Mean velocity profiles for turbulent shear flow (Turbulent shear flow mean velocity profiles, calculating eddy diffusivity for momentum and Reynolds stress)

1972 ◽  
Vol 6 (1) ◽  
pp. 60-62 ◽  
Author(s):  
C. J. GARRISON
Keyword(s):  
Shear Flow ◽  
Reynolds Stress ◽  
Eddy Diffusivity ◽  
Velocity Profiles ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Velocity

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.

scholarly journals MAGNETIC RESONANCE SIGNAL LOSS IN TURBULENT SHEAR FLOW

2002 ◽  
Vol 14 (01) ◽  
pp. 1-11
Author(s):  
LIANG-DER JOU
Keyword(s):  
Shear Flow ◽  
Velocity Fluctuation ◽  
Phase Fluctuation ◽  
Eddy Diffusivity ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Signal Loss ◽  
Flow Shear ◽  
Magnetic Gradient ◽  
Spin Echo Sequence

NMR signal loss due to turbulent shear flow is discussed, and a general expression for the phase fluctuation is derived. In the presence of flow shear, the velocity fluctuation perpendicular to the direction of magnetic gradient and the Reynolds stress can cause loss of MR signal Most of signal loss results from the boundary layer, where the flow shear is strong in turbulent pipe flaw, Half the signal loss within the mixing layer distal to a moderate stenosis is caused by the velocity fluctuation in the direction of magnetic gradient, while the remaining results from the velocity, fluctuation perpendicular to the magnetic gradient. The use of eddy diffusivity for the description of signal dephasing in a spin echo sequence is also addressed; A positive, constant eddy diffusivity can not describe the temporal change of phase fluctuation correctly.

The Development of the Reynolds Stress Tensor in a Turbulent Shear Flow

1970 ◽  
Vol 92 (4) ◽  
pp. 836-842
Author(s):  
S. J. Shamroth ◽  
H. G. Elrod
Keyword(s):  
Shear Flow ◽  
Stress Tensor ◽  
Linear Model ◽  
Reynolds Stress ◽  
Experimental Results ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stress Tensor ◽  
Theoretical Predictions

The development of the normalized Reynolds stress tensor, uiuj/q2, in the region upstream of a fully developed, turbulent shear flow is investigated. An inviscid, linear model is used to predict values of the normalized Reynolds stress tensor as a function of position. The theoretical predictions are then compared with experimental results.

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.

Sign in / Sign up

Export Citation Format

Share Document