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.

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.

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.

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.

scholarly journals Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles

2011 ◽  
Vol 670 ◽  
pp. 204-213 ◽  
Author(s):  
B. ROLLIN ◽  
Y. DUBIEF ◽  
C. R. DOERING
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Turbulent Energy ◽  
Dissipation Factor ◽  
Turbulent Shear ◽  
Flow Profile ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Flow Profiles

The relation between the form of a body force driving a turbulent shear flow and the dissipation factor β = ϵℓ/U3 is investigated by means of rigorous upper bound analysis and direct numerical simulation. We consider unidirectional steady forcing functions in a three-dimensional periodic domain and observe that a rigorous infinite Reynolds number bound on β displays the same qualitative behaviour as the computationally measured dissipation factor at finite Reynolds number as the force profile is varied. We also compare the measured mean flow profiles with the Stokes flow profile for the same forcing. The mean and Stokes flow profiles are strikingly similar at the Reynolds numbers obtained in the numerical simulations, lending quantitative credence to the notion of a turbulent eddy viscosity.

Direct Numerical Simulation of Homogeneous Turbulent Shear Flow Containing Bubbles

2006 ◽  
Author(s):  
T. Kawamura ◽  
T. Nakatani
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Production Rate ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Hypothetical Model ◽  
Turbulent Reynolds Number

Direct numerical simulations of homogeneous shear turbulent flows containing deformable bubbles were carried out for clarifying the mechanism of drag reduction by microbubbles. The results show that presence of bubbles can suppress or enhance the development of turbulence depending on condition. The dissipation rate of turbulent kinetic energy is always increased by bubbles, while the production rate can be either increased or decreased depending on the turbulent and shear Reynolds numbers. As a result, the growth rate of turbulent kinetic energy can be either increased or decreased by bubbles depending on conditions. It was shown that the production rate tends to decrease at smaller shear Reynolds number, at larger turbulent Reynolds number, and at larger Weber number. Based on the results, a hypothetical model to explain the dependency on the Reynolds numbers has been proposed.

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.

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.

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.

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