Fine-structure turbulence in the wall region of a turbulent boundary layer

1975 ◽  
Vol 67 (1) ◽  
pp. 125-143 ◽  
Author(s):  
H. Ueda ◽  
J. O. Hinze
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Fine Structure ◽  
Turbulent Boundary Layer ◽  
Power Law ◽  
Outer Part ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Hot Wire ◽  
Frequency Range

Measurements have been made concerning the fine structure of the turbulence in the part adjacent to the wall of the wall region of a plane turbulent boundary layer. The objective was to gain further information concerning the larger-scale disturbance mechanism which is mainly responsible for the generation of turbulence. Hot-wire anemomet.ry was used and information on the fine structure was obtained by differentiating and filtering the hot-wire signal.The distributions of the Kolmogorov microscale and of the flatness and skewness factors of the axial fluctuating velocity u and its first and second derivative determined at two Reynolds numbers suggest the existence of Reynolds number similarity. In the region y+ < 15 the flatness and skewness factors of u increase with decreasing y+. At approximately y+ = 15 the flatness factor shows a minimum value, while the skewness factor becomes zero. This location agrees with that where the turbulence intensity u′ has a maximum value. In the outer part of the wall region (y+ > 100) the flatness and skewness factors approach values obtained in shear-free turbulence at the same turbulence Reynolds number.The fine structure of the turbulence is strongly associated with and dominated by the random, larger-scale, intermittent inrush-ejection cycle. In the viscous sublayer both the fine structure, and the large-scale mechanism of the turbulence are influenced mainly by the inrush phase, while further out in the wall region (y+ > 40) they are influenced by both inrush and ejection. As a result, in the viscous sublayer the average burst periods of the high frequency turbulence components and their flatness factors (of ∂u/∂t and of ∂2u/∂t2) attain values twice those in the outer part.The change in the mechanism of the fine structure with distance from the wall is clearly demonstrated by the spectra of non-negative variables, i.e. (∂u/∂t)2 and (∂2u/∂t2)2. The spectra agree with each other and decrease with increasing frequency, following a power law as predicted by Gurvich & Yaglom (1967). The power law applies to almost the whole frequency range, when the highest, viscous, frequency range is excluded. However, the exponent is different for the viscous sublayer and the outer part of the wall region. In the buffer layer the spectra have two distinct power-law regions. In the lower frequency range the exponent is the same as that for the viscous sublayer, while in the higher frequency range it is the same as that for the outer part of the wall region.

Power Law Velocity Profile in the Turbulent Boundary Layer on Transitional Rough Surfaces

2007 ◽  
Vol 129 (8) ◽  
pp. 1083-1100 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Boundary Layer ◽  
Functional Equation ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Power Law ◽  
Wall Roughness ◽  
Closure Model ◽  
Log Law

A new approach to scaling of transitional wall roughness in turbulent flow is introduced by a new nondimensional roughness scale ϕ. This scale gives rise to an inner viscous length scale ϕν∕uτ, inner wall transitional variable, roughness friction Reynolds number, and roughness Reynolds number. The velocity distribution, just above the roughness level, turns out to be a universal relationship for all kinds of roughness (transitional, fully smooth, and fully rough surfaces), but depends implicitly on roughness scale. The open turbulent boundary layer equations, without any closure model, have been analyzed in the inner wall and outer wake layers, and matching by the Izakson-Millikan-Kolmogorov hypothesis leads to an open functional equation. An alternate open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation of Izakson and Millikan, which admits two functional solutions: the power law velocity profile and the log law velocity profile. The envelope of the skin friction power law gives the log law, as well as the power law index and prefactor as the functions of roughness friction Reynolds number or skin friction coefficient as appropriate. All the results for power law and log law velocity and skin friction distributions, as well as power law constants are explicitly independent of the transitional wall roughness. The universality of these relations is supported very well by extensive experimental data from transitional rough walls for various different types of roughnesses. On the other hand, there are no universal scalings in traditional variables, and different expressions are needed for various types of roughness, such as inflectional roughness, monotonic roughness, and others. To the lowest order, the outer layer flow is governed by the nonlinear turbulent wake equations that match with the power law theory as well as log law theory, in the overlap region. These outer equations are in equilibrium for constant value of m, the pressure gradient parameter, and under constant eddy viscosity closure model, the analytical and numerical solutions are presented.

