Stabilization and destabilization of turbulent shear flow in a rotating fluid

1992 ◽  
Vol 241 ◽  
pp. 503-523 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Reynolds Stress ◽  
Rotation Rate ◽  
Turbulent Shear ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Rotation Rates ◽  
Principal Axes ◽  
The Mean

We consider turbulent shear flows in a rotating fluid, with the rotation axis parallel or antiparallel to the mean flow vorticity. It is already known that rotation such that the shear becomes cyclonic is stabilizing (with reference to the non-rotating case), whereas the opposite rotation is destabilizing for low rotation rates and restabilizing for higher. The arguments leading to and quantifying these statement are heuristic. Their status and limitations require clarification. Also, it is useful to formulate them in ways that permit direct comparison of the underlying concepts with experimental data.An extension of a displaced particle analysis, given by Tritton & Davies (1981) indicates changes with the rotation rate of the orientation of the motion directly generated by the shear/Coriolis instability occurring in the destabilized range.The ‘simplified Reynolds stress equations scheme’, proposed by Johnston, Halleen & Lezius (1972), has been reformulated in terms of two angles, representing the orientation of the principal axes of the Reynolds stress tensor (αa) and the orientation of the Reynolds stress generating processes (αb), that are approximately equal according to the scheme. The scheme necessarily fails at large rotation rates because of internal inconsistency, additional to the fact that it is inapplicable to two-dimensional turbulence. However, it has a wide range of potential applicability, which may be tested with experimental data. αa and αb have been evaluated from numerical data for homogeneous shear flow (Bertoglio 1982) and laboratory data for a wake (Witt & Joubert 1985) and a free shear layer (Bidokhti & Tritton 1992). The trends with varying rotation rate are notably similar for the three cases. There is a significant range of near equality of αa and αb. An extension of the scheme, allowing for evolution of the flow, relates to the observation of energy transfer from the turbulence to the mean flow.

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.

A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet

1982 ◽  
Vol 123 ◽  
pp. 523-535 ◽  
Author(s):  
J. W. Oler ◽  
V. W. Goldschmidt
Keyword(s):  
Experimental Data ◽  
Reynolds Stress ◽  
Turbulent Jet ◽  
Vortex Street ◽  
Two Dimensional ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Core ◽  
The Mean ◽  
Similarity Relationships

The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted.

3D Reynolds Stress Modelling of Turbulent Flow in Linear Turbine Cascade

1997 ◽  
Author(s):  
M. Kanniche ◽  
R. Boudjemadi ◽  
F. Déjean ◽  
F. Archambeau
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Strain Tensor ◽  
Secondary Flows ◽  
Turbulence Closure ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Principal Axes ◽  
The Mean

The flow in a linear turbine cascade (Gregory-Smith et al. (1990)) is numerically investigated using a Reynolds Stress Turbulence closure. A particular attention is given to secondary flows where the normal Reynolds stresses are expected to play an important role. The most classical turbulence closure, the k-epsilon model uses the Boussinesq Eddy Viscosity concept which assumes an isotropic turbulent viscosity. The Reynolds stresses are then related to local velocity gradients by this isotropic eddy viscosity. Corollary, the principal axes of the Reynolds stress tensor are colinear with those of the mean strain tensor. The advantage of Reynolds Stress Turbulence closure is the calculation of Reynolds stresses by their own individual transport equations. This leads to a more realistic description of the turbulence and of its dependance on the mean flow. The most classical Second Order turbulence model (Launder et al. (1975)) is applied to a linear turbine cascade, and the results are compared to secondary velocity and turbulence measurements at cross-passage planes.

On the application of successive plane strains to grid-generated turbulence

1979 ◽  
Vol 93 (3) ◽  
pp. 501-513 ◽  
Author(s):  
J. N. Gence ◽  
J. Mathieu
Keyword(s):  
Shear Flow ◽  
Detailed Analysis ◽  
Stress Tensor ◽  
Plane Strain ◽  
Reynolds Stress ◽  
Homogeneous Turbulence ◽  
Reynolds Stress Tensor ◽  
Principal Axes ◽  
The Mean

A grid-generated turbulence is subjected to a pure plane strain and the principal axes of the Reynolds stress tensor become those of the strain. This ‘oriented’ homogeneous turbulence is then submitted to a new strain the principal axes of which have a different orientation. We show that in such a situation it is possible to observe a transfer of energy from the fluctuating motion to the mean one. Such transfer is necessarily associated with a forced decay of the anisotropy of the motion. A detailed analysis of the reorientation of the principal axes of the Reynolds stress tensor in the frame of those of the second strain gives an explanation of the evolution of the principal axes of the Reynolds stress tensor in a shear flow.

