A generalization of Yaglom's equation which accounts for the large-scale forcing in heated decaying turbulence

1999 ◽  
Vol 391 ◽  
pp. 359-372 ◽  
Author(s):  
L. DANAILA ◽  
F. ANSELMET ◽  
T. ZHOU ◽  
R. A. ANTONIA
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Second Order ◽  
Grid Turbulence ◽  
Third Order ◽  
Production Term ◽  
Decaying Turbulence ◽  
Energy Dissipated

In most real or numerically simulated turbulent flows, the energy dissipated at small scales is equal to that injected at very large scales, which are anisotropic. Despite this injection-scale anisotropy, one generally expects the inertial-range scales to be locally isotropic. For moderate Reynolds numbers, the isotropic relations between second-order and third-order moments for temperature (Yaglom's equation) or velocity increments (Kolmogorov's equation) are not respected, reflecting a non-negligible correlation between the scales responsible for the injection, the transfer and the dissipation of energy. In order to shed some light on the influence of the large scales on inertial-range properties, a generalization of Yaglom's equation is deduced and tested, in heated grid turbulence (Rλ=66). In this case, the main phenomenon responsible for the non-universal inertial-range behaviour is the non-stationarity of the second-order moments, acting as a negative production term.

scholarly journals Effects of initial conditions in decaying turbulence generated by passive grids

2007 ◽  
Vol 585 ◽  
pp. 395-420 ◽  
Author(s):  
P. LAVOIE ◽  
L. DJENIDI ◽  
R. A. ANTONIA
Keyword(s):  
Power Law ◽  
Large Scale ◽  
Velocity Structure ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Recent Analysis ◽  
Grid Turbulence ◽  
Power Law Exponent ◽  
Decaying Turbulence

The effects of initial conditions on grid turbulence are investigated for low to moderate Reynolds numbers. Four grid geometries are used to yield variations in initial conditions and a secondary contraction is introduced to improve the isotropy of the turbulence. The hot-wire measurements, believed to be the most detailed to date for this flow, indicate that initial conditions have a persistent impact on the large-scale organization of the flow over the length of the tunnel. The power-law coefficients, determined via an improved method, also depend on the initial conditions. For example, the power-law exponent m is affected by the various levels of large-scale organization and anisotropy generated by the different grids and the shape of the energy spectrum at low wavenumbers. However, the results show that these effects are primarily related to deviations between the turbulence produced in the wind tunnel and true decaying homogenous isotropic turbulence (HIT). Indeed, when isotropy is improved and the intensity of the large-scale periodicity, which is primarily associated with round-rod grids, is decreased, the importance of initial conditions on both the character of the turbulence and m is diminished. However, even in the case where the turbulence is nearly perfectly isotropic, m is not equal to −1, nor does it show an asymptotic trend in x towards this value, as suggested by recent analysis. Furthermore, the evolution of the second- and third-order velocity structure functions satisfies equilibrium similarity only approximately.

scholarly journals Dynamics of Convectively Driven Banded Jets in the Laboratory

2007 ◽  
Vol 64 (11) ◽  
pp. 4031-4052 ◽  
Author(s):  
Peter L. Read ◽  
Yasuhiro H. Yamazaki ◽  
Stephen R. Lewis ◽  
Paul D. Williams ◽  
Robin Wordsworth ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Large Scale ◽  
Zonal Flow ◽  
Inertial Range ◽  
Instability Criterion ◽  
Rossby Wave Breaking ◽  
Outer Planets ◽  
Zonal Jets ◽  
Geostrophic Turbulence

Abstract The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

Kolmogorov’s contributions to the physical and geometrical understanding of small-scale turbulence and recent developments

1991 ◽  
Vol 434 (1890) ◽  
pp. 183-210 ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Inertial Range ◽  
Small Scale ◽  
Small Scales ◽  
Recent Developments ◽  
Self Similar ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Non Gaussian

This paper reviews how Kolmogorov postulated for the first time the existence of a steady statistical state for small-scale turbulence, and its defining parameters of dissipation rate and kinematic viscosity. Thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes. We present theoretical arguments and experimental evidence to indicate when the small-scale motions might tend to a universal form (paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic), and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the - 5/3 inertial range spectrum. These may be particular forms of eddy or ‘eigenstructure’ such as spiral vortices, which may not be unique to turbulent flows. Also, they tend to lead to the notable spiral contours of scalars in turbulence, whose self-similar structure enables the ‘box-counting’ technique to be used to measure the ‘capacity’ D K of the contours themselves or of their intersections with lines, D' K . Although the capacity, a term invented by Kolmogorov (and studied thoroughly by Kolmogorov & Tikhomirov), is like the exponent 2 p of a spectrum in being a measure of the distribution of length scales ( D' K being related to 2 p in the limit of very high Reynolds numbers), the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the Reynolds number. Thus Kolmogorov & Tikhomirov provide the basis for a more widely applicable measure of the self-similar structure of turbulence. Finally, we also review how Kolmogorov’s concept of the universal spatial structure of the small scales, together with appropriate additional physical hypotheses, enables other aspects of turbulence to be understood at these scales; in particular the general forms of the temporal statistics such as the high-frequency (inertial range) spectra in eulerian and lagrangian frames of reference, and the perturbations to the small scales caused by non-isotropic, non-gaussian and inhomogeneous large-scale motions.

