Local Isotropy in the Turbulent Wake of a Cylinder

1948 ◽  
Vol 1 (2) ◽  
pp. 161 ◽  
Author(s):  
AA Townnsend
Keyword(s):  
Shear Flow ◽  
Turbulent Flow ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
General Applicability ◽  
Local Isotropy ◽  
Air Stream ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
High Reynolds

To investigate the validity of Kolmogoroff's theory of local isotropy, a series of turbulence measurements have been made in the wake of a circular cylinder, and the results have been compared with the predictions of the theory. Using a cylinder of 0.953 cm. diameter in an air-stream of velocity 1,280 cm. sec.-1, measurements have been made of the mean squares of the spatial derivatives in the mean-stream direction of the three components of the turbulent velocity fluctuation, and also of the skewness and flattening factors of the statistical distributions of these derivatives. Observations were taken at three traverses across the wake, respectively at 80, 120, and 160 cylinder diameters down-stream from the cylinder. Except in the immediate neighbourhood of the wake centre, the turbulent flow is observed to be intermittent, consisting of regions of fully developed turbulent flow separated by comparatively sharp boundaries from regions of almost completely laminar motion. If an "intermittency factor " is introduced to describe this phenomenon, and if inside each turbulent region local isotropy exists, then all the experimental results are consistent with the theory of local isotropy, and in agreement with previous measurements in flows possessing ordinary isotropy. It is concluded that, within the boundaries of the turbulent regions, local isotropy in the sense used by Kolmogoroff exists, and that the theory is applicable to this example of shear flow. The general applicability of the theory to turbulent shear flow at high Reynolds numbers must be considered very probable.

Turbulent Shear Flow Over Surface Mounted Obstacles

1990 ◽  
Vol 112 (4) ◽  
pp. 376-385 ◽  
Author(s):  
W. H. Schofield ◽  
E. Logan
Keyword(s):  
Shear Flow ◽  
Shear Layers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Wide Range ◽  
Flow Features ◽  
Model Geometry ◽  
The Mean ◽  
High Reynolds

The mean flow field surrounding obstacles attached to a wall under a turbulent boundary layer is analyzed. The analysis concentrates on how major features of the flow are influenced by model geometry and the incident shear flow. Experimental data are analyzed in terms of nondimensionalized variables chosen on the basis that their effect on major flow features can be simply appreciated. The data are restricted to high Reynolds number shear layers thicker than the attached obstacle. The work shows that data from a wide range of flows can be collapsed if appropriate nondimensional scales are used.

scholarly journals The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study

1997 ◽  
Vol 330 ◽  
pp. 307-338 ◽  
Author(s):  
A. SIMONE ◽  
G.N. COLEMAN ◽  
C. CAMBON
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Kinetic Energy ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Pure Shear ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Rapid Distortion Theory ◽  
The Mean

The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure–strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure–dilatation correlation or the dilatational dissipation. The central role of a ‘distortion Mach number’ Md =  S[lscr ]/a, where S is the mean strain or shear rate, [lscr ] a lengthscale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This ‘crossover’ behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier–Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.

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.

Bounds for turbulent shear flow

1970 ◽  
Vol 41 (1) ◽  
pp. 219-240 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Shear Flow ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Experimental Values

Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

Turbulent shear flow over active and passive porous surfaces

2001 ◽  
Vol 442 ◽  
pp. 89-117 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
MARKUS UHLMANN ◽  
ALFREDO PINELLI ◽  
GENTA KAWAHARA
Keyword(s):  
Shear Flow ◽  
Pressure Fluctuations ◽  
Shear Layers ◽  
Linear Instability ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Flow Mechanism ◽  
Helmholtz Instability ◽  
Local Pressure ◽  
The Mean

The behaviour of turbulent shear flow over a mass-neutral permeable wall is studied numerically. The transpiration is assumed to be proportional to the local pressure fluctuations. It is first shown that the friction coefficient increases by up to 40% over passively porous walls, even for relatively small porosities. This is associated with the presence of large spanwise rollers, originating from a linear instability which is related both to the Kelvin–Helmholtz instability of shear layers, and to the neutral inviscid shear waves of the mean turbulent profile. It is shown that the rollers can be forced by patterned active transpiration through the wall, also leading to a large increase in friction when the phase velocity of the forcing resonates with the linear eigenfunctions mentioned above. Phase-lock averaging of the forced solutions is used to further clarify the flow mechanism. This study is motivated by the control of separation in boundary layers.

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.

On the interactions between large-scale structure and finegrained turbulence in a free shear flow II. The development of spatial interactions in the mean

1978 ◽  
Vol 359 (1699) ◽  
pp. 497-523 ◽  
Keyword(s):  
Shear Flow ◽  
Shear Layer ◽  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Free Shear Layer ◽  
Mean Flow ◽  
The Mean

Organized structures in turbulent shear flow have been observed both in the laboratory and in the atmosphere and ocean. Recent work on modelling such structures in a temporally developing, horizontally homogeneous turbulent free shear layer (Liu & Merkine 19766) has been extended to the spatially developing mixing layer, there being no available rational transformation between the two nonlinear problems. We consider the kinetic energy development of the mean flow, large-scale structure and finegrained turbulence with a conditional average, supplementing the usual time average, to separate the non-random from the random part of the fluctuations. The integrated form of the energy equations and the accompanying shape assumptions are used to derive ‘ amplitude ’ equations for the mean flow, characterized by the shear layer thickness, the non-random and the random components of flow (which are characterized by their respective energy densities). The closure problem was overcome by the shape assumptions which entered into the interaction integrals: the instability-wavelike large-scale structure was taken to be two-dimensional and the local vertical distribution function was obtained by solving the Rayleigh equation for various local frequencies; the vertical shape of the mean stresses of the fine-grained turbulence was estimated by making use of experimental results; the vertical shapes of the wave-induced stresses were calculated locally from their corresponding equations.

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