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.

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.

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.

Mechanisms underlying transient growth of planar perturbations in unbounded compressible shear flow

2009 ◽  
Vol 639 ◽  
pp. 479-507 ◽  
Author(s):  
NIKOLAOS A. BAKAS
Keyword(s):  
Shear Flow ◽  
Acoustic Wave ◽  
Reynolds Stress ◽  
Acoustic Waves ◽  
Compressible Flows ◽  
Streamwise Velocity ◽  
Transient Growth ◽  
Mean Flow ◽  
The Mean ◽  
Mach Numbers

Non-modal mechanisms underlying transient growth of propagating acoustic waves and non-propagating vorticity perturbations in an unbounded compressible shear flow are investigated, making use of closed form solutions. Propagating acoustic waves amplify mainly due to two mechanisms: growth due to advection of streamwise velocity that is typically termed as the lift-up mechanism leading for large Mach numbers to an almost linear increase in streamwise velocity with time and growth due to the downgradient irrotational component of the Reynolds stress leading to linear growth of acoustic wave energy for large times. Synergy between these mechanisms along with the downgradient solenoidal component of the Reynolds stress produces large and robust energy amplification.On the other hand, non-propagating vorticity perturbations amplify due to kinematic deformation of vorticity by the mean flow. For weakly compressible flows, an initial vorticity perturbation abruptly excites acoustic waves with exponentially small amplitude, and the energy gained by vorticity perturbations is transferred back to the mean flow. For moderate Mach numbers, a strong coupling between vorticity perturbations and acoustic waves is found with the energy gained by vorticity perturbations being transferred to acoustic waves that are abruptly excited by the vortex.Calculation of the optimal perturbations for a viscous flow shows that for low Mach numbers, acoustic wave excitation by vorticity perturbations and the subsequent growth of acoustic waves leads to robust energy growth of the order of Reynolds number, while for large Mach numbers, synergy between the lift-up mechanism and the downgradient solenoidal component of the Reynolds stress dominates the growth and leads to a comparable large amplification of streamwise velocity.

Experiments on nearly homogeneous turbulent shear flow

1970 ◽  
Vol 41 (1) ◽  
pp. 81-139 ◽  
Author(s):  
F. H. Champagne ◽  
V. G. Harris ◽  
S. Corrsin
Keyword(s):  
Shear Stress ◽  
Energy Transfer ◽  
Shear Flow ◽  
Velocity Gradient ◽  
Turbulent Velocity ◽  
Wave Number ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Principal Axes ◽  
The Mean

With a transverse array of channels of equal widths but differing resistances, we have generated an improved approximation to spatially homogeneous turbulent shear flow. The scales continue to grow with downstream distance, even in a region where the mean velocity gradient and one-point turbulence moments (component energies and shear stress) have attained essentially constant values. This implies asymptotic non-stationarity in the basic Eulerian frame convected with the mean flow, behaviour which seems to be inherent to homogeneous turbulent shear flow.Two-point velocity correlations with space separation and with space-time separation yield characteristic departures from isotropy, including clear ‘upstream–downstream’ unsymmetries which cannot be classified simply as axis tilting of ellipse-like iso-correlation contours.The high wave-number structure is roughly locally isotropic although the turbulence Reynolds number based on Taylor ‘microscale’ and r.m.s. turbulent velocity is only 130. Departures from isotropy in the turbulent velocity gradient moments are measurable.The approximation to homogeneity permits direct estimation of all components of the turbulent pressure/velocity-gradient tensor, which accounts for inter-component energy transfer and helps to regulate the turbulent shear stress. It is found that its principal axes are aligned with those of the Reynolds stress tensor. Finally, the Rotta (1951, 1962) linear hypothesis for intercomponent energy transfer rate is roughly confirmed.

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