The Influence of Large-Scale High-Intensity Turbulence on Vane Heat Transfer

1997 ◽  
Vol 119 (1) ◽  
pp. 23-30 ◽  
Author(s):  
F. E. Ames
Keyword(s):  
Heat Transfer ◽  
High Intensity ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Surface Heat ◽  
Grid Turbulence ◽  
Stagnation Region ◽  
Linear Cascade ◽  
Pressure Surface ◽  
Scale Turbulence

An experimental research program was undertaken to examine the influence of large-scale high-intensity turbulence on vane heat transfer. The experiment was conducted in a four-vane linear cascade at exit Reynolds numbers of 500,000 and 800,000 based on chord length. Heat transfer measurements were made for four inlet turbulence conditions including a low turbulence case (Tu ≅ 1 percent), a grid turbulence case (Tu ≅ 7.5 percent), and two levels of large-scale turbulence generated with a mock combustor at two upstream locations (Tu ≅ 12 percent and 8 percent). The heat transfer data demonstrated that the length scale, Lu, has a significant effect on stagnation region and pressure surface heat transfer.

scholarly journals A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

2011 ◽  
Vol 681 ◽  
pp. 537-566 ◽  
Author(s):  
ROMAIN MATHIS ◽  
NICHOLAS HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Pressure Gradient ◽  
Turbulent Flows ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Gradient Flows ◽  
Streamwise Pressure Gradient ◽  
Logarithmic Region ◽  
Inner Region

A model is proposed with which the statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows are predicted from a measured large-scale velocity signature from an outer position in the logarithmic region of the flow. Results, including spectra and all moments up to sixth order, are shown and compared to experimental data for zero-pressure-gradient flows over a large range of Reynolds numbers. The model uses universal time-series and constants that were empirically determined from zero-pressure-gradient boundary layer data. In order to test the applicability of these for other flows, the model is also applied to channel, pipe and adverse-pressure-gradient flows. The results support the concept of a universal inner region that is modified through a modulation and superposition of the large-scale outer motions, which are specific to the geometry or imposed streamwise pressure gradient acting on the flow.

Structure of Turbulent Flows Over Forward Facing Steps With Adverse Pressure Gradient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Hassan Iftekhar ◽  
Martin Agelin-Chaab
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Turbulent Flows ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Step Height ◽  
Reattachment Length ◽  
Mean Velocity ◽  
The Mean

This paper reports an experimental study on the effects of adverse pressure gradient (APG) and Reynolds number on turbulent flows over a forward facing step (FFS) by employing three APGs and three Reynolds numbers. A particle image velocimetry (PIV) technique was used to conduct velocity measurements at several locations downstream, and the flow statistics up to 68 step heights are reported. The step height was maintained at 6 mm, and the Reynolds numbers based on the step height and freestream mean velocity were 1600, 3200, and 4800. The mean reattachment length increases with the increase in Reynolds number without the APG whereas the mean reattachment length remains constant for increasing APG. The proper orthogonal decomposition (POD) results confirmed that higher Reynolds numbers caused the large-scale structures to be more defined and organized close to the step surface.

scholarly journals Turbulent fluctuations above the buffer layer of wall-bounded flows

2008 ◽  
Vol 611 ◽  
pp. 215-236 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
SERGIO HOYAS
Keyword(s):  
Reynolds Number ◽  
Buffer Layer ◽  
Turbulent Flows ◽  
Large Scale ◽  
Pressure Fluctuations ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Normal Velocity ◽  
Channel Statistics

The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Reτ≤2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are ‘attached’ in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at http://torroja.dmt.upm.es/ftp/channels/.

Reynolds number scaling of inertial particle statistics in turbulent channel flows

2014 ◽  
Vol 758 ◽  
Author(s):  
Matteo Bernardini
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Organization ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Wall Region ◽  
Inertial Particles ◽  
Turbulent Channel Flows ◽  
Strong Segregation

AbstractThe effect of the Reynolds number on the behaviour of inertial particles in wall-bounded turbulent flows is investigated through large-scale direct numerical simulations (DNS) of particle-laden canonical channel flow spanning almost a decade in the friction Reynolds number, from $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau } = 150$ to $\mathit{Re}_{\tau } = 1000$. Lagrangian particle tracking is used to study the motion of six different particle sets, described by a Stokes number in the range $\mathit{St} = 1\text {--}1000$. At all Reynolds numbers a strong segregation in the near-wall region is observed for particles characterized by intermediate Stokes number, in the range $\mathit{St} =10\text {--}100$. The wall-normal concentration profiles of such particles collapse in inner scaling, thus suggesting the independence of the turbophoretic drift from the large-scale outer motions. This observation is also supported by the spatial organization of the suspended phase in the inner layer, which is found to be universal with the Reynolds number. The deposition rate coefficient increases with $\mathit{Re}_{\tau }$ for a given $\mathit{St}$. Suitable inner and outer scalings are proposed to collapse the deposition curves across the available ranges of Reynolds and Stokes numbers for the different deposition regimes.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Non-Gaussian Statistics in Turbulence

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4316-4320
Author(s):  
J. Qian
Keyword(s):  
Large Scale ◽  
Scale Effects ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Anomalous Scaling ◽  
Self Similarity ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Probability Density Function Pdf ◽  
Reasonable Model

It is believed that non-Gaussian statistics of intermittency leads to anomalous scaling in turbulence, and self-similarity normal scaling corresponds to Gaussian assumptions. By a reasonable model of probability density function (PDF) of intermittent velocity increment, we demonstrate the possibility that non-Gaussian statistics may lead to self-similarity and normal scaling. The experimental facts of scaling-range exponents being anomalous, are not against a non-Gaussian self-similarity in the inertial range. In scaling ranges at experimental Reynolds numbers, viscous and large-scale effects are not negligible, the non-Gaussian self-similarity is broken due to viscous and large-scale effects, and anomalous scaling is observed.

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