Zero and negative entrainment in turbulent shear flow

In certain accelerated flows the entrainment in the boundary layer, as normally defined, may be either zero or negative; on the other hand, there is no reason to suppose, on physical grounds, that the spread of mean or fluctuating vorticity should cease or become negative in such flows. This paradox is resolved in the present paper. It is also shown that in the equilibrium turbulent sink-flow boundary layer, where the entrainment as normally defined is zero, the reduced advection along streamlines in the outer part of the layer comes about mainly through increased dissipation: there is no reason to assume any radical change in the turbulence structure.

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Lagrangian similarity hypothesis applied to diffusion in turbulent shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112063000045 ◽

1963 ◽

Vol 15 (1) ◽

pp. 49-64 ◽

Cited By ~ 38

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.

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

Journal of Basic Engineering ◽

10.1115/1.3653040 ◽

1964 ◽

Vol 86 (2) ◽

pp. 221-225 ◽

Cited By ~ 10

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.

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Polymer mixing in shear-driven turbulence

Journal of Fluid Mechanics ◽

10.1017/s0022112007007033 ◽

2007 ◽

Vol 585 ◽

pp. 487-497 ◽

Cited By ~ 8

Author(s):

T. VAITHIANATHAN ◽

ASHISH ROBERT ◽

JAMES G. BRASSEUR ◽

LANCE R. COLLINS

Keyword(s):

Shear Flow ◽

Vertical Velocity ◽

Polymer Concentration ◽

Turbulent Shear ◽

Elastic Model ◽

Turbulence Structure ◽

Shear Direction ◽

Turbulent Shear Flow ◽

Velocity Fluctuations ◽

Polymer Mixing

We investigate numerically the influence of polymer mixing on shear-driven turbulence. Of particular interest is the suppression of mixing that accompanies drag reduction with dilute polymer solutions. The simulations use the finite extensible nonlinear elastic model with the Peterlin closure (FENE-P) to describe the polymer stresses in the momentum equation, with polymer concentration allowed to vary in space and time. A thin slab of concentrated polymer was placed in an initially Newtonian homogeneous turbulent shear flow on a plane perpendicular to the mean velocity gradient, and allowed to mix in the gradient direction while actively altering the turbulence. The initially higher concentration of polymer near the centreplane suppressed production of turbulent kinetic energy and Reynolds stress in that region, while turbulence outside the polymer-rich region remained shear-dominated Newtonian turbulence. The rate of mixing in the shear direction was severely damped by the action of the polymer compared to a passive scalar in the corresponding Newtonian turbulent shear flow. This, in part, was a result of the same damping of vertical velocity fluctuations by the polymer that leads to the suppression of momentum flux. However, the cross-correlation between the polymer concentration and vertical velocity fluctuations was also suppressed, indicating that the explanation for the reduction in polymer mixing involves both the suppression of vertical velocity fluctuations and an alteration of turbulence structure by the polymer–turbulence interactions.

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