Статті в журналах: "Turbulent/non-Turbulent interface"

1

Teixeira, M. A. C., and C. B. da Silva. "Turbulence dynamics near a turbulent/non-turbulent interface." Journal of Fluid Mechanics 695 (February 13, 2012): 257–87. http://dx.doi.org/10.1017/jfm.2012.17.

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AbstractThe characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate ($\varepsilon $), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer),$\varepsilon $decays as${z}^{\ensuremath{-} 6} $, where$z$is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and$\varepsilon $display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness$\delta $of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that$\delta \ensuremath{\sim} \eta $(where$\eta $is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

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2

Elsinga, G. E., and C. B. da Silva. "How the turbulent/non-turbulent interface is different from internal turbulence." Journal of Fluid Mechanics 866 (March 5, 2019): 216–38. http://dx.doi.org/10.1017/jfm.2019.85.

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The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20$^{\text{o}}$. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.

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3

Borrell, Guillem, and Javier Jiménez. "Properties of the turbulent/non-turbulent interface in boundary layers." Journal of Fluid Mechanics 801 (July 26, 2016): 554–96. http://dx.doi.org/10.1017/jfm.2016.430.

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The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the Reynolds number range$Re_{{\it\theta}}=2800{-}6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This requires the introduction of a new definition of the distance between a point and a general surface, which is compared with the more usual vertical distance to the top of the layer. Interfaces are obtained by thresholding the enstrophy field and the magnitude of the rate-of-strain tensor, and it is concluded that, while the former are physically relevant features, the latter are not. By varying the threshold, a topological transition is identified as the interface moves from the free stream into the turbulent core. A vorticity scale is defined which collapses that transition for different Reynolds numbers, roughly equivalent to the root-mean-squared vorticity at the edge of the boundary layer. Conditionally averaged flow variables are analysed as functions of the new distance, both within and outside the interface. It is found that the interface contains a non-equilibrium layer whose thickness scales well with the Taylor microscale, enveloping a self-similar layer spanning a fixed fraction of the boundary-layer thickness. Interestingly, the straining structure of the flow is similar in both regions. Irrotational pockets within the turbulent core are also studied. They form a self-similar set whose size decreases with increasing depth, presumably due to breakup by the turbulence, but the rate of viscous diffusion is independent of the pocket size. The raw data used in the analysis are freely available from our web page (http://torroja.dmt.upm.es).

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4

Ferrey, P., and B. Aupoix. "Behaviour of turbulence models near a turbulent/non-turbulent interface revisited." International Journal of Heat and Fluid Flow 27, no. 5 (October 2006): 831–37. http://dx.doi.org/10.1016/j.ijheatfluidflow.2006.03.022.

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5

BISSET, DAVID K., JULIAN C. R. HUNT, and MICHAEL M. ROGERS. "The turbulent/non-turbulent interface bounding a far wake." Journal of Fluid Mechanics 451 (January 25, 2002): 383–410. http://dx.doi.org/10.1017/s0022112001006759.

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The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. (1998) are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations on either side of a thin randomly moving interface. Comparisons are made with a wake that is ‘forced’ by amplifying initial velocity fluctuations. A temperature field T, with constant values of 1.0 and 0 above and below the wake, is transported across the wake as a passive scalar. The value of the Reynolds number based on the centreplane mean velocity defect and half-width b of the wake is Re ≈ 2000.The thickness of the continuous interface is about 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement yI(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of yI and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y−yI the conditional mean velocity 〈U〉 and temperature 〈T〉 profiles show sharp jumps at the interface adjacent to a thick zone where 〈U〉 and 〈T〉 vary much more slowly.Statistics for the conditional vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. While mean Reynolds stresses (in the fixed reference frame) decrease gradually in the intermittent zone, conditional stresses are roughly constant and then decrease sharply towards zero at the interface. Flow fields around the interface, analysed in terms of the local streamline pattern, confirm and explain previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion.Terms used in one-point turbulence models are evaluated both conventionally and conditionally in the interface region, and the current practice in statistical models of approximating entrainment by a diffusion process is assessed.

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6

Li, Sicheng, Yanguang Long, and Jinjun Wang. "Turbulent/non-turbulent interface for laminar boundary flow over a wall-mounted fence." Physics of Fluids 34, no. 12 (December 2022): 125113. http://dx.doi.org/10.1063/5.0128609.

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The turbulent/non-turbulent interface plays an important role in the exchange of mass, momentum, and energy between turbulent and nonturbulent flows. However, the role played by the interface in the separation and reattachment flow remains poorly understood. This study, thus, investigates the geometrical and dynamic properties of the interface in the separation and reattachment flow induced by a wall-mounted fence by using particle image velocimetry in a water tunnel. The flow undergoes laminar separation, reattachment, and the recovery of the boundary layer. Finally, the fully developed turbulent boundary layer is established. The geometrical and dynamic properties of the interface vary consistently with the vortex structure. The geometrical properties change most quickly above the reattachment point, where the dynamic properties are maximal. Before the reattachment point, the shear motion of the fluid contributes significantly to the interface properties. As a result, the interface thickness does not scale with the size of the nearby vortex until reattachment. Additionally, quasiperiodic shedding vortices significantly affect the interface properties. Remarkable bulges and troughs of the interface form corresponding to the spatial arrangement of the shedding vortices. In addition, the conditional averaged dynamic quantities peak along the interface coordinate as the turbulence intensity is enhanced by the shedding vortex. This study provides a new perspective of the turbulent/non-turbulent interface, improves our understanding of turbulent diffusion in the separation and reattachment flow, and clarifies how the separated flow and shedding vortices affect the interface properties.

