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

1972 ◽  
Vol 54 (2) ◽  
pp. 263-288 ◽  
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.

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

1972 ◽  
Vol 54 (2) ◽  
pp. 241-261 ◽  
Author(s):  
A. K. M. F. Hussain ◽  
W. C. Reynolds
Keyword(s):  
Shear Flow ◽  
Turbulent Channel Flow ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Dynamical Equations ◽  
Wave Disturbances ◽  
Flow Part ◽  
Flow Turbulence ◽  
Weak Plane ◽  
Attenuation Characteristics

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.

On the generation of surface waves by shear flows. Part 5

1967 ◽  
Vol 30 (1) ◽  
pp. 163-175 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Momentum Transfer ◽  
Vertical Velocity ◽  
Equations Of Motion ◽  
Field Measurements ◽  
Singular Part ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stresses ◽  
The Mean ◽  
Wave Induced

Laboratory and field measurements of the generation of gravity waves by turbulent winds imply that a theoretical model based on laminar flow may be adequate on a laboratory, but not an oceanographic, scale. This suggests that the significance of wave-induced perturbations in the turbulent Reynolds stresses for momentum transfer from wind to waves must increase with an appropriate scale parameter. A generalization of the laminar model is constructed by averaging the linearized equations of motion for a turbulent shear flow in a direction (say y) parallel to the wave crests of a particular Fourier component of the surface-wave field. It is shown that the resulting, mean momentum transfer to this component comprises: (i) a singular part, which is proportional to the product of the velocity-profile curvature and the mean square of the wave-induced vertical velocity in the critical layer, where the mean wind speed is equal to the wave speed; (ii) a vertical integral of the mean product of the vertical velocity and the vorticity ω, where ω is the wave-induced perturbation in the total vorticity along a streamline of the y-averaged motion; (iii) the perturbation in the mean turbulent shear stress at the air-water interface. The equation that governs the advection of the vorticity ω under the action of the perturbations in the turbulent Reynolds stresses is derived. Further theoretical progress appears to demand some ad hoc hypothesis for the specification of these turbulent Reynolds stresses. Two such hypotheses are discussed briefly, but it does not appear worth while, in the absence of more detailed experimental data, to carry out elaborate numerical calculations at this time.

scholarly journals Turbulent flow over a liquid layer revisited: multi-equation turbulence modelling

2011 ◽  
Vol 683 ◽  
pp. 357-394 ◽  
Author(s):  
Lennon Ó Náraigh ◽  
Peter D. M. Spelt ◽  
Tamer A. Zaki
Keyword(s):  
Turbulent Flow ◽  
Significant Role ◽  
Travelling Wave ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stresses ◽  
Flow Past ◽  
Wave Induced ◽  
Fully Coupled ◽  
Layer Problem

AbstractThe mechanisms by which turbulent shear flow causes waves on a gas–liquid interface are studied analytically, with a critical assessment of the possible role played by wave-induced Reynolds stresses (WIRSs). First, turbulent flow past a corrugated surface of a small slope is analysed; the surface can either be stationary or support a travelling wave. This problem serves as a useful model because direct numerical simulation (DNS) and experimental data are available to test the analysis, and because this picture is itself a model for the fully coupled two-layer problem. It is demonstrated that the WIRSs play no significant role in shear-driven turbulent flow past a moving wavy wall, and that they alter the structure of the flow only in a quantitative fashion in the pressure-driven case. In the shear-driven case in particular, excellent agreement is obtained with previously reported DNS results. Two closure assumptions are made in our model: the first concerns the wave-induced dissipation of turbulent kinetic energy; the second concerns the importance of rapid distortion. The results of our calculations are sensitive to the assumptions used to close the wave-induced dissipation but are insensitive to the details of the rapid-distortion modelling. Finally, the fully coupled two-layer problem is addressed in the setting of waves of small amplitude, where it is demonstrated that the WIRSs do not play a significant role in the growth of interfacial waves, even at relatively high Reynolds numbers. Again, good agreement is obtained between data from experiments and DNS.

The Influence of Small Particles on the Structure of a Turbulent Shear Flow

2004 ◽  
Vol 126 (4) ◽  
pp. 613-619 ◽  
Author(s):  
David I. Graham
Keyword(s):  
Shear Flow ◽  
General Trend ◽  
Turbulent Shear ◽  
Mass Loading ◽  
Turbulent Shear Flow ◽  
Algebraic Equations ◽  
Reynolds Stresses ◽  
Temporal Correlations ◽  
Fluid Velocities ◽  
Nonlinear Algebraic Equations

In this paper, an analytical solution is found for the Reynolds equations describing a simple turbulent shear flow carrying small, wake-less particles. An algebraic stress model is used as the basis of the model, the particles leading to source terms in the equations for the turbulent stresses in the flow. The sources are proportional to the mass loading of the particles and depend on the temporal correlations of the fluid velocities seen by particles, Rijτ. The resulting set of equations is a system of nonlinear algebraic equations for the Reynolds stresses and the dissipation. The system is solved exactly and the influence of the particles can be quantified. The predictions are compared with DNS results and are shown to predict trends quite well. Different scenarios are investigated, including the effects of isotropic, anisotropic and non-equilibrium time scales and negative loops in Rijτ. The general trend is to increase anisotropy and attenuate turbulence with higher mass loadings. The occurrence of turbulence enhancement is investigated and shown to be theoretically possible, but physically unlikely.

scholarly journals Numerical Evidence of Turbulence Generated by Nonbreaking Surface Waves

2015 ◽  
Vol 45 (1) ◽  
pp. 174-180 ◽  
Author(s):  
Wu-ting Tsai ◽  
Shi-ming Chen ◽  
Guan-hung Lu
Keyword(s):  
Surface Waves ◽  
Water Surface ◽  
Nonlinear Boundary Conditions ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Langmuir Turbulence ◽  
Near Surface ◽  
Order Of Magnitude ◽  
Turbulence Production ◽  
Wave Induced

AbstractNumerical simulation of monochromatic surface waves propagating over a turbulent field is conducted to reveal the mechanism of turbulence production by nonbreaking waves. The numerical model solves the primitive equations subject to the fully nonlinear boundary conditions on the exact water surface. The result predicts growth rates of turbulent kinetic energy consistent with previous measurements and modeling. It also validates the observed horizontal anisotropy of the near-surface turbulence that the spanwise turbulent intensity exceeds the streamwise component. Such a flow structure is found to be attributed to the formation of streamwise vortices near the water surface, which also induces elongated surface streaks. The averaged spacing between the streaks and the depth of the vortical cells approximates that of Langmuir turbulence. The strength of the vortices arising from the wave–turbulence interaction, however, is one order of magnitude less than that of Langmuir cells, which arises from the interaction between the surface waves and the turbulent shear flow. In contrast to Langmuir turbulence, production from the Stokes shear does not dominate the energetics budget in wave-induced turbulence. The dominant production is the advection of turbulence by the velocity straining of waves.

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

2011 ◽  
Vol 675 ◽  
pp. 199-222 ◽  
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.

Surface-wave generation revisited

1993 ◽  
Vol 256 ◽  
pp. 427-441 ◽  
Author(s):  
John Miles
Keyword(s):  
Energy Transfer ◽  
Surface Wave ◽  
Shear Flow ◽  
Reynolds Stress ◽  
Water Waves ◽  
Critical Layer ◽  
Turbulent Shear ◽  
Reynolds Stresses ◽  
Wave Induced ◽  
Laminar Model

The quasi-laminar model for the transfer of energy to a surface wave from a turbulent shear flow (Miles 1957) is modified to incorporate the wave-induced perturbations of the Reynolds stresses, which are related to the wave-induced velocity field through the Boussinesq closure hypothesis and the ancillary hypothesis that the eddy viscosity is conserved along streamlines. It is assumed that the basic mean velocity is U(z) = (U*/κ)log(z/z0) for sufficiently large z (elevation above the level interface) and that U(z1) [Gt ] U* for kz1 = O(1), where k is the wavenumber. The resulting vorticity-transport equation is reduced, through the neglect of diffusion, to a modification of Rayleigh's equation for wave motion in an inviscid shear flow. The energy transfer to the surface wave, which comprises independent contributions from the critical layer (where U = c, the wave speed) and the wave-induced Reynolds stresses, is calculated through a variational approximation and, independently, through matched asymptotic expansions. The critical-layer component is equivalent to that for the quasi-laminar model. The Reynolds-stress component is similar to, but differs quantitatively from, that obtained by Knight (1977, Jacobs (1987) and van Duin & Janssen (1992). The predicted energy transfer agrees with the observational data compiled by Plant (1982) for 1 [lsim ] c/U* [lsim ] 20, but the validity of the logarithmic profile for the calculation of the energy transfer in the critical layer for c/U* < 5 remains uncertain. The basic model is unreliable (for water waves) if c/U* [lsim ] 1, but this domain is of limited oceanographic importance. It is suggested that Kelvin–Helmholtz instability of air blowing over oil should provide a good experimental test of the present Reynolds-stress modelling and that this modelling may be relevant in other geophysical contexts.

Experimental investigation of turbulent shear flow with quadratic mean-velocity profiles

1976 ◽  
Vol 73 (1) ◽  
pp. 165-188 ◽  
Author(s):  
H. K. Richards ◽  
J. B. Morton
Keyword(s):  
Flow Direction ◽  
Correlation Coefficients ◽  
Velocity Profiles ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Quadratic Mean ◽  
The Mean

Three turbulent shear flows with quadratic mean-velocity profiles are generated by using an appropriately designed honeycomb and parallel-rod grids with adjustable rod spacing. The details of two of the flow fields, with quadratic mean-velocity profiles with constant positive mean-shear gradients ($\partial^2\overline{U}_1/\partial X^2_2 >0$), are obtained, and include, in the mean flow direction, the development and distribution of mean velocities, fluctuating velocities, Reynolds stresses, microscales, integral scales, energy spectra, shear correlation coefficients and two-point spatial velocity correlation coefficients. A third flow field is generated with a quadratic mean velocity profile with constant negative mean-shear gradient ($\partial^2\overline{U}_1/\partial X^2_2 < 0$), to investigate in the mean flow direction the effect of the change in sign on the resulting field. An open-return wind tunnel with a 2 × 2 × 20 ft test-section is used.

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