Further experiments in nearly homogeneous turbulent shear flow

1977 ◽  
Vol 81 (4) ◽  
pp. 657-687 ◽  
Author(s):  
V. G. Harris ◽  
J. A. H. Graham ◽  
S. Corrsin
Keyword(s):  
Wind Tunnel ◽  
Shear Flow ◽  
Energy Exchange ◽  
Turbulent Energy ◽  
Turbulent Shear ◽  
Asymptotic State ◽  
Turbulent Shear Flow ◽  
Tensor Structure ◽  
Mean Velocity ◽  
Exchange Hypothesis

The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.

Lagrangian similarity hypothesis applied to diffusion in turbulent shear flow

1963 ◽  
Vol 15 (1) ◽  
pp. 49-64 ◽  
Author(s):  
J. E. Cermak
Keyword(s):  
Boundary Layer ◽  
Surface Layer ◽  
Shear Flow ◽  
Turbulent Shear ◽  
Solid Boundary ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
Similarity Hypothesis ◽  
Neutral Boundary Layer ◽  
Continuous Point

The concept suggested by Batchelor that motion of a marked particle in turbulent shear flow may be similar at stations downstream from the point of release is applied to a variety of diffusion data obtained in the laboratory and in the surface layer of the atmosphere. Two types of shear flow parallel to a plane solid boundary are considered. In the first case mean velocity is a linear function of logz(neutral boundary layer) and in the second case the mean velocity is slightly perturbed from the logarithmic relationship by temperature variation in thez-direction (diabatic boundary layer). Besides the parameters introduced in previous applications of the Lagrangian similarity hypothesis to turbulent diffusion, the ratio of source height to roughness lengthh/z0is shown to be of major importance. Predictions of the variation of maximum ground-level concentration for continuous point and line sources and the variation of plume width for a continuous point source with distance downstream from the source agree with the assorted data remarkably well for a range of length scales extending over three orders-of-magnitude. It is concluded that results from application of the Lagrangian similarity hypothesis are significant for the laboratory modelling of diffusion in the atmospheric surface layer.

Outline of a theory of turbulent shear flow

1956 ◽  
Vol 1 (5) ◽  
pp. 521-539 ◽  
Author(s):  
W. V. R. Malkus
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Boundary Conditions ◽  
Momentum Transport ◽  
Turbulent Shear ◽  
Spectral Structure ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

In this paper the spatial variations and spectral structure of steady-state turbulent shear flow in channels are investigated without the introduction of empirical parameters. This is made possible by the assumption that the non-linear momentum transport has only stabilizing effects on the mean field of flow. Two constraints on the possible momentum transport are drawn from this assumption: first, that the mean flow will be statistically stable if an Orr-Sommerfeld type equation is satisfied by fluctuations of the mean; second, that the smallest scale of motion that can be present in the spectrum of the momentum transport is the scale of the marginally stable fluctuations of the mean. Within these two constraints, and for a given mass transport, an upper limit is sought for the rate of dissipation of potential energy into heat. Solutions of the stability equation depend upon the shape of the mean velocity profile. In turn, the mean velocity profile depends upon the spatial spectrum of the momentum transport. A variational technique is used to determine that momentum transport spectrum which is both marginally stable and produces a maximum dissipation rate. The resulting spectrum determines the velocity profile and its dependence on the boundary conditions. Past experimental work has disclosed laminar, ‘transitional’, logarithmic and parabolic regions of the velocity profile. Several experimental laws and their accompanying constants relate the extent of these regions to the boundary conditions. The theoretical profile contains each feature and law that is observed. First approximations to the constants are found, and give, in particular, a value for the logarithmic slope (von Kármán's constant) which is within the experimental error. However, the theoretical boundary constant is smaller than the observed value. Turbulent channel flow seems to achieve the extreme state found here, but a more decisive quantitative comparison of theory and experiment requires improvement in the solutions of the classical laminar stability problem.

scholarly journals Mean velocity and suspended sediment concentration profile model of turbulent shear flow with probability density function

2017 ◽  
Vol 21 (3) ◽  
pp. 129-134
Author(s):  
Guanglin Wu ◽  
Liangsheng Zhu ◽  
Fangcheng Li
Keyword(s):  
Probability Density Function ◽  
Shear Flow ◽  
Probability Density ◽  
Density Function ◽  
Suspended Sediment Concentration ◽  
Sediment Concentration ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
Profile Model

This work purposes a general mean velocity and a suspended sediment concentration (SSC) model to express distribution at every point of the cross section of turbulent shear flow by using a probability density function method. The probability density function method was used to describe the velocity and concentration profiles interacted on directly by fluid particles in the turbulent shear flow to solve turbulent flow and avoid different dynamical mechanics. The velocity profile model was obtained by solving for the profile integral with the product of the laminar velocity and probability density, through adopting an exponential probability density function to express probability distribution of velocity alteration of a fluid particle in turbulent shear flow. An SSC profile model was also created following a method similar to the above and based on the Schmidt diffusion equation. Different velocity and SSC profiles were created while changing the parameters of the models. The models were verified by comparing the calculated results with traditional models. It was shown that the probability density function model was superior to log-law in predicting stream-wise velocity profiles in coastal currents, and the probability density function SSC profile model was superior to the Rouse equation for predicting average SSC profiles in rivers and estuaries. Outlooks for precision investigation are stated at the end of this article.

The effects of heat release on the energy exchange in reacting turbulent shear flow

2002 ◽  
Vol 450 ◽  
pp. 35-66 ◽  
Author(s):  
D. LIVESCU ◽  
F. A. JABERI ◽  
C. K. MADNIA
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Heat Release ◽  
Turbulent Kinetic Energy ◽  
Energy Exchange ◽  
Turbulent Shear ◽  
Heat Of Reaction ◽  
Turbulent Shear Flow ◽  
Production Term ◽  
Irreversible Reaction

The energy exchange between the kinetic and internal energies in non-premixed reacting compressible homogeneous turbulent shear flow is studied via data generated by direct numerical simulations (DNS). The chemical reaction is modelled by a one- step exothermic irreversible reaction with Arrhenius-type reaction rate. The results show that the heat release has a damping effect on the turbulent kinetic energy for the cases with variable transport properties. The growth rate of the turbulent kinetic energy is primarily in uenced by the reaction through temperature-induced changes in the solenoidal dissipation and modifications in the explicit dilatational terms (pressure–dilatation and dilatational dissipation). The production term in the scaled kinetic energy equation, which is proportional to the Reynolds shear stress anisotropy, is less affected by the heat release. However, the dilatational part of the production term increases during the time when the reaction is important. Additionally, the pressure–dilatation correlation, unlike the non-reacting case, transfers energy in the reacting cases, on the average, from the internal to the kinetic energy. Consequently, the dilatational part of the kinetic energy is enhanced by the reaction. On the contrary, the solenoidal part of the kinetic energy decreases in the reacting cases mainly due to an enhanced viscous dissipation. Similarly to the non-reacting case, it is found that the direct coupling between the solenoidal and dilatational parts of the kinetic energy is small. The structure of the flow with regard to the normal Reynolds stresses is affected by the heat of reaction. Compared to the non-reacting case, the kinetic energy in the direction of the mean velocity decreases during the time when the reaction is important, while it increases in the direction of the shear. This increase is due to the amplification of the dilatational kinetic energy in the x2-direction by the reaction. Moreover, the dilatational effects occur primarily in the direction of the shear. These effects are amplified if the heat release is increased or the reaction occurs at later times. The non-reacting models tested for the explicit dilatational terms are not supported by the DNS data for the reacting cases, although it appears that some of the assumptions employed in these models hold also in the presence of heat of reaction.

The effect of contraction on a homogeneous turbulent shear flow

1985 ◽  
Vol 154 ◽  
pp. 187-213 ◽  
Author(s):  
K. R. Sreenivasan
Keyword(s):  
Shear Flow ◽  
Area Ratio ◽  
Turbulent Shear ◽  
Shear Strain Rate ◽  
Turbulent Shear Flow ◽  
Turbulent Stress ◽  
Mean Velocity ◽  
Stage Of Development ◽  
Flow Through ◽  
The Mean

A homogeneous turbulent shear flow in its asymptotic stage of development was subjected to an additional (longitudinal) strain by passing the flow through gradual contraction in the direction perpendicular to that of the mean shear. Two contractions, of area ratio 1.4 and 2.6, were used. Mean velocity and turbulent stress (both normal and shear) distributions were measured at several streamwise locations in the contraction region. The mean velocity distributions agree quite well with calculations based on the (inviscid) Bernoulli equation. Until at least half-way down the contraction with the larger area ratio, the rapid-distortion calculations considering only the streamwise acceleration were found to be reasonably successful in predicting the turbulent intensities. For the smaller-area-ratio contraction, corrections for the ‘natural development’ of the shear flow become important nearly everywhere. Similar calculations considering the shear as the only straining mechanism are generally less successful, although the shear strain rate is at least as rapid as, or even more so than, the longitudinal one. The pressure-rate-of-strain covariance terms estimated from the approximate component energy balance were used to test the adequacy of three models with varying degrees of complexity. Although none of these models appears general enough, their performance is generally adequate for the lower-area-ratio contraction; perhaps not surprisingly, the more complex the model the better its performance.

On the Separation, Reattachment, and Redevelopment of Incompressible Turbulent Shear Flow

1964 ◽  
Vol 86 (2) ◽  
pp. 221-225 ◽  
Author(s):  
T. J. Mueller ◽  
H. H. Korst ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Shear Flow ◽  
Roughness Element ◽  
Single Step ◽  
Parameter Family ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
The Mean

An experimental and theoretical investigation is presented which describes the character of the mean motion and the structure of turbulence for the separation, reattachment, and redevelopment of the incompressible turbulent shear flow downstream of a single step-type roughness element. For the redeveloping turbulent boundary layer downstream of reattachment, it is shown that the mean velocity profiles constitute a one-parameter family and that as far as the shape parameters are concerned, this one-parameter family is essentially the same as for a boundary layer developing toward separation. This similarity between developing (toward separation) and redeveloping (after reattachment) turbulent shear layers is utilized to establish an integral method for calculating the redeveloping turbulent boundary layer at essentially zero pressure gradient.

Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1

1981 ◽  
Vol 104 ◽  
pp. 311-347 ◽  
Author(s):  
Stavros Tavoularis ◽  
Stanley Corrsin
Keyword(s):  
Wind Tunnel ◽  
Temperature Gradient ◽  
Shear Flow ◽  
Correlation Functions ◽  
Temperature Fluctuations ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Integral Scales ◽  
Probability Densities ◽  
Point Correlation

A reasonably uniform mean temperature gradient has been superimposed upon a nearly homogeneous turbulent shear flow in a wind tunnel. The overheat is small enough to have negligible effect on the turbulence. Away from the wind-tunnel entrance, the transverse statistical homogeneity is good and the temperature fluctuations and their integral scales grow monotonically like the corresponding velocity fluctuations (Harris, Graham & Corrsin 1977). Measurements of several moments, one- and two-point correlation functions, spectra, integral scales, microscales, probability densities, and joint probability densities of the turbulent velocities, temperature fluctuations, and temperature-velocity products are reported. The heat-transport characteristics are much like those of momentum transport, with the turbulent Prandtl number nearly 1. The temperature fluctuation is better correlated with the streamwise than the transverse velocity component, and the cross-component D12 of the turbulent diffusivity tensor has sign opposite to and about twice the magnitude of the diagonal component D22. Some resemblance of directional properties (relative magnitudes of correlation functions, integral scales, microscales) of the temperature with those of the streamwise velocity is also observed. Comparisons of the present data with measurements in the inner part of a heated boundary layer and a fully turbulent pipe flow (x2/d = 0·25) show comparable magnitudes of temperature-velocity correlation coefficients, turbulent Prandtl numbers and ratios of turbulent diffusivities, and show similar shapes of two-point correlation functions.

The maintenance of Reynolds stress in turbulent shear flow

1967 ◽  
Vol 27 (1) ◽  
pp. 131-144 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Reynolds Stress ◽  
Mixing Layer ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
The Mean

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence\[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where${\cal A}$is a number, Θ the convected integral time scale of thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.

Velocity gradient statistics in turbulent shear flow: an extension of Kolmogorov's local equilibrium theory

2021 ◽  
Vol 929 ◽  
Author(s):  
Yukio Kaneda ◽  
Yoshinobu Yamamoto
Keyword(s):  
Shear Flow ◽  
Local Equilibrium ◽  
Turbulent Channel Flow ◽  
Turbulent Energy ◽  
Turbulent Shear ◽  
Local Similarity ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Velocity Gradients ◽  
Local Mean

This paper presents an extension of Kolmogorov's local similarity hypotheses of turbulence to include the influence of mean shear on the statistics of the fluctuating velocity in the dissipation range of turbulent shear flow. According to the extension, the moments of the fluctuating velocity gradients are determined by the local mean rate of the turbulent energy dissipation $\left \langle \epsilon \right \rangle$ per unit mass, kinematic viscosity $\nu$ and parameter $\gamma \equiv S (\nu /\left \langle \epsilon \right \rangle )^{1/2}$ , provided that $\gamma$ is small in an appropriate sense, where $S$ is an appropriate norm of the local gradients of the mean flow. The statistics of the moments are nearly isotropic for sufficiently small $\gamma$ , and the anisotropy of moments decreases approximately in proportion to $\gamma$ . This paper also presents a report on the second-order moments of the fluctuating velocity gradients in direct numerical simulations (DNSs) of turbulent channel flow (TCF) with the friction Reynolds number $Re_\tau$ up to $\approx 8000$ . In the TCF, there is a range $y$ where $\gamma$ scales approximately $\propto y^ {-1/2}$ , and the anisotropy of the moments of the gradients decreases with $y$ nearly in proportion to $y^ {-1/2}$ , where $y$ is the distance from the wall. The theoretical conjectures proposed in the first part are in good agreement with the DNS results.

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