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7

Lee, Jin, Hyung Jin Sung, and Tamer A. Zaki. "Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers." Journal of Fluid Mechanics 819 (April 18, 2017): 165–87. http://dx.doi.org/10.1017/jfm.2017.170.

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The effect of large-scale motions (LSMs) on the turbulent/non-turbulent (T/NT) interface is examined in a turbulent boundary layer. Using flow fields from direct numerical simulation, the shape of the interface and near-interface statistics are evaluated conditional on the position of the LSM. The T/NT interface is identified using the vorticity magnitude and a streak detection algorithm is adopted to identify and track the LSMs. Two-point correlation and spectral analysis of variations in the interface height show that the spatial undulation of the interface is longer in streamwise wavelength than the boundary-layer thickness, and grows with the Reynolds number in a similar manner to the LSMs. The average variation in the interface height was evaluated conditional on the position of the LSMs. The result provides statistical evidence that the interface is locally modulated by the LSMs in both the streamwise and spanwise directions. The modulation is different when the coherent structure is high- versus low-speed motion: high-speed structures lead to a wedge-shaped deformation of the T/NT interface, which causes an anti-correlation between the angles of the interface and the internal shear layer. On the other hand, low-speed structures are correlated with crests in the interface. Finally, the sudden changes in turbulence statistics across the interface are in line with the changes in the population of low-speed structures, which consist of slower mean streamwise velocity and stronger turbulence than the high-speed counterparts.

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8

Yu, Jia-Long, and Xi-Yun Lu. "Topological evolution near the turbulent/non-turbulent interface in turbulent mixing layer." Journal of Turbulence 20, no. 5 (May 4, 2019): 300–321. http://dx.doi.org/10.1080/14685248.2019.1640368.

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9

Steiner, Helfried, and Christian Walchshofer. "Small-scale mixing at the turbulent/non-turbulent interface in turbulent jets." PAMM 11, no. 1 (December 2011): 601–2. http://dx.doi.org/10.1002/pamm.201110290.

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10

Neuhaus, Lars, Matthias Wächter, and Joachim Peinke. "The fractal turbulent–non-turbulent interface in the atmosphere." Wind Energy Science 9, no. 2 (February 22, 2024): 439–52. http://dx.doi.org/10.5194/wes-9-439-2024.

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Abstract. With their constant increase in size, wind turbines are reaching unprecedented heights. Therefore, at these heights, they are influenced by wind conditions that have not yet been studied in detail. With increasing height, a transition to laminar conditions becomes more and more likely. In this paper, the presence of the turbulent–non-turbulent interface (TNTI) in the atmosphere is investigated. Three different on- and offshore locations are investigated. Our fractal scaling analysis leads to typical values known from ideal laboratory and numerical studies. The height distribution of the probability of the TNTI is determined and shows a frequent occurrence at the height of the rotor of future multi-megawatt turbines. The indicated universality of the fractality of the TNTI allows the use of simplified models in laboratory and numerical investigations.

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11

Westerweel, Jerry, Alberto Petracci, René Delfos, and Julian C. R. Hunt. "Characteristics of the turbulent/non-turbulent interface of a non-isothermal jet." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1937 (February 28, 2011): 723–37. http://dx.doi.org/10.1098/rsta.2010.0308.

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The turbulent/non-turbulent interface of a jet is characterized by sharp jumps (‘discontinuities’) in the conditional flow statistics relative to the interface. Experiments were carried out to measure the conditional flow statistics for a non-isothermal jet, i.e. a cooled jet. These experiments are complementary to previous experiments on an isothermal Re =2000 jet, where, in the present experiments on a non-isothermal jet, the thermal diffusivity is intermediate to the diffusivity of momentum and the diffusivity of mass. The experimental method is a combined laser-induced fluorescence/particle image velocimetry method, where a temperature-sensitive fluorescent dye (rhodamine 6G) is used to measure the instantaneous temperature fluctuations. The results show that the cooled jet can be considered to behave like a self-similar jet without any significant buoyancy effects. The detection of the interface is based on the instantaneous temperature, and provides a reliable means to detect the interface. Conditional flow statistics reveal the superlayer jump in the conditional vorticity and in the temperature.

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12

Breda, M., and O. R. H. Buxton. "Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets." Journal of Fluid Mechanics 879 (September 20, 2019): 187–216. http://dx.doi.org/10.1017/jfm.2019.676.

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Tomographic particle image velocimetry experiments were conducted in the near and intermediate fields of two different types of jet, one fitted with a circular orifice and another fitted with a repeating-fractal-pattern orifice. Breda & Buxton (J. Vis., vol. 21 (4), 2018, pp. 525–532; Phys. Fluids, vol. 30, 2018, 035109) showed that this fractal geometry suppressed the large-scale coherent structures present in the near field and affected the rate of entrainment of background fluid into, and subsequent development of, the fractal jet, relative to the round jet. In light of these findings we now examine the modification of the turbulent/non-turbulent interface (TNTI) and spatial evolution of the small-scale behaviour of these different jets, which are both important factors behind determining the entrainment rate. This evolution is examined in both the streamwise direction and within the TNTI itself where the fluid adapts from a non-turbulent state, initially through the direct action of viscosity and then through nonlinear inertial processes, to the state of the turbulence within the bulk of the flow over a short distance. We show that the suppression of the coherent structures in the fractal jet leads to a less contorted interface, with large-scale excursions of the inner TNTI (that between the jet’s azimuthal shear layer and the potential core) being suppressed. Further downstream, the behaviour of the TNTI is shown to be comparable for both jets. The velocity gradients develop into a canonical state with streamwise distance, manifested as the development of the classical tear-drop shaped contours of the statistical distribution of the velocity-gradient-tensor invariants $\mathit{Q}$ and $\mathit{R}$. The velocity gradients also develop spatially through the TNTI from the irrotational boundary to the bulk flow; in particular, there is a strong small-scale anisotropy in this region. This strong inhomogeneity of the velocity gradients in the TNTI region has strong consequences for the scaling of the thickness of the TNTI in these spatially developing flows since both the Taylor and Kolmogorov length scales are directly computed from the velocity gradients.