Experimental studies of the viscous boundary layer properties in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 605 ◽  
pp. 79-113 ◽  
Author(s):  
CHAO SUN ◽  
YIN-HAR CHEUNG ◽  
KE-QING XIA
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Rayleigh Number ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Viscous Sublayer ◽  
Viscous Boundary Layer ◽  
Velocity Boundary Layer ◽  
Viscous Boundary

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh number Ra varying from 109 to 1010 and the Prandtl number Pr fixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυ follows the classical Blasius-like laminar boundary layer in the present range of Ra, and it scales with the Reynolds number Re as δυ/H = 0.64Re−0.50±0.03 (where H is the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar for Ra < 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent at Ra ~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend on Ra and varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw ~ Re1.55, the viscous sublayer δw ~ Re−0.91, the friction velocity uτ ~ Re0.80, and the skin-friction coefficient cf ~ Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that of cf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (at z+ = z/δw ≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

Characterization of Visually Detected Coherent Motions in the Turbulent Boundary Layer

2001 ◽  
Author(s):  
Christopher Robin Hirschi
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Flow Characteristics ◽  
Viscous Sublayer ◽  
Vertical Transport ◽  
Momentum Transport ◽  
Coherent Motion ◽  
The Past

Abstract Research over the past 40 years indicates that coherent motions within the turbulent boundary layer account for disproportionate contributions to momentum transport (Robinson, 1991). To better understand these motions, low-Reynolds number turbulent boundary layer experiments were conducted to investigate the instantaneous velocity and vorticity fields associated with near-wall coherent motion interactions. The present study identifies and explores the most prevalent flow characteristics associated with the vertical transport of injected passive marker from the viscous sublayer.

The dynamics of coherent structures in the wall region of a turbulent boundary layer

1988 ◽  
Vol 192 ◽  
pp. 115-173 ◽  
Author(s):  
Nadine Aubry ◽  
Philip Holmes ◽  
John L. Lumley ◽  
Emily Stone
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Outer Part ◽  
Streamwise Vortex ◽  
Decomposition Theorem ◽  
Chaotic Regime ◽  
Galerkin Projection ◽  
Wall Region ◽  
Low Dimensional

We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem (Lumley 1967, 1981). We truncate the representation to obtain low-dimensional sets of ordinary differential equations, from the Navier–Stokes equations, via Galerkin projection. The experimentally determined eigenfunctions of Herzog (1986) are used; these are in the form of streamwise rolls. Our model equations represent the dynamical behaviour of these rolls. We show that these equations exhibit intermittency, which we analyse using the methods of dynamical systems theory, as well as a chaotic regime. We argue that this behaviour captures major aspects of the ejection and bursting events associated with streamwise vortex pairs which have been observed in experimental work (Kline et al. 1967). We show that although this bursting behaviour is produced autonomously in the wall region, and the structure and duration of the bursts is determined there, the pressure signal from the outer part of the boundary layer triggers the bursts, and determines their average frequency. The analysis and conclusions drawn in this paper appear to be among the first to provide a reasonably coherent link between low-dimensional chaotic dynamics and a realistic turbulent open flow system.

