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Global and local aspects of entrainment in temporal plumes

Published online by Cambridge University Press:  22 December 2016

Dominik Krug Open the ORCID record for Dominik Krug [Opens in a new window] ,
Daniel Chung Open the ORCID record for Daniel Chung [Opens in a new window] ,
Jimmy Philip  and
Ivan Marusic
Dominik Krug*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
Daniel Chung
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
Jimmy Philip
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

To date, the understanding of the role buoyancy plays in the entrainment process in unstable configurations such as turbulent plumes remains incomplete. Towards addressing this question, we set up a flow in which a plume evolves in time instead of space. We demonstrate that the temporal problem is equivalent to a spatial plume in a strong coflow and address in detail how the temporal plume can be realized via direct numerical simulation. Using numerical data of plume simulations up to $Re_{\unicode[STIX]{x1D706}}\approx 100$, we show that the entrainment coefficient can be determined consistently using a global entrainment analysis in an integral framework as well as via a local approach. The latter is based on a study of the local propagation of the turbulent/non-turbulent interface relative to the fluid. Locally, this process is dominated by small-scale diffusion which is amplified by interface convolutions such that the total entrained flux is independent of viscosity. Further, we identify a direct buoyancy contribution to entrainment by baroclinic torque, which accounts for 8 %–12 % of the entrained flux locally, comparable to the 15 % buoