Journal Article•
The Turbulent/Non-turbulent Interface and Entrainment in a Boundary Layer
TL;DR: In this paper, the turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer at high Reynolds number was examined using particle image velocimetry.
Abstract: Abstract The turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer at high Reynolds number ( $\mathit{Re}_\tau =14\, 500$ ) is examined using particle image velocimetry. An experimental set-up is utilized that employs multiple high-resolution cameras to capture a large field of view that extends $2\delta \times 1.1\delta $ in the streamwise/wall-normal plane with an unprecedented dynamic range. The interface is detected using a criteria of local turbulent kinetic energy and proves to be an effective method for boundary layers. The presence of a turbulent/non-turbulent superlayer is corroborated by the presence of a jump for the conditionally averaged streamwise velocity across the interface. The steep change in velocity is accompanied by a discontinuity in vorticity and a sharp rise in the Reynolds shear stress. The conditional statistics at the interface are in quantitative agreement with the superlayer equations outlined by Reynolds (J. Fluid Mech., vol. 54, 1972, pp. 481–488). Further analysis introduces the mass flux as a physically relevant parameter that provides a direct quantitative insight into the entrainment. Consistency of this approach is first established via the equality of mean entrainment calculations obtained using three different methods, namely, conditional, instantaneous and mean equations of motion. By means of ‘mass-flux spectra’ it is shown that the boundary-layer entrainment is characterized by two distinctive length scales which appear to be associated with a two-stage entrainment process and have a substantial scale separation.
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TL;DR: The Structure of Turbulent Shear Flow by Dr. A.Townsend as mentioned in this paper is a well-known work in the field of fluid dynamics and has been used extensively in many applications.
Abstract: The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.
1,050 citations
TL;DR: In this paper, a turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at Reτ ≈ 3900.
Abstract: A turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at Reτ ≈ 3900.. The three velocity components resulting from this experiment reveal a pronounced spanwise periodicity in all single-point velocity statistics. Consistent with previous hot-wire studies over similar-type riblets, we observe a weak time-average secondary flow in the form of δ-filling streamwise vortices. The observed differences in the surface and secondary flow characteristics, compared to other heterogeneous-roughness studies, may suggest that different mechanisms are responsible for the flow modifications in this case. Observations of instantaneous velocity fields reveal modified and rearranged turbulence structures. The instantaneous snapshots also suggest that the time-average secondary flow may be an artefact arising from superpositions of much stronger instantaneous turbulent events enhanced by the surface texture. In addition, the observed instantaneous secondary motions seem to have promoted a free-stream-engulfing behaviour in the outer layer, which would indicate an increase turbulent/non-turbulent flow mixing. It is overall demonstrated that the presence of large-scale directionality in transitional surface roughness can cause a modification throughout the entire boundary layer, even when the roughness height is 0.5 % of the layer thickness.
84 citations
Cites background or methods from "The Turbulent/Non-turbulent Interfa..."
...These regions occur below the turbulent/non-turbulent (T/NT) ‘interface outline’ defined by Chauhan et al. (2014), and typically reside underneath the leaning low-momentum eruptions described in § 5....
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...These T/NT regions are identified using the kinetic-energy criteria of Chauhan et al. (2014), and the aforementioned interface outline is also highlighted....
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TL;DR: In this article, the characteristics of interfaces and internal shear layers that are present in a turbulent boundary layer (TBL) were investigated and it was shown that they exhibit similar characteristics as the external T/NT interface.
Abstract: New experimental research is presented on the characteristics of interfaces and internal shear layers that are present in a turbulent boundary layer (TBL). The turbulent/non-turbulent (T/NT) interface at the outer boundary of the TBL shows the presence of a finite jump in streamwise velocity and is characterised by a thin shear layer. It appears that similar layers of high shear occur also within the TBL which separate regions of almost uniform momentum. It turns out that they exhibit similar characteristics as the external T/NT interface. Furthermore, the spatial growth rate of the TBL, that is derived from theoretical analysis, can be correctly predicted from a momentum balance near the external T/NT interface. Similarly, the entrainment velocities for the average internal layers have been determined. Results indicate that internal layers move slower in the vicinity of the wall, whereas they move faster than the large scale boundary layer growth rate in the outer region of the TBL. It is believed that shear layers bound large scale flow regions of approximately uniform momentum. Hence, the entrainment velocities of these internal layers may be interpreted as growth rates of the large scale motions in a TBL.