A measure of scale-dependent asymmetry in turbulent boundary layer flows: scaling and Reynolds number similarity

2016 ◽  
Vol 797 ◽  
pp. 549-563 ◽  
Author(s):  
Arvind Singh ◽  
Kevin B. Howard ◽  
Michele Guala
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Transfer ◽  
Turbulent Boundary Layer ◽  
Inertial Range ◽  
Wall Region ◽  
Local Energy ◽  
Boundary Layer Flows ◽  
Non Local ◽  
Velocity Increments

The distribution of temporal scale-dependent streamwise velocity increments is investigated in turbulent boundary layer flows at laboratory and atmospheric Reynolds numbers, using the St. Anthony Falls Laboratory wind tunnel and the Surface Layer Turbulence and Environmental Science Test dataset, respectively. The third-order moments of velocity increments, or asymmetry index $A(a,z)$, is computed for varying wall distance $z$ and time scale separation $a$, where it was observed to leave a robust, distinct signature in the form of a hump, independent of Reynolds number and located across the inertial range. The hump is observed in wall region limited to $z^{+}<5\times 10^{3}$, with a tendency to shift towards smaller time scales as the surface is approached ($z^{+}<70$). Comparing the two datasets, the hump, and its location, are found to obey inner wall scaling and is regarded as a genuine feature of the canonical turbulent boundary layer. The magnitude cumulant analysis of the scale-dependent velocity increments further reveals that intermittency is also enhanced near the wall, in the same flow region where the asymmetry signature was observed. The combination of asymmetry and intermittency is inferred to point at non-local energy transfer and scale coupling across a range of scales. From a turbulent structure perspective, such non-local energy transfer can be seen as the result of strong scale-interaction processes between outer scale motions in the logarithmic layer impacting and distorting smaller scales at the wall, through abrupt energy transfer across scales bypassing the typical energy cascade of the inertial range.

Spatial structure in the viscous sublayer

1971 ◽  
Vol 50 (3) ◽  
pp. 493-512 ◽  
Author(s):  
A. K. Gupta ◽  
J. Laufer ◽  
R. E. Kaplan
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Turbulent Boundary Layer ◽  
Spatial Structure ◽  
Flow Visualization ◽  
Quantitative Description ◽  
Spatial Coherence ◽  
Viscous Sublayer ◽  
Hot Wire ◽  
Extract Information

An experimental investigation was performed to study the spatial coherence of structures in the sublayer of a turbulent boundary layer observed previously by flow visualization. The present work verifies these observations in an Eulerian reference frame and develops a statistical description of the phenomenon. The technique involves simultaneous digital sampling of an array of constant temperature hot-wire anemometers arranged to extract information about a spanwise variation in flow quantities. The quantitative description agrees with dimensionless measures of the structure scales previously published.

A Study of Incompressible Turbulent Boundary Layers in Channel Flow

1968 ◽  
Vol 90 (4) ◽  
pp. 455-467 ◽  
Author(s):  
J. A. Clark
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Viscous Sublayer ◽  
Turbulent Boundary Layers ◽  
Sufficient Accuracy ◽  
Hot Wire ◽  
Reasonable Estimate ◽  
Mean Velocity ◽  
Incompressible Turbulent Boundary Layer ◽  
The Mean

The fully developed incompressible turbulent boundary layer in a channel has been explored using constant-temperature hot-wire anemometry. Particular attention was paid to measurements well into the viscous sublayer, yielding results which are believed to be new. Frequency spectral analyses of the fluctuating velocity components have been obtained for the inner layers. The mean velocity distribution in the sublayer has been determined with sufficient accuracy for a reasonable estimate of skin friction to be made. The results are compared with those of Laufer [11] and Comte-Bellot [4].

On the dynamics of near-wall turbulence

1991 ◽  
Vol 336 (1641) ◽  
pp. 131-175 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Surface Layer ◽  
Turbulent Boundary Layer ◽  
Wall Turbulence ◽  
Wall Region ◽  
Hairpin Vortices ◽  
Basic Fluid ◽  
High Reynolds ◽  
Near Wall

A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described. The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer. It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall. The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface. The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of ‘kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer. Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given. An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow.

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