The mechanics of an organized wave in turbulent shear flow. Part 2. Experimental results

Results on the behaviour of controlled wave disturbances introduced artificially into turbulent channel flow are reported. Weak plane-wave disturbances are introduced by vibrating ribbons near each wall. The amplitude and relative phase of the streamwise component of the induced wave is educed from a hot-wire signal, allowing the wave speed, the attenuation characteristics and the wave shape to be traced downstream. These results form a basis for evaluation of closure models for the dynamical equations describing wave components in shear-flow turbulence.

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The mechanics of an organized wave in turbulent shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112070000605 ◽

1970 ◽

Vol 41 (2) ◽

pp. 241-258 ◽

Cited By ~ 512

Author(s):

A. K. M. F. Hussain ◽

W. C. Reynolds

Keyword(s):

Wave Speed ◽

Relative Phase ◽

Normal Component ◽

Turbulent Channel Flow ◽

Turbulent Shear ◽

Turbulent Shear Flow ◽

Wave Shape ◽

Wave Disturbances ◽

Weak Plane ◽

Attenuation Characteristics

Some preliminary results on the behaviour of controlled wave disturbances introduced artificially into turbulent channel flow are reported. Weak plane-wave disturbances are introduced by vibrating ribbons near each wall. The amplitude and relative phase of the streamwise component of the induced wave is educed from a hot wire signal, allowing the wave speed and attenuation characteristics and the wave shape to be traced downstream. The normal component and wave Reynolds stress have been inferred from these data. It appears that Orr–Sommerfeld theories attempted to date are inadequate for description of these waves.

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The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments

Journal of Fluid Mechanics ◽

10.1017/s0022112072000679 ◽

1972 ◽

Vol 54 (2) ◽

pp. 263-288 ◽

Cited By ~ 552

Author(s):

W. C. Reynolds ◽

A. K. M. F. Hussain

Keyword(s):

Eddy Viscosity ◽

Theoretical Models ◽

Turbulent Shear ◽

Turbulent Shear Flow ◽

Reynolds Stresses ◽

Dynamical Equations ◽

Simple Closure ◽

Wave Disturbances ◽

Flow Part ◽

Wave Induced

The dynamical equations governing small amplitude wave disturbances in turbulent shear flows are derived. These equations require additional equations or assumptions about the wave-induced fluctuations in the turbulence Reynolds stresses before a closed system can be obtained. Some simple closure models are proposed, and the results of calculations using these models are presented. When the predictions are compared with our data for channel flow, we find it essential that these oscillations in the Reynolds stresses be included in the model. A simple eddy-viscosity representation serves surprisingly well in this respect.

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Subaqueous barchan dunes in turbulent shear flow. Part 1. Dune motion

Journal of Fluid Mechanics ◽

10.1017/s0022112011000139 ◽

2011 ◽

Vol 675 ◽

pp. 199-222 ◽

Cited By ~ 48

Author(s):

E. M. FRANKLIN ◽

F. CHARRU

Keyword(s):

Erosion Rate ◽

Friction Velocity ◽

Turbulent Channel Flow ◽

Minimum Size ◽

Turbulent Shear ◽

Turbulent Shear Flow ◽

Rate Minimum ◽

Flow Part ◽

Barchan Dunes ◽

And Migration

Experiments are reported on the formation and migration of isolated dunes in a turbulent channel flow. These dunes have a very robust crescentic shape with horns pointing downstream, very similar to that of the barchan dunes observed in deserts at a much larger scale. Their main geometrical and dynamical properties are studied in detail, for four types of grains: the conditions for their formation, their morphology, the threshold shear stress for their motion, their velocity, erosion rate, minimum size and the longitudinal stripes of grains hollowed by fluid streaks in the boundary layer. In particular, the law for the dune velocity is found to involve two dimensionless parameters, the Shields number and the sedimentation Reynolds number, in contrast with predictions based on classical laws for particle transport. As the dune migrates, its size slowly decreases because of a small leakage of particles at the horn tips, and the erosion law is given. A minimum size is evidenced, which is shown to increase with the friction velocity and scale with a settling length.

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Velocity gradient statistics in turbulent shear flow: an extension of Kolmogorov's local equilibrium theory

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.815 ◽

2021 ◽

Vol 929 ◽

Author(s):

Yukio Kaneda ◽

Yoshinobu Yamamoto

Keyword(s):

Shear Flow ◽

Local Equilibrium ◽

Turbulent Channel Flow ◽

Turbulent Energy ◽

Turbulent Shear ◽

Local Similarity ◽

Turbulent Shear Flow ◽

Mean Flow ◽

Velocity Gradients ◽

Local Mean

This paper presents an extension of Kolmogorov's local similarity hypotheses of turbulence to include the influence of mean shear on the statistics of the fluctuating velocity in the dissipation range of turbulent shear flow. According to the extension, the moments of the fluctuating velocity gradients are determined by the local mean rate of the turbulent energy dissipation $\left \langle \epsilon \right \rangle$ per unit mass, kinematic viscosity $\nu$ and parameter $\gamma \equiv S (\nu /\left \langle \epsilon \right \rangle )^{1/2}$ , provided that $\gamma$ is small in an appropriate sense, where $S$ is an appropriate norm of the local gradients of the mean flow. The statistics of the moments are nearly isotropic for sufficiently small $\gamma$ , and the anisotropy of moments decreases approximately in proportion to $\gamma$ . This paper also presents a report on the second-order moments of the fluctuating velocity gradients in direct numerical simulations (DNSs) of turbulent channel flow (TCF) with the friction Reynolds number $Re_\tau$ up to $\approx 8000$ . In the TCF, there is a range $y$ where $\gamma$ scales approximately $\propto y^ {-1/2}$ , and the anisotropy of the moments of the gradients decreases with $y$ nearly in proportion to $y^ {-1/2}$ , where $y$ is the distance from the wall. The theoretical conjectures proposed in the first part are in good agreement with the DNS results.

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