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13

Zhang, Xinxian, Tomoaki Watanabe, and Koji Nagata. "Passive scalar mixing near turbulent/non-turbulent interface in compressible turbulent boundary layers." Physica Scripta 94, no. 4 (January 30, 2019): 044002. http://dx.doi.org/10.1088/1402-4896/aafbdf.

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14

Yang, Jongmin, Min Yoon, and Hyung Jin Sung. "The turbulent/non-turbulent interface in an adverse pressure gradient turbulent boundary layer." International Journal of Heat and Fluid Flow 86 (December 2020): 108704. http://dx.doi.org/10.1016/j.ijheatfluidflow.2020.108704.

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Gampert, Markus, Jonas Boschung, Fabian Hennig, Michael Gauding, and Norbert Peters. "The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface." Journal of Fluid Mechanics 750 (June 10, 2014): 578–96. http://dx.doi.org/10.1017/jfm.2014.280.

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AbstractBased on a direct numerical simulation (DNS) of a temporally evolving mixing layer, we present a detailed study of the turbulent/non-turbulent (T/NT) interface that is defined using the two most common procedures in the literature, namely either a vorticity or a scalar criterion. The different detection approaches are examined qualitatively and quantitatively in terms of the interface position, conditional statistics and orientation of streamlines and vortex lines at the interface. Computing the probability density function (p.d.f.) of the mean location of the T/NT interface from vorticity and scalar allows a detailed comparison of the two methods, where we observe a very good agreement. Furthermore, conditional mean profiles of various quantities are evaluated. In particular, the position p.d.f.s for both criteria coincide and are found to follow a Gaussian distribution. The terms of the governing equations for vorticity and passive scalar are conditioned on the distance to the interface and analysed. At the interface, vortex stretching is negligible and the displacement of the vorticity interface is found to be determined by diffusion, analogous to the scalar interface. In addition, the orientation of vortex lines at the vorticity and the scalar based T/NT interface are analyzed. For both interfaces, vorticity lines are perpendicular to the normal vector of the interface, i.e. parallel to the interface isosurface.

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Silva, Tiago S., Marco Zecchetto, and Carlos B. da Silva. "The scaling of the turbulent/non-turbulent interface at high Reynolds numbers." Journal of Fluid Mechanics 843 (March 21, 2018): 156–79. http://dx.doi.org/10.1017/jfm.2018.143.

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The scaling of the turbulent/non-turbulent interface (TNTI) at high Reynolds numbers is investigated by using direct numerical simulations (DNS) of temporal turbulent planar jets (PJET) and shear free turbulence (SFT), with Reynolds numbers in the range $142\leqslant Re_{\unicode[STIX]{x1D706}}\leqslant 400$. For $Re_{\unicode[STIX]{x1D706}}\gtrsim 200$ the thickness of the TNTI ($\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D714}}$), like that of its two sublayers – the viscous superlayer (VSL, $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$) and the turbulent sublayer (TSL, $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D70E}}$) – all scale with the Kolmogorov micro-scale $\unicode[STIX]{x1D702}$, while the particular scaling constant depends on the sublayer. Specifically, for $Re_{\unicode[STIX]{x1D706}}\gtrsim 200$ while the VSL is always of the order of $\unicode[STIX]{x1D702}$, with $4\leqslant \langle \unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}\rangle /\unicode[STIX]{x1D702}\leqslant 5$, the TSL and the TNTI are typically equal to $10\unicode[STIX]{x1D702}$, with $10.4\leqslant \langle \unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D70E}}\rangle /\unicode[STIX]{x1D702}\leqslant 12.5$, and $15.4\leqslant \langle \unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D714}}\rangle /\unicode[STIX]{x1D702}\leqslant 16.8$, respectively.

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17

Chauhan, Kapil, Jimmy Philip, and Ivan Marusic. "Scaling of the turbulent/non-turbulent interface in boundary layers." Journal of Fluid Mechanics 751 (June 19, 2014): 298–328. http://dx.doi.org/10.1017/jfm.2014.298.

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AbstractScaling of the interface that demarcates a turbulent boundary layer from the non-turbulent free stream is sought using theoretical reasoning and experimental evidence in a zero-pressure-gradient boundary layer. The data-analysis, utilising particle image velocimetry (PIV) measurements at four different Reynolds numbers ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\delta u_{\tau }/\nu =1200\mbox{--}14\, 500$), indicates the presence of a viscosity dominated interface at all Reynolds numbers. It is found that the mean normal velocity across the interface and the tangential velocity jump scale with the skin-friction velocity$u_{\tau }$and are approximately$u_{\tau }/10$and$u_{\tau }$, respectively. The width of the superlayer is characterised by the local vorticity thickness$\delta _{\omega }$and scales with the viscous length scale$\nu /u_{\tau }$. An order of magnitude analysis of the tangential momentum balance within the superlayer suggests that the turbulent motions also scale with inner velocity and length scales$u_{\tau }$and$\nu /u_{\tau }$, respectively. The influence of the wall on the dynamics in the superlayer is considered via Townsend’s similarity hypothesis, which can be extended to account for the viscous influence at the turbulent/non-turbulent interface. Similar to a turbulent far-wake the turbulent motions in the superlayer are of the same order as the mean velocity deficit, which lends to a physical explanation for the emergence of the wake profile in the outer part of the boundary layer.

