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

Published online by Cambridge University Press:  15 June 2017

H. C. Burridge Open the ORCID record for H. C. Burridge [Opens in a new window] ,
D. A. Parker ,
E. S. Kruger ,
J. L. Partridge  and
P. F. Linden
H. C. Burridge*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK Department of Civil and Environmental Engineering, Skempton Building, Imperial College London, London SW7 2AZ, UK
D. A. Parker
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
E. S. Kruger
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
J. L. Partridge
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: h.burridge@imperial.ac.uk
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Abstract

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.

JFM classification

Convection: Convection Wakes/Jets: Jets Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 26 - 56
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Copyright
© 2017 Cambridge University Press 

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