A Three-Dimensional Mathematical Model of Dispersion in Turbulent Shear Flow

A three-dimensional numerical model for turbulent shear flow in a channel with large Reynolds number is employed for the investigation of turbulent diffusion of finite inertia particulates. A stochastic nonlinear equation describing the motion of particles is integrated to obtain Lagrangian information. Special attention is paid to the effects of shear flow and wall boundary conditions. The results of these studies are compared to previous theoretical and empirical results. A cubic time dependency for separation is found at intermediate values of time while linear dependency is observed at large times. Schmidt numbers are always found to be smaller than one in the non-homogeneous region. It was concluded that special attention must be paid to appropriate computation times necessary to obtain a statistical equilibrium.

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Characterization of the low‐pressure filaments in a three‐dimensional turbulent shear flow

Physics of Fluids ◽

10.1063/1.868586 ◽

1995 ◽

Vol 7 (3) ◽

pp. 630-646 ◽

Cited By ~ 156

Author(s):

O. Cadot ◽

S. Douady ◽

Y. Couder

Keyword(s):

Shear Flow ◽

Three Dimensional ◽

Low Pressure ◽

Turbulent Shear ◽

Turbulent Shear Flow

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A Mathematical Model Of Dispersion In Turbulent Shear Flow

International Journal of Modelling and Simulation ◽

10.1080/02286203.1984.11759869 ◽

1984 ◽

Vol 4 (2) ◽

pp. 61-64 ◽

Cited By ~ 1

Author(s):

T. Tirabassi ◽

M. Tagliazucca ◽

R. Lupini ◽

F. Fortezza

Keyword(s):

Mathematical Model ◽

Shear Flow ◽

Turbulent Shear ◽

Turbulent Shear Flow

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The effect of axial stretching on the three-dimensional stability of a vortex pair

Journal of Fluid Mechanics ◽

10.1017/s002211209200209x ◽

1992 ◽

Vol 241 ◽

pp. 403-419 ◽

Cited By ~ 3

Author(s):

J. S. Marshall

Keyword(s):

Shear Flow ◽

Three Dimensional ◽

Vortex Pair ◽

Turbulent Shear ◽

Percentage Increase ◽

Hairpin Vortex ◽

Turbulent Shear Flow ◽

Perturbation Amplitude ◽

The Stability ◽

Stretching Flow

The stability of a pair of counter-rotating vortices to three-dimensional disturbances in the presence of a stretching flow is studied for vortices of small circular cross-section. The problem is reduced to a system of two first-order, linear ordinary differential equations, which can be integrated numerically to obtain the change in the perturbation of the vortex pair with time. The stability of the vortex pair depends upon four dimensionless constants, two of which characterize the stretching flow. Computations indicate that stretching usually exerts a stabilizing influence on the vortex pair, although in many cases the perturbation amplitude may initially increase and then decrease at some later time due to the effects of stretching. The results of the study are applied to investigate stability of hairpin vortices that are typically observed in turbulent shear flows. An estimate of the percentage increase in perturbation amplitude of a hairpin vortex in a homogeneous turbulent shear flow is given as a function of the stretch of the hairpin for different values of the dimensionless perturbation wavenumber and the microscale Reynolds number Reλ = λq/ν (based on the Taylor microscale λ and the turbulent kinetic energy ½q2). The maximum percentage growth of a perturbation of the legs of a hairpin vortex in a turbulent shear flow is found to decrease with increase in Reλ.

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