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18

da Silva, Carlos Bettencourt, and Ricardo José Nunes dos Reis. "The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1937 (February 28, 2011): 738–53. http://dx.doi.org/10.1098/rsta.2010.0300.

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The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale R lsvs ≈ λ , while the radius of the IVS is of the order of the Kolmogorov micro-scale R ivs ∼ η . The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.

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Zhou, Y., and J. C. Vassilicos. "Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation." Journal of Fluid Mechanics 821 (May 25, 2017): 440–57. http://dx.doi.org/10.1017/jfm.2017.262.

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The scalings of the local entrainment velocity$v_{n}$of the turbulent/non-turbulent interface and of the turbulence dissipation rate are closely related to each other in an axisymmetric and self-similar turbulent wake. The turbulence dissipation scaling implied by the Kolmogorov equilibrium cascade phenomenology is consistent with a Kolmogorov scaling of$v_{n}$whereas the non-equilibrium dissipation scaling reported for various turbulent flows in Vassilicos (Annu. Rev. Fluid Mech., vol. 47, 2015, pp. 95–114), Dairayet al.(J. Fluid Mech., vol. 781, 2015, pp. 166–195), Goto & Vassilicos (Phys. Lett. A, vol. 379 (16), 2015, pp. 1144–1148) and Obligadoet al.(Phys. Rev. Fluids, vol. 1 (4), 2016, 044409) is consistent with a different scaling of $v_{n}$. We present results from a direct numerical simulation of a spatially developing axisymmetric and self-similar turbulent wake which supports this conclusion and the assumptions that it is based on.

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20

WESTERWEEL, J., C. FUKUSHIMA, J. M. PEDERSEN, and J. C. R. HUNT. "Momentum and scalar transport at the turbulent/non-turbulent interface of a jet." Journal of Fluid Mechanics 631 (July 17, 2009): 199–230. http://dx.doi.org/10.1017/s0022112009006600.

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Conditionally sampled measurements with particle image velocimetry (PIV) of a turbulent round submerged liquid jet in a laboratory have been taken at Re = 2 × 103 between 60 and 100 nozzle diameters from the nozzle in order to investigate the dynamics and transport processes at the continuous and well-defined bounding interface between the turbulent and non-turbulent regions of flow. The jet carries a fluorescent dye measured with planar laser-induced fluorescence (LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment’ velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centreline. Profiles of the conditional mean velocity, mean scalar and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar and a tendency towards a singularity in mean vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations by Mathew & Basu (Phys. Fluids, vol. 14, 2002, pp. 2065–2072) in showing that for a jet flow (without forcing) the entrainment process is dominated by small-scale eddying at the highly sheared interface (‘nibbling’), with large-scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. (Turbulent jets differ greatly from the free shear layer in this respect.) To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity. Theoretical arguments, following Hunt, Eames & Westerweel (in Proc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence, ed. Y. Kaneda, vol. 4, 2008, pp. 331–338, Springer), are proposed for how the vortex sheet develops, how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side and why the dominant entrainment process of jets and wakes differs from that of free shear layers.

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21

Watanabe, T., Y. Sakai, K. Nagata, Y. Ito, and T. Hayase. "Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers." Physics of Fluids 27, no. 8 (August 2015): 085109. http://dx.doi.org/10.1063/1.4928199.

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22

Chauhan, Kapil, Jimmy Philip, Charitha M. de Silva, Nicholas Hutchins, and Ivan Marusic. "The turbulent/non-turbulent interface and entrainment in a boundary layer." Journal of Fluid Mechanics 742 (February 21, 2014): 119–51. http://dx.doi.org/10.1017/jfm.2013.641.

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AbstractThe 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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23

Krug, Dominik, Markus Holzner, Beat Lüthi, Marc Wolf, Wolfgang Kinzelbach, and Arkady Tsinober. "The turbulent/non-turbulent interface in an inclined dense gravity current." Journal of Fluid Mechanics 765 (January 20, 2015): 303–24. http://dx.doi.org/10.1017/jfm.2014.738.

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AbstractWe present an experimental investigation of entrainment and the dynamics near the turbulent/non-turbulent interface in a dense gravity current. The main goal of the study is to investigate changes in the interfacial physics due to the presence of stratification and to examine their impact on the entrainment rate. To this end, three-dimensional data sets of the density and the velocity fields are obtained through a combined scanning particle tracking velocimetry/laser-induced fluorescence approach for two different stratification levels with inflow Richardson numbers of $\mathit{Ri}_{0}=0.23$ and $\mathit{Ri}_{0}=0.46$, respectively, at a Reynolds number around $\mathit{Re}_{0}=3700$. An analysis conditioned on the instantaneous position of the turbulent/non-turbulent interface as defined by a threshold on enstrophy reveals an interfacial region that is in many aspects independent of the initial level of stratification. This is reflected most prominently in matching peaks of the gradient Richardson number $\mathit{Ri}_{g}\approx 0.1$ located approximately $10{\it\eta}$ from the position of the interface inside the turbulent region, where ${\it\eta}=({\it\nu}^{3}/{\it\epsilon})^{1/4}$ is the Kolmogorov scale, and ${\it\nu}$ and ${\it\epsilon}$ denote the kinematic viscosity and the rate of turbulent dissipation, respectively. A possible explanation for this finding is offered in terms of a cyclic evolution in the interaction of stratification and shear involving the buildup of density and velocity gradients through inviscid amplification and their subsequent depletion through molecular effects and pressure. In accordance with the close agreement of the interfacial properties for the two cases, no significant differences were found for the local entrainment velocity, $v_{n}$ (defined as the propagation velocity of an enstrophy isosurface relative to the fluid), at different initial stratification levels. Moreover, we find that the baroclinic torque does not contribute significantly to the local entrainment velocity. Comparing results for the surface area of the convoluted interface to estimates from fractal scaling theory, we identify differences in the interface geometry as the major factor in the reduction of the entrainment rate due to density stratification.

