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Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

  • H. C. Burridge (a1) (a2), D. A. Parker (a1), E. S. Kruger (a1), J. L. Partridge (a1) and P. F. Linden (a1)...

We present simultaneous two-dimensional velocity and scalar measurements on a central vertical plane in an axisymmetric pure turbulent plume. We use an edge-detection algorithm to determine the edge of the plume, and compare the data obtained in both a fixed Eulerian frame and a frame relative to local coordinates defined in terms of the instantaneous plume edge. In an Eulerian frame we observe that the time-averaged distributions of vertical and horizontal velocity are self-similar, the vertical velocity being well represented by a Gaussian distribution. We condition these measurements on whether fluid is inside or outside of the plume, and whether fluid inside is mixed plume fluid or engulfed ambient fluid. We find that, on average, 5 % of the total vertical volume transport occurs outside the plume and this figure rises to nearly 14 % at heights between large-scale coherent structures. We show that the fluxes of engulfed fluid within the plume envelope are slightly larger than the vertical transport outside the plume – indicating that ambient fluid is engulfed into the plume envelope before being nibbled across the turbulent/non-turbulent interface (TNTI) and then ultimately irreversibly mixed. Our new measurements in the plume coordinate (following the meandering fluctuating plume) show the flow within the plume and in the nearby ambient fluid is strongly influenced by whether an eddy is present locally within the plume, or absent. When an eddy is present and the plume is wide, the vertical velocities near the plume edge are small and hence all vertical transport is inside the plume. In regions where the plume is narrow and there is no eddy, large vertical velocities and hence transport are observed outside the plume suggesting that pressure forces associated with the eddies accelerate ambient fluid which is then engulfed into the plume. Finally, we show that observing significant vertical velocities beyond the scalar edge of the plume does not suggest that the characteristic width of the velocity distribution is greater than that of the scalar field; on the contrary, we show our observations to be consistent with a buoyancy distribution that is up to 20 % wider than that of the velocity. Measurements in the plume coordinates show that the mixing of momentum across the plume results in a distribution for which the differential entropy is close to maximal and the mixing of momentum is uninhibited (i.e. not bounded) by the TNTI of the plume. Furthermore, our measurements suggest that the scalar mixing across the plume may also result in a distribution for which the differential entropy is close to maximal but, in contrast to the momentum, the scalar mixing is strictly bounded by the plume edge.

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Burridge, H. C., Partridge, J. L. & Linden, P. F. 2016 The fluxes and behaviour of plumes inferred from measurements of coherent structures within images of the bulk flow. Atmos.-Ocean 54 (4), 403417.
Canny, J. 1986 A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 6, 679698.
Carazzo, G., Kaminski, E. & Tait, S. 2006 The route to self-similarity in turbulent jets and plumes. J. Fluid Mech. 547, 137148.
Corrsin, S. & Kistler, A. L.1955 Free-stream boundaries of turbulent flows. Tech. Rep. National Advisory Committee for Aeronautics.
Craske, J. & van Reeuwijk, M. 2016 Generalised unsteady plume theory. J. Fluid Mech. 792, 10131052.
Ezzamel, A., Salizzoni, P. & Hunt, G. R. 2015 Dynamical variability of axisymmetric buoyant plumes. J. Fluid Mech. 765, 576611.
Gampert, M., Boschung, J., Hennig, F., Gauding, M. & Peters, N. 2014 The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface. J. Fluid Mech. 750, 578596.
Holzner, M., Lüthi, B., Tsinober, A. & Kinzelbach, W. 2009 Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface. J. Fluid Mech. 639, 153165.
Hunt, G. R. & Kaye, N. G. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377396.
Hunt, G. R. & Linden, P. F. 2001 Steady-state flows in an enclosure ventilated by buoyancy forces assisted by wind. J. Fluid Mech. 426, 355386.
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361376.
Mistry, D., Philip, J., Dawson, J. R. & Marusic, I. 2016 Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690725.
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport vol. 3. Cambridge University Press.
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J. Fluid Mech. 246, 197223.
Papantoniou, D. & List, E. J. 1989 Large-scale structure in the far field of buoyant jets. J. Fluid Mech. 209, 151190.
Philip, J., Meneveau, C., de Silva, C. M. & Marusic, I. 2014 Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids 26 (1), 015105.
Priestly, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81, 144157.
van Reeuwijk, M. & Craske, J. 2015 Energy-consistent entrainment relations for jets and plumes. J. Fluid Mech. 782, 333355.
van Reeuwijk, M., Salizzoni, P., Hunt, G. R. & Craske, J. 2016 Turbulent transport and entrainment in jets and plumes: a DNS study. Phys. Rev. Fluids 1, 074301.
Shabbir, A. & George, W. K. 1994 Experiments in a round turbulent buoyant plume. J. Fluid Mech. 275, 132.
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567590.
de Silva, C. M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111 (4), 044501.
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421, 79108.
Taveira, R. R. & da Silva, C. B. 2013 Kinetic energy budgets near the turbulent/nonturbulent interface in jets. Phys. Fluids 25 (1), 015114.
Terashima, O., Sakai, Y., Nagata, K., Ito, Y., Onishi, K. & Shouji, Y. 2016 Simultaneous measurement of velocity and pressure near the turbulent/non-turbulent interface of a planar turbulent jet. Exp. Therm. Fluid Sci. 75, 137146.
Wang, H. & Law, A. W.-K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397428.
Westerweel, J., Fukushima, C., Pedersen, J. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199230.
Ying, C., Davidson, M. J., Wang, H. W. & Law, A. W. K. 2004 Radial velocities in axisymmetric jets and plumes. J. Hydraul Res. 42 (1), 2933.
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Journal of Fluid Mechanics
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  • EISSN: 1469-7645
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