The dispersion of marked fluid in turbulent shear flow

Elder, J. W.

doi:10.1017/s0022112059000374

Cited by 848 publications

(435 citation statements)

References 7 publications

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“…velocity fluctuations ( v 2 ) and U 0 are both proportional to the friction velocity u * . Thus, U 2 0 / v 2 ∝ u * yielding D ∞ S ∝ u * L, consistent with the turbulent dispersion results of Taylor (1954) and Elder (1959).…”

Section: Relationship To Turbulent Dispersion In Pipes and Channelssupporting

confidence: 87%

The effect of a non-zero Lagrangian time scale on bounded shear dispersion

Spydell

Feddersen

2011

J. Fluid Mech.

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Previous studies of shear dispersion in bounded velocity fields have assumed random velocities with zero Lagrangian time scale (i.e. velocities are$\delta $-function correlated in time). However, many turbulent (geophysical and engineering) flows with mean velocity shear exist where the Lagrangian time scale is non-zero. Here, the longitudinal (along-flow) shear-induced diffusivity in a two-dimensional bounded velocity field is derived for random velocities with non-zero Lagrangian time scale${\tau }_{L} $. A non-zero${\tau }_{L} $results in two-time transverse (across-flow) displacements that are correlated even for large (relative to the diffusive time scale${\tau }_{D} $) times. The longitudinal (along-flow) shear-induced diffusivity${D}_{S} $is derived, accurate for all${\tau }_{L} $, using a Lagrangian method where the velocity field is periodically extended to infinity so that unbounded transverse particle spreading statistics can be used to determine${D}_{S} $. The non-dimensionalized${D}_{S} $depends on time and two parameters: the ratio of Lagrangian to diffusive time scales${\tau }_{L} / {\tau }_{D} $and the release location. Using a parabolic velocity profile, these dependencies are explored numerically and through asymptotic analysis. The large-time${D}_{S} $is enhanced relative to the classic Taylor diffusivity, and this enhancement increases with$ \sqrt{{\tau }_{L} } $. At moderate${\tau }_{L} / {\tau }_{D} = 0. 1$this enhancement is approximately a factor of 3. For classic shear dispersion with${\tau }_{L} = 0$, the diffusive time scale${\tau }_{D} $determines the time dependence and large-time limit of the shear-induced diffusivity. In contrast, for sufficiently large${\tau }_{L} $, a shear time scale${\tau }_{S} = \mathop{ ({\tau }_{L} {\tau }_{D} )}\nolimits ^{1/ 2} $, anticipated by a simple analysis of the particle’s domain-crossing time, determines both the${D}_{S} $time dependence and the large-time limit. In addition, the scalings for turbulent shear dispersion are recovered from the large-time${D}_{S} $using properties of wall-bounded turbulence.

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Section: Relationship To Turbulent Dispersion In Pipes and Channelssupporting

confidence: 87%

The effect of a non-zero Lagrangian time scale on bounded shear dispersion

Spydell

Feddersen

2011

J. Fluid Mech.

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“…Therefore α hor = 0.15 has been adopted. This value is higher than the value of 0.067 derived by Elder [8] for the vertical mixing only. This is motivated by the higher turbulence intensities and larger length scales associated with the motion in the horizontal plane than in the vertical [9].…”

Section: Model Set-upcontrasting

confidence: 67%

“…A direct measurement of this coefficient is difficult to obtain but the associated value for α hor is in the range of 0.1-0.2. Following Elder [8], the ratio between the eddy diffusivity and eddy viscosity (Prandtl-Schmidt number) turned out to be approximately 1 for vertical mixing, (see e.g. [9]).…”

Section: Model Set-upmentioning

confidence: 99%

The Relevance of a Back-Scatter Model for Depth-Averaged Flow Simulation

Prooijen

Uijttewaal

2008

Flow Turbulence Combust

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This study demonstrates the importance of a sophisticated sub-grid model when performing a depth-averaged unsteady RANS simulation of a shallow flow. The reduction of resolution and the spatial dimensions exclude important physical processes as present in three-dimensional turbulence. Especially the effect of the bottom turbulence on the formation of horizontal eddies appears of key importance. A method is proposed to incorporate these effects by means of a kinematic simulation that mimics the residual turbulent fluctuations in a straight channel flow after depthaveraging. This method is developed in the context of the evolution of large eddies in a shallow mixing layer. A comparison with experiments shows that the proposed method works satisfactory. Naturally, it does not fully account for the omission of all 3D-effects.

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“…The kinematic eddy viscosities are the only turbulent parameters directly affecting the solutions of the governing equations and need to be predicted accurately by the turbulence model. In this work, the turbulent exchange coefficients are calculated by using the parabolic eddy-viscosity model (Elder 1959, Fischer et al 1979, Rodi 1993)…”

Section: Turbulence Modellingmentioning

confidence: 99%

A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

Zerihun¹

2017

Archives of Hydro-Engineering and Environmental Mechanics

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The flow field of many practical open channel flow problems, e.g. flow over natural bed forms or hydraulic structures, is characterised by curved streamlines that result in a non-hydrostatic pressure distribution. The essential vertical details of such a flow field need to be accounted for, so as to be able to treat the complex transition between hydrostatic and non-hydrostatic flow regimes. Apparently, the shallow-water equations, which assume a mild longitudinal slope and negligible vertical acceleration, are inappropriate to analyse these types of problems. Besides, most of the current Boussinesq-type models do not consider the effects of turbulence. A novel approach, stemming from the vertical integration of the Reynolds-averaged Navier-Stokes equations, is applied herein to develop a non-hydrostatic model which includes terms accounting for the effective stresses arising from the turbulent characteristics of the flow. The feasibility of the proposed model is examined by simulating flow situations that involve non-hydrostatic pressure and/or nonuniform velocity distributions. The computational results for free-surface and bed pressure profiles exhibit good correlations with experimental data, demonstrating that the present model is capable of simulating the salient features of free-surface flows over sharply-curved overflow structures and rigid-bed dunes.

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The dispersion of marked fluid in turbulent shear flow

Cited by 848 publications

References 7 publications

The effect of a non-zero Lagrangian time scale on bounded shear dispersion

The effect of a non-zero Lagrangian time scale on bounded shear dispersion

The Relevance of a Back-Scatter Model for Depth-Averaged Flow Simulation

A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

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