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24

Watanabe, Tomoaki, Yasuhiko Sakai, Kouji Nagata, Yasumasa Ito, and Toshiyuki Hayase. "Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet." Journal of Fluid Mechanics 758 (October 13, 2014): 754–85. http://dx.doi.org/10.1017/jfm.2014.559.

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AbstractVortex stretching and compression, which cause enstrophy production by inviscid processes, are investigated near the turbulent/non-turbulent (T/NT) interface in a planar jet by using a direct numerical simulation (DNS). The enstrophy production is investigated by analysing the relationship among a vorticity vector, strain-rate eigenvectors and strain-rate eigenvalues. The statistics are calculated individually for three different interface orientations. The vorticity near the T/NT interface is oriented in the tangential direction to the interface. The enstrophy production is affected by the interface orientation because the intensity of vortex stretching depends on the interface orientation, and the alignment between the vorticity vector and the strain-rate eigenvectors is confined by the interface. The enstrophy production near the T/NT interface is analysed by considering the motion of turbulent fluid relative to that of the interface. The results show that the alignment between the interface and the strain-rate eigenvectors changes depending on the velocity field near the T/NT interface. When the turbulent fluid moves toward the T/NT interface, the enstrophy is generated by vortex stretching without being greatly affected by vortex compression. In contrast, when the turbulent fluid relatively moves away from the T/NT interface, large enstrophy reduction frequently occurs by vortex compression. Thus, it is shown that the velocity field near the T/NT interface affects the enstrophy production near the interface through the alignment between the vorticity and the strain-rate eigenvectors.

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25

Watanabe, Tomoaki, Carlos B. da Silva, Yasuhiko Sakai, Koji Nagata, and Toshiyuki Hayase. "Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers." Physics of Fluids 28, no. 3 (March 2016): 031701. http://dx.doi.org/10.1063/1.4942959.

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26

Gampert, Markus, Venkat Narayanaswamy, Philip Schaefer, and Norbert Peters. "Conditional statistics of the turbulent/non-turbulent interface in a jet flow." Journal of Fluid Mechanics 731 (August 29, 2013): 615–38. http://dx.doi.org/10.1017/jfm.2013.327.

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AbstractUsing two-dimensional high-speed measurements of the mixture fraction $Z$ in a turbulent round jet with nozzle-based Reynolds numbers $R{e}_{0} $ between 3000 and 18 440, we investigate the scalar turbulent/non-turbulent (T/NT) interface of the flow. The mixture fraction steeply changes from $Z= 0$ to a final value which is typically larger than 0.1. Since combustion occurs in the vicinity of the stoichiometric mixture fraction, which is around $Z= 0. 06$ for typical fuel/air mixtures, it is expected to take place largely within the turbulent/non-turbulent interface. Therefore, deep understanding of this part of the flow is essential for an accurate modelling of turbulent non-premixed combustion. To this end, we use a composite model developed by Effelsberg & Peters (Combust. Flame, vol. 50, 1983, pp. 351–360) for the probability density function (p.d.f.) $P(Z)$ which takes into account the different contributions from the fully turbulent as well as the turbulent/non-turbulent interface part of the flow. A very good agreement between the measurements and the model is observed over a wide range of axial and radial locations as well as at varying intermittency factor $\gamma $ and shear. Furthermore, we observe a constant mean mixture fraction value in the fully turbulent region. The p.d.f. of this region is thus of non-marching character, which is attributed physically to the meandering nature of the fully turbulent core of the jet flow. Finally, the location and in particular the scaling of the thickness $\delta $ of the scalar turbulent/non-turbulent interface are investigated. We provide the first experimental results for the thickness of the interface over the above-mentioned Reynolds number range and observe $\delta / L\sim R{ e}_{\lambda }^{- 1} $, where $L$ is an integral length scale and $R{e}_{\lambda } $ the local Reynolds number based on the Taylor scale $\lambda $, meaning that $\delta \sim \lambda $. This result also supports the assumption often made in modelling of the stoichiometric scalar dissipation rate ${\chi }_{st} $ being a Reynolds-number-independent quantity.

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27

da Silva, Carlos B., Ricardo J. N. dos Reis, and José C. F. Pereira. "The intense vorticity structures near the turbulent/non-turbulent interface in a jet." Journal of Fluid Mechanics 685 (September 5, 2011): 165–90. http://dx.doi.org/10.1017/jfm.2011.296.

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AbstractThe characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$, ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$, and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$, where ${u}_{0} $, and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$, tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$, ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.

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28

Wu, Di, JinJun Wang, GuangYao Cui, and Chong Pan. "Effects of surface shapes on properties of turbulent/non-turbulent interface in turbulent boundary layers." Science China Technological Sciences 63, no. 2 (June 6, 2019): 214–22. http://dx.doi.org/10.1007/s11431-018-9434-5.

