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.

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 The role of wave kinematics in turbulent flow over waves

2019 ◽  
Vol 880 ◽  
pp. 890-915 ◽  
Author(s):  
Espen Åkervik ◽  
Magnus Vartdal
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Functional Dependencies ◽  
Form Drag ◽  
Higher Harmonics ◽  
Wave Kinematics ◽  
Induced Stresses ◽  
Wave Induced

The turbulent flow over monochromatic waves of moderate steepness is studied by means of wall resolved large eddy simulations. The simulations cover a range of wave ages and Reynolds numbers. At low wave ages the form drag is highly sensitive to Reynolds number changes, and the interaction between turbulent and wave-induced stresses increases with Reynolds number. At higher wave ages, the flow enters a quasi-laminar regime where wave-induced stresses are primarily balanced by viscous stresses, and the form drag displays a simple Reynolds number dependence. To exploit the quasi-laminar response to the wave kinematics, we split the flow field into a laminar wave-generated response and a turbulent shear flow. The former is driven by the non-homogeneous boundary conditions, whereas the latter is driven by the laminar solution as well as turbulent stresses. For high wave ages, the splitting enables approximate functional dependencies for the form drag to be formulated. In the low wave age regime, where the wave-induced stresses are tightly connected with higher harmonics in the turbulent stresses, the flow is more challenging to analyse. Nevertheless, the importance of higher harmonics in the turbulent stresses can be quantified by explicitly choosing which modes to include in the split-system forcing.

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 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.

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.

Bounds for turbulent shear flow

1970 ◽  
Vol 41 (1) ◽  
pp. 219-240 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Shear Flow ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Experimental Values

Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

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.

A thermodynamical theory of turbulence. I. Basic developments

1989 ◽  
Vol 327 (1595) ◽  
pp. 415-448 ◽  
Keyword(s):  
Turbulent Flow ◽  
Continuum Model ◽  
Microscopic Level ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Macroscopic Scale ◽  
Cambridge University ◽  
Turbulent Fluctuations ◽  
Wide Range ◽  
Special Case

This paper is concerned with the construction of a thermodynamical theory for turbulence based on a continuum model consistent with a wide range of experimental results and observations. A complete theory with appropriate constitutive equations is developed for viscous turbulent flow but the special case of (rate-independent) inviscid turbulent flow is also discussed. The theoretical results obtained readily account for such mechanical aspects of turbulent flow as anisotropy, as well as the energetic effects of turbulent fluctuations, in addition to the more standard thermomechanical effects. More specifically, three different scales of motion and modelling, namely molecular, microscopic and macroscopic, are considered in the construction of the basic theory. Whereas the ordinary thermal effects (such as temperature) on the macroscopic scale represent the manifestation of vibratory motions at the molecular level, similar variables are used to represent the energetic turbulent effects on the macroscopic level that arise from turbulent fluctuations at the microscopic level. The various ingredients of the thermodynamical aspects (both due to thermal and turbulent effects) of the continuum model are incorporated into the theory by means of a recent procedure to thermodynamics by Green & Naghdi ( Proc. R. Soc. Lond. A 357, 253 (1977)). The mechanical aspects of the model for a turbulent fluid requires admission of additional balance laws for eddy concentration and for a kinematical variable which represents the effect of alignment of these eddies (at the microscopic level) along a particular direction on the macroscopic scale, in accordance with observations by Townsend ( The structure of turbulent shear flow , Cambridge University Press (1976)) and others.

Turbulent Flow of Dilute Aqueous Polymer Solutions

1967 ◽  
Vol 89 (4) ◽  
pp. 814-822 ◽  
Author(s):  
Y. Goren ◽  
J. F. Norbury
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Polymer Concentration ◽  
Flow Characteristics ◽  
Detailed Examination ◽  
Turbulent Shear ◽  
Solid Boundary ◽  
Polymer Additives ◽  
Turbulent Shear Flow

This paper summarizes some of the research into the effect of polymer additives on turbulent shear flow, which was conducted at the University of Liverpool between October, 1964, and October, 1966. The paper contains a brief description of the research together with a summary of the principal results and conclusions. The present work was devoted to a detailed examination of the mechanism of a particular flow by gathering information on friction drag, velocity distribution, concentration distribution, and correlation with Reynolds number and polymer concentration level. The particular flow chosen was the fully developed turbulent flow in a 2-in-dia pipe of Polyox WSR-301 solutions. A maximum drag reduction of 71 percent was obtained at a Reynolds number of 1.5 × 105 for solutions having polymer concentration of 10 weight parts per million. The drag reduction effect occurred only above some “critical” Reynolds number which was independent of concentration. The polymer additives were found to influence the flow in the neighborhood of a solid boundary. In this zone of the flow, the eddy viscosity was found to be much lower than that of water. In the absence of a boundary, as in free jet flow, the polymer additives had no effect on the flow characteristics. The experiments showed for the first time that the polymer molecules were uniformly distributed across the pipe diameter under all turbulent flow conditions investigated. A method of determining polymer concentration was devised for this purpose.

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