(s):  
Robert H. Kraichnan
Keyword(s):  
Velocity Field ◽  
Magnetic Fields ◽  
System Analysis ◽  
Isotropic Turbulence ◽  
Direct Interaction ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Negative Contribution ◽  
Weak Magnetic Fields ◽  
Magnetic Diffusivity

The diffusion of slowly varying, weak magnetic fields by a statistically isotropic and stationary velocity field in a perfectly conducting fluid is studied by Eulerian analysis. The characteristic wavenumber and variance of the velocity field are k0 and 3v20, thus defining the eddy-circulation time τ0 = 1/v0k0. The velocity field is assumed constant on intervals of duration 2τ1 and statistically independent for distinct intervals. Thus the correlation time is τ1. The α-effect dynamo mechanism in the quasi-linear approximation is corroborated. Both the quasilinear and the direct-interaction approximations give identical diffusion of magnetic and passive scalar fields in reflexionally invariant turbulence. This result is found to be exact for τ1/τ0 → 0 but is demonstrated to be incorrect in general for finite τ1/τ0 because of effects of helicity fluctuations. The nature of the failure of the direct-interaction approximation is exhibited by an exactly soluble model system. Analysis based on a double-averaging device shows that longrange, persistent helicity fluctuations in reflexionally invariant turbulence give an anomalous negative contribution to the magnetic diffusivity which depends on the helicity covariance function. We term this the α2 effect. The magnitude of the effect depends sensitively on the turbulence statistics. If the characteristic scales of the helicity fluctuations are sufficiently larger than τ0 and 1/k0, the magnetic diffusivity is negative, implying unstable growth, while a passive scalar field diffuses normally. On the other hand, a crude estimate suggests that the α2 effect is small in normally distributed turbulence.

Sign in / Sign up

Export Citation Format

Share Document