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29

Westerweel, J., T. Hofmann, C. Fukushima, and J. Hunt. "The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet." Experiments in Fluids 33, no. 6 (December 2002): 873–78. http://dx.doi.org/10.1007/s00348-002-0489-5.

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30

Ishihara, Takashi, Hiroki Ogasawara, and Julian C. R. Hunt. "Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers." Journal of Fluids and Structures 53 (February 2015): 50–57. http://dx.doi.org/10.1016/j.jfluidstructs.2014.10.008.

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31

Hayashi, M., T. Watanabe, and K. Nagata. "The relation between shearing motions and the turbulent/non-turbulent interface in a turbulent planar jet." Physics of Fluids 33, no. 5 (May 2021): 055126. http://dx.doi.org/10.1063/5.0045376.

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32

Watanabe, T., Y. Sakai, K. Nagata, Y. Ito, and T. Hayase. "Wavelet analysis of coherent vorticity near the turbulent/non-turbulent interface in a turbulent planar jet." Physics of Fluids 26, no. 9 (September 2014): 095105. http://dx.doi.org/10.1063/1.4896298.

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33

HOLZNER, MARKUS, B. LÜTHI, A. TSINOBER, and W. KINZELBACH. "Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface." Journal of Fluid Mechanics 639 (October 23, 2009): 153–65. http://dx.doi.org/10.1017/s0022112009991522.

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This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy, ω2 = ωiωi, and strain, s2 = sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt ≃ ∂u/∂t ≃ −∇ p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) ≃ (∂/∂t)(s2/2) ≃ −sijp,ij > 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski > 0 start to set in. Comparison of the results at Taylor-based Reynolds numbers Reλ = 50 and Reλ = 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuations.

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34

HOLZNER, MARKUS, A. LIBERZON, N. NIKITIN, B. LÜTHI, W. KINZELBACH, and A. TSINOBER. "A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation." Journal of Fluid Mechanics 598 (February 25, 2008): 465–75. http://dx.doi.org/10.1017/s0022112008000141.

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We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, uη.

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35

Watanabe, T., Y. Sakai, K. Nagata, Y. Ito, and T. Hayase. "Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow." Physics of Fluids 26, no. 10 (October 2014): 105103. http://dx.doi.org/10.1063/1.4898208.

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36

Terashima, Osamu, Yasuhiko Sakai, Kouji Nagata, Yasumasa Ito, Kazuhiro Onishi, and Yuichi Shouji. "Simultaneous measurement of velocity and pressure near the turbulent/non-turbulent interface of a planar turbulent jet." Experimental Thermal and Fluid Science 75 (July 2016): 137–46. http://dx.doi.org/10.1016/j.expthermflusci.2016.02.007.

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37

Cimarelli, Andrea, Giacomo Cocconi, Bettina Frohnapfel, and Elisabetta De Angelis. "Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface." Physics of Fluids 27, no. 12 (December 2015): 125106. http://dx.doi.org/10.1063/1.4937433.

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38

Attili, Antonio, Juan C. Cristancho, and Fabrizio Bisetti. "Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer." Journal of Turbulence 15, no. 9 (June 2, 2014): 555–68. http://dx.doi.org/10.1080/14685248.2014.919394.

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39

ZHANG, Xinxian, Tomoaki WATANABE, and Koji NAGATA. "Direct numerical simulation study on turbulent/non-turbulent interface in compressible boundary layer." Proceedings of Conference of Tokai Branch 2017.66 (2017): 432. http://dx.doi.org/10.1299/jsmetokai.2017.66.432.

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40

KIT, E. L. G., E. J. STRANG, and H. J. S. FERNANDO. "Measurement of turbulence near shear-free density interfaces." Journal of Fluid Mechanics 334 (March 10, 1997): 293–314. http://dx.doi.org/10.1017/s0022112096004442.

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The results of an experimental study carried out to investigate the structure of turbulence near a shear-free density interface are presented. The experimental configuration consisted of a two-layer fluid medium in which the lower layer was maintained in a turbulent state by an oscillating grid. The measurements included the root-mean-square (r.m.s.) turbulent velocities, wavenumber spectra, dissipation of turbulent kinetic energy and integral lengthscales. It was found that the introduction of a density interface to a turbulent flow can strongly distort the structure of turbulence near the interface wherein the horizontal velocity components are amplified and the vertical component is damped. The modification of r.m.s velocities is essentially limited to distances smaller than about an integral lengthscale. Inspection of spectra shows that these distortions are felt only at small wavenumbers of the order of the integral scale and a range of low-wavenumbers of the inertial subrange; the distortions become pronounced as the interface is approached. Comparison of the horizontal velocity data with the rapid distortion theory (RDT) analyses of Hunt & Graham (1978) and Hunt (1984) showed a qualitative agreement near the interface and a quantitative agreement away from the interface. On the other hand, the RDT predictions for the vertical component were in general agreement with the data. The near-interface horizontal velocity data, however, showed quantitative agreement with a model proposed by Hunt (1984) based on nonlinear vortex dynamics near the interface. The effects due to interfacial waves appear to be important for distances less than about 10% of the integral lengthscale. As a consequence of the non-zero energy flux divergence, the introduction of a density interface to oscillating grid turbulence increases the rate of dissipation in the turbulent layer except near the interface, where a sharp drop occurs. The present measurements provide useful information on the structure of turbulence in shear-free boundary layers, such as atmospheric and oceanic convective boundary layers, thus improving modelling capabilities for such flows.