81 citations
TL;DR: In this paper, a low-dimensional representation of the small-scale time-varying spectrum via two new time series: the instantaneous amplitude of the energy and the instantaneous frequency is constructed by employing a spectral separation scale.
Abstract: Wavelet analysis is employed to examine amplitude and frequency modulations in broadband signals. Of particular interest are the streamwise velocity fluctuations encountered in wall-bounded turbulent flows. Recent studies have shown that an important feature of the near-wall dynamics is the modulation of small scales by large-scale motions. Small- and large-scale components of the velocity time series are constructed by employing a spectral separation scale. Wavelet analysis of the small-scale component decomposes the energy in joint time–frequency space. The concept is to construct a low-dimensional representation of the small-scale time-varying spectrum via two new time series: the instantaneous amplitude of the small-scale energy and the instantaneous frequency. Having the latter in a time-continuous representation allows a more thorough analysis of frequency modulation. By correlating the large-scale velocity with the concurrent small-scale amplitude and frequency realizations, both amplitude and frequency modulations are studied. In addition, conditional averages of the small-scale amplitude and frequency realizations depict unique features of the scale interaction. For both modulation phenomena, the much studied time shifts, associated with peak correlations between the large-scale velocity and small-scale amplitude and frequency traces, are addressed. We confirm that the small-scale amplitude signal leads the large-scale fluctuation close to the wall. It is revealed that the time shift in frequency modulation is smaller than that in amplitude modulation. The current findings are described in the context of a conceptual mechanism of the near-wall modulation phenomena.
79 citations
Cites background from "The Turbulent/Non-turbulent Interfa..."
...The black solid line indicates an error function profile representing the intermittency γ, which is defined as the fraction of time that the boundary layer flow is in a turbulent state (Chauhan et al. 2014)....
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TL;DR: In this paper, the scaling of the mass flux and entrainment velocity across the turbulent/non-turbulent interface (TNTI) in the far field of an axisymmetric jet at high Reynolds number is considered.
Abstract: We consider the scaling of the mass flux and entrainment velocity across the turbulent/non-turbulent interface (TNTI) in the far field of an axisymmetric jet at high Reynolds number. Time-resolved, simultaneous multi-scale particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to identify and track the TNTI, and directly measure the local entrainment velocity along it. Application of box-counting and spatial-filtering methods, with filter sizes spanning over two decades in length, show that the mean length of the TNTI exhibits a power-law behaviour with a fractal dimension . More importantly, we invoke a multi-scale methodology to confirm that the mean mass flux, which is equal to the product of the entrainment velocity and the surface area, remains constant across the range of filter sizes. The results, within experimental uncertainty, also show that the entrainment velocity along the TNTI exhibits a power-law behaviour with , such that the entrainment velocity increases with increasing . In fact, the mean entrainment velocity scales at a rate that balances the scaling of the TNTI length such that the mass flux remains independent of the coarse-grain filter size, as first suggested by Meneveau & Sreenivasan (Phys. Rev. A, vol. 41, no. 4, 1990, pp. 2246–2248). Hence, at the smallest scales the entrainment velocity is small but is balanced by the presence of a very large surface area, whilst at the largest scales the entrainment velocity is large but is balanced by a smaller (smoother) surface area.
67 citations
Cites background from "The Turbulent/Non-turbulent Interfa..."
...This is achieved by directly measuring the velocity at which non-turbulent fluid flows into the turbulent region, in a manner similar to Chauhan et al. (2014b); a description of this process follows....
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...Similar fractal dimensions are also observed by Chauhan et al. (2014b) in the TNTI of a turbulent boundary layer, and by Zubair & Catrakis (2009) in separated shear layers but for general scalar isosurfaces....
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...This is also supported by Chauhan et al. (2014b), who report a fractal dimension of D2 = 1.3, and by Zubair & Catrakis (2009), who report a fractal dimension for scalar isocontours in a shear layer flow of D2= 1.3....
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...The TNTI is a region of finite thickness across which the vorticity smoothly transitions from the non-turbulent levels to the magnitude of the turbulent region (Taveira & da Silva 2014; Chauhan et al. 2014a)....
