Diffusion in free turbulent shear flows

1957 ◽  
Vol 3 (1) ◽  
pp. 67-80 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Time Scales ◽  
Particle Velocity ◽  
Random Function ◽  
Shear Flows ◽  
Fluid Particle ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
Stationary Random Function

This paper is concerned with some statistical properties of the displacement of a marked fluid particle released from a given position in a turbulent shear flow, and in particular with the dispersion about the mean position after a long time. It is known that the dispersion takes a simple asymptotic form when the particle velocity is a stationary random function of time, and that analogous results are obtainable when the particle velocity can be transformed to a stationary random function by suitable stretching of the velocity and time scales. The basic hypothesis of the paper is that, in steady free turbulent shear flows which are generated at a point and have a similar structure at different stations downstream, the velocity of a fluid particle exhibits a corresponding Lagrangian similarity and can be so transformed to a stationary random function.The velocity and time scales characterizing the motion of a fluid particle at time t after release at the origin are determined in terms of the powers with which the Eulerian length and velocity scales of the turbulence vary with distance x from the origin. The time scale has the same dependence on t for all jets, wakes and mixing layers (and also for decaying homogeneous turbulence) possessing the usual kind of Eulerian similarity. The dispersion of a particle in the longitudinal or mean-flow direction (and likewise that in the lateral direction in cases of two-dimensional mean flow) is found to vary with t in such a way as to be proportional to the thickness of the shear layer at the mean position of the particle. The way in which the maximum value of the mean concentration of marked fluid falls off with t (for release of a single particle) or with x (for continuous release) is also found.

Upper bounds on general dissipation functionals in turbulent shear flows: revisiting the ‘efficiency’ functional

2002 ◽  
Vol 461 ◽  
pp. 239-275 ◽  
Author(s):  
R. R. KERSWELL
Keyword(s):  
Shear Flows ◽  
Momentum Balance ◽  
Total Power ◽  
Function Technique ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Special Cases ◽  
Turbulent Shear Flows ◽  
Long Time ◽  
The Mean

We show how the variational formulation introduced by Doering & Constantin to rigorously bound the long-time-averaged total dissipation rate [ ] in turbulent shear flows can be extended to treat other long-time-averaged functionals lim supT→∞(1/T)×∫0Tf(D, Dm, Dv)dt of the total dissipation D, dissipation in the mean field Dm and dissipation in the fluctuation field Dv. Attention is focused upon the suite of functionals f = D(Dv/Dm)n and f = Dm(Dv/Dm)n (n [ges ] 0) which include the ‘efficiency’ functional f = D(Dv/Dm) (Malkus & Smith 1989; Smith 1991) and the dissipation in the mean flow f = Dm (Malkus 1996) as special cases. Complementary lower estimates of the rigorous bounds are produced by generalizing Busse's multiple-boundary-layer trial function technique to the appropriate Howard–Busse variational problems built upon the usual assumption of statistical stationarity and constraints of total power balance, mean momentum balance, incompressibility and boundary conditions. The velocity field that optimizes the ‘efficiency’ functional is found not to capture the asymptotic structure of the observed mean flow in either plane Couette flow or plane Poiseuille flow. However, there is evidence to suppose that it is ‘close’ to a neighbouring functional that may.

Asymptotic theory of turbulent shear flows

1970 ◽  
Vol 42 (2) ◽  
pp. 411-427 ◽  
Author(s):  
Kirit S. Yajnik
Keyword(s):  
Shear Flows ◽  
Functional Relationship ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Underdetermined System ◽  
Different Types ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
The Law

A theory is proposed in this paper to describe the behaviour of a class of turbulent shear flows as the Reynolds number approaches infinity. A detailed analysis is given for simple representative members of this class, such as fully developed channel and pipe flows and two-dimensional turbulent boundary layers. The theory considers an underdetermined system of equations and depends critically on the idea that these flows consist of two rather different types of regions. The method of matched asymptotic expansions is employed together with asymptotic hypotheses describing the order of various terms in the equations of mean motion and turbulent kinetic energy. As these hypotheses are not closure hypotheses, they do not impose any functional relationship between quantities determined by the mean velocity field and those determined by the Reynolds stress field. The theory leads to asymptotic laws corresponding to the law of the wall, the logarithmic law, the velocity defect law, and the law of the wake.

Monte Carlo Simulation of Colliding Particles Suspended in Gas-Solid Homogeneous Turbulent Shear Flows

2003 ◽  
Author(s):  
Mathieu Moreau ◽  
Pascal Fede ◽  
Olivier Simonin ◽  
Philippe Villedieu
Keyword(s):  
Monte Carlo ◽  
Particle Velocity ◽  
Shear Flows ◽  
Monte Carlo Algorithm ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Particle Collisions ◽  
Eddy Simulation ◽  
Turbulent Shear Flows ◽  
The Moment

The purpose of this paper is the modelling of particle-particle collisions by Stochastic Lagrangian approach in gas-solid turbulent shear flows. A generalized Monte Carlo algorithm is introduced which takes into account the correlation between the colliding particles. Particle-particle and fluid-particle velocity correlations from Stochastic Lagrangian simulations are compared with results from Deterministic Particles Simulation coupled with Large Eddy Simulation of a gas turbulent shear flow (DPS/LES), and with predictions computed in the frame of the moment method using separate transport equation for the fluid and particle velocity correlations.

scholarly journals Self-sustaining processes at all scales in wall-bounded turbulent shear flows

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160088 ◽  
Author(s):  
Carlo Cossu ◽  
Yongyun Hwang
Keyword(s):  
Large Scale ◽  
Shear Flows ◽  
Stokes Equations ◽  
Wall Turbulence ◽  
Turbulent Shear ◽  
Large Reynolds Number ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Full Account ◽  
Turbulent Shear Flows

We collect and discuss the results of our recent studies which show evidence of the existence of a whole family of self-sustaining motions in wall-bounded turbulent shear flows with scales ranging from those of buffer-layer streaks to those of large-scale and very-large-scale motions in the outer layer. The statistical and dynamical features of this family of self-sustaining motions, which are associated with streaks and quasi-streamwise vortices, are consistent with those of Townsend’s attached eddies. Motions at each relevant scale are able to sustain themselves in the absence of forcing from larger- or smaller-scale motions by extracting energy from the mean flow via a coherent lift-up effect. The coherent self-sustaining process is embedded in a set of invariant solutions of the filtered Navier–Stokes equations which take into full account the Reynolds stresses associated with the residual smaller-scale motions. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

A unified approach for symmetries in plane parallel turbulent shear flows

2001 ◽  
Vol 427 ◽  
pp. 299-328 ◽  
Author(s):  
MARTIN OBERLACK
Keyword(s):  
Shear Flows ◽  
Stokes Equations ◽  
Turbulent Shear ◽  
Large Set ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Law Of The Wall ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
Logarithmic Law

A new theoretical approach for turbulent flows based on Lie-group analysis is presented. It unifies a large set of ‘solutions’ for the mean velocity of stationary parallel turbulent shear flows. These results are not solutions in the classical sense but instead are defined by the maximum number of possible symmetries, only restricted by the flow geometry and other external constraints. The approach is derived from the Reynolds-averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile not previously reported that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near-wall regions in both experimental and DNS data of turbulent channel flows. In the case of the logarithmic law of the wall, the scaling with the distance from the wall arises as a result of the analysis and has not been assumed in the derivation. All solutions are consistent with the similarity of the velocity product equations to arbitrary order. A method to derive the mean velocity profiles directly from the two-point correlation equations is shown.

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