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41

WOODS, ANDREW W., C. P. CAULFIELD, J. R. LANDEL, and A. KUESTERS. "Non-invasive turbulent mixing across a density interface in a turbulent Taylor–Couette flow." Journal of Fluid Mechanics 663 (November 4, 2010): 347–57. http://dx.doi.org/10.1017/s0022112010004295.

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In this paper, we present new experimental measurements of the turbulent transport of salt across an interface between two layers of fluid of equal depth but different salinities. The fluid is confined to a cylindrical annulus with a vertical axis. The outer cylinder is stationary and the inner cylinder rotates to produce a turbulent flow field consisting of an approximately irrotational mean azimuthal flow, with narrow boundary layers on the inner and outer cylinders. We focus on the limit of high-Richardson-number flow, defined as Ri = gΔρH/(ρ0u2rms), where ρ0 is a reference density, Δρ is the time-dependent difference of the layers' mean densities, urms is the root mean square of the turbulent velocity fluctuations and H is the layer depth. The mean flow has Reynolds number of the order of 104−105, and the turbulent fluctuations in the azimuthal and radial directions have root-mean-square speed of order 10% of the mean azimuthal flow. Measurements based on our experimental system show that when the Richardson number is in the range 7 < Ri < 200, the interface between the two layers remains sharp, each layer remains well mixed, and the vertical flux of salt between the layers, Fs ~(1.15 ± 0.15)Ri−1𝒜(H/ΔR)urmsΔS, where ΔS is the spatially-averaged time-dependent salinity difference between the layers and in general 𝒜(H/ΔR) is a dimensionless function of the tank aspect ratio, here taken to be unity, with ΔR being the gap width of the annulus. The salt transport appears to be caused by turbulent eddies scouring and sharpening the interface and implies a constant rate of conversion of the turbulent kinetic energy to potential energy, independent of the density contrast between the layers. For smaller values of Ri, the flow regime changes qualitatively, with eddies penetrating the interface, causing fluid in the two layers to co-mingle and rapidly homogenize.

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42

Chandrasekhara, M. S., and B. R. Ramaprian. "Intermittency and Length Scale Distributions in a Plane Turbulent Plume." Journal of Fluids Engineering 112, no. 3 (September 1, 1990): 367–69. http://dx.doi.org/10.1115/1.2909413.

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Previous studies have shown that normalized Reynolds shear stress and turbulent heat fluxes in asymptotic plane turbulent plumes are significantly higher than in asymptotic plane turbulent jets. This paper describes an attempt to relate this increase to the length scales in the flow. Hot/cold interface intermittency and integral-length-scale distributions were measured in both these flows. The interface-intermittency distributions were found to be bell-shaped in the plume in contrast to a nearly top-hat shape in a jet, thus providing confirmation of the role of buoyancy in generating larger scales in plumes. These larger scales cause the integral length of turbulence in the plume to increase by nearly 15 percent relative to the non-buoyant jet.

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43

Watanabe, Tomoaki, James J. Riley, Koji Nagata, Ryo Onishi, and Keigo Matsuda. "A localized turbulent mixing layer in a uniformly stratified environment." Journal of Fluid Mechanics 849 (June 18, 2018): 245–76. http://dx.doi.org/10.1017/jfm.2018.400.

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Localized turbulence bounded by non-turbulent flow in a uniformly stratified environment is studied with direct numerical simulations of stably stratified shear layers. Of particular interest is the turbulent/non-turbulent interfacial (TNTI) layer, which is detected by identifying the turbulent region in terms of its potential vorticity. Fluid near the outer edge of the turbulent region gains potential vorticity and becomes turbulent by diffusion arising from both viscous and molecular effects. The flow properties near the TNTI layer change depending on the buoyancy Reynolds number near the interface,$Re_{bI}$. The TNTI layer thickness is approximately 13 times the Kolmogorov length scale for large$Re_{bI}$($Re_{bI}\gtrsim 30$), consistent with non-stratified flows, whereas it is almost equal to the vertical length scale of the stratified flow,$l_{vI}=l_{hI}Re^{-1/2}$(here$l_{hI}$is the horizontal length scale near the TNTI layer, and$Re$is the Reynolds number), in the low-$Re_{bI}$regime ($Re_{bI}\lesssim 2$). Turbulent fluid is vertically transported towards the TNTI layer when$Re_{bI}$is large, sustaining the thin TNTI layer with large buoyancy frequency and mean shear. This sharpening effect is weakened as$Re_{bI}$decreases and eventually becomes negligible for very low$Re_{bI}$. Overturning motions occur near the TNTI layer for large$Re_{bI}$. The dependence on buoyancy Reynolds number is related to the value of$Re_{bI}$near the TNTI layer, which is smaller than the value deep inside the turbulent core region. An imprint of the internal gravity waves propagating in the non-turbulent region is found for vorticity within the TNTI layer, inferring an interaction between turbulence and internal gravity waves. The wave energy flux causes a net loss of the kinetic energy in the turbulent core region bounded to the TNTI layer, and the amount of kinetic energy extracted from the turbulent region by internal gravity waves is comparable to the amount dissipated in the turbulent region.

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44

GERASHCHENKO, S., G. GOOD, and Z. WARHAFT. "Entrainment and mixing of water droplets across a shearless turbulent interface with and without gravitational effects." Journal of Fluid Mechanics 668 (January 26, 2011): 293–303. http://dx.doi.org/10.1017/s002211201000577x.

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We describe experiments of the entrainment and mixing of water (sub-Kolmogorov scale) droplets across a turbulent–non-turbulent interface (TNI) as well a turbulent–turbulent interface (TTI) in shearless grid turbulence, over a time scale in which evaporation is insignificant. The flow is produced by means of a splitter plate with an active grid and water sprays on one side and screens or an active grid on the other side. The Taylor microscale Reλ on the turbulent side is 275 and the average dissipation scale Stokes number, Stη ≈ 0.2, and based on the integral scale, Stl ≈ 0.003. By changing the orientation of the grid system, gravitational effects may be excluded or included. We show that in the absence of gravity, for the Stokes number range studied (0.06 ≤ Stη ≤ 1.33), the droplet distribution does not change across the interface. With gravity, the larger drops are selectively mixed and this is more pronounced for the TNI than for the TTI. The particle concentration distribution is an error function for the TTI but departs significantly for the TNI due to the intermittency in the flow. In terms of particle concentration, the entrainment is most efficient for the TTI with gravity. The results are related to droplet entrainment in clouds.

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45

Silva, Tiago S., and Carlos B. da Silva. "The behaviour of the scalar gradient across the turbulent/non-turbulent interface in jets." Physics of Fluids 29, no. 8 (August 2017): 085106. http://dx.doi.org/10.1063/1.4997951.

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46

Cocconi, G., E. De Angelis, B. Frohnapfel, M. Baevsky, and A. Liberzon. "Small scale dynamics of a shearless turbulent/non-turbulent interface in dilute polymer solutions." Physics of Fluids 29, no. 7 (July 2017): 075102. http://dx.doi.org/10.1063/1.4991921.

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47

Jahanbakhshi, R., N. S. Vaghefi, and C. K. Madnia. "Baroclinic vorticity generation near the turbulent/ non-turbulent interface in a compressible shear layer." Physics of Fluids 27, no. 10 (October 2015): 105105. http://dx.doi.org/10.1063/1.4933250.

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48

Mistry, Dhiren, Jimmy Philip, James R. Dawson, and Ivan Marusic. "Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet." Journal of Fluid Mechanics 802 (August 10, 2016): 690–725. http://dx.doi.org/10.1017/jfm.2016.474.

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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 $\unicode[STIX]{x1D6E5}$ spanning over two decades in length, show that the mean length of the TNTI exhibits a power-law behaviour with a fractal dimension $D\approx 0.31{-}0.33$. 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 $\unicode[STIX]{x1D6E5}$, such that the entrainment velocity increases with increasing $\unicode[STIX]{x1D6E5}$. 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.

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49

Scalo, Carlo, Ugo Piomelli, and Leon Boegman. "Self-similar decay and mixing of a high-Schmidt-number passive scalar in an oscillating boundary layer in the intermittently turbulent regime." Journal of Fluid Mechanics 726 (June 5, 2013): 338–70. http://dx.doi.org/10.1017/jfm.2013.228.

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AbstractWe performed numerical simulations of dissolved oxygen (DO) transfer from a turbulent flow, driven by periodic boundary-layer turbulence in the intermittent regime, to underlying DO-absorbing organic sediment layers. A uniform initial distribution of oxygen is left to decay (with no re-aeration) as the turbulent transport supplies the sediment with oxygen from the outer layers to be absorbed. A very thin diffusive sublayer at the sediment–water interface (SWI), caused by the high Schmidt number of DO in water, limits the overall decay rate. A decomposition of the instantaneous decaying turbulent scalar field is proposed, which results in the development of similarity solutions that collapse the data in time. The decomposition is then tested against the governing equations, leading to a rigorous procedure for the extraction of an ergodic turbulent scalar field. The latter is composed of a statistically periodic and a steady non-decaying field. Temporal averaging is used in lieu of ensemble averaging to evaluate flow statistics, allowing the investigation of turbulent mixing dynamics from a single flow realization. In spite of the highly unsteady state of turbulence, the monotonically decaying component is surprisingly consistent with experimental and numerical correlations valid for steady high-Schmidt-number turbulent mass transfer. Linearly superimposed onto it is the statistically periodic component, which incorporates all the features of the non-equilibrium state of turbulence. It is modulated by the evolution of the turbulent coherent structures driven by the oscillating boundary layer in the intermittent regime, which are responsible for the violent turbulent production mechanisms. These cause, in turn, a rapid increase of the turbulent mass flux at the edge of the diffusive sublayer. This outer-layer forcing mechanism drives a periodic accumulation of high scalar concentration levels in the near-wall region. The resulting modulated scalar flux across the SWI is delayed by a quarter of a cycle with respect to the wall-shear stress, consistently with the non-equilibrium state of the turbulent mixing.

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Neamtu-Halic, Marius M., Dominik Krug, George Haller, and Markus Holzner. "Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current." Journal of Fluid Mechanics 877 (August 27, 2019): 824–43. http://dx.doi.org/10.1017/jfm.2019.635.

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In this paper, we employ the theory of Lagrangian coherent structures for three-dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical Lagrangian coherent structures (VLCSs), a fully automated three-dimensional extraction algorithm for multiple flow structures based on the so-called Lagrangian-averaged vorticity deviation method is implemented. The size, the orientation and the shape of the VLCSs are analysed and the results show that these characteristics depend only weakly on the strength of the stratification. Through conditional analysis, we provide evidence that VLCSs modulate the average TNTI height, consequently affecting the entrainment process. Furthermore, VLCSs influence the local entrainment velocity and organize the flow field on both the turbulent and non-turbulent sides of the gravity current boundary.

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