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...One of the consequences of the self-similarity of the flow is that the distribution of the TNTI radial position, rI , is also self-similar (Bisset et al. 2002; Westerweel et al. 2005; Gampert et al. 2014; Chauhan et al. 2014b)....
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References
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TL;DR: In this article, Spark shadow pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainedment rates, and large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle.
Abstract: Plane turbulent mixing between two streams of different gases (especially nitrogen and helium) was studied in a novel apparatus Spark shadow pictures showed that, for all ratios of densities in the two streams, the mixing layer is dominated by large coherent structures High-speed movies showed that these convect at nearly constant speed, and increase their size and spacing discontinuously by amalgamation with neighbouring ones The pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainment rates Large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle; it is concluded that the strong effects, which are observed when one stream is supersonic, are due to compressibility effects, not density effects, as has been generally supposed
3,339 citations
"The Turbulent/Non-turbulent Interfa..." refers background in this paper
...One can then define a vorticity thickness (e.g. Brown & Roshko 1974) based on the measured change in 〈Ũ〉 and its local gradient as δω ≡ D[〈Ũ〉] d〈Ũ〉 dz ∣∣∣∣ max ....
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...In the second case, since the flows have been observed to be dominated by large-scale motions (such as those observed in jets by Brown & Roshko (1974) and in wakes by Cannon, Champagne & Glezer (1993), to name a few), it is not clear how important the turbulent diffusion is compared with the role…...
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TL;DR: In this article, the authors examined the effect of roughness on boundary layer characteristics and showed that the wall is aerodynamically smooth for a turbulent boundary layer if the roughness elements are so small as to be buried in the laminar sublayer.
Abstract: Publisher Summary This chapter discusses the simple case of the turbulent boundary layer in a constant pressure field and considers the complex problem of the effects of pressure gradients, and variable wall roughness The concepts of boundary layer phenomena, in general, and turbulent boundary layers, in particular, have found application in a wide range of fields including aeronautics, guided missiles, marine engineering, hydraulics, meteorology, oceanography, chemical engineering, atomic reactors, and the flow of liquids and gases in the human body Many ideas for turbulent boundary layers involve assumptions other than those for turbulent shear stresses and in these cases, the validity of the results is examined first for laminar layers and then interpreted in the light of the possible shear stress patterns of turbulent layers The effect of roughness on boundary layer characteristics is examined in the chapter The wall is aerodynamically smooth for a turbulent boundary layer if the roughness elements are so small as to be buried in the laminar sublayer Pressure gradients, Reynolds number, or roughness does not affect the constants of proportionality The assumption of a constant outer viscosity has been investigated only for the case of equilibrium layers
1,367 citations
"The Turbulent/Non-turbulent Interfa..." refers background in this paper
...Kovasznay (1970) forwarded the understanding that large-scale turbulent bursts that emerge from near the wall survive long enough to reach the outer part of the boundary layer resulting in the external intermittency characterized by turbulent/non-turbulent regions....
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...The large-scale organization of the interface in the form of appearance of bulges and valleys can be either an outcome of local instability at the interface (Townsend 1966) or motions triggered by the near-wall turbulence (Kovasznay 1970)....
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TL;DR: The hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments as discussed by the authors.
Abstract: Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.
1,176 citations
"The Turbulent/Non-turbulent Interfa..." refers result in this paper
...These views are consistent with the views of Adrian (2007) where the bulges/valleys in the outer region are interpreted as large-scale motions in the form of packets of attached eddies that extend to the edge of the boundary layer....
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TL;DR: The Structure of Turbulent Shear Flow by Dr. A.Townsend as mentioned in this paper is a well-known work in the field of fluid dynamics and has been used extensively in many applications.
Abstract: The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.
1,050 citations
"The Turbulent/Non-turbulent Interfa..." refers background in this paper
...…the TNTI; and two, that the spreading process of the turbulent region in shear flows is similar to turbulent diffusion (gauged by the observation of wake shadowgraphs, which unfortunately do not show the entrapped non-turbulent fluid inside the turbulent region, as mentioned by Townsend (1976))....
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TL;DR: The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales as mentioned in this paper.
Abstract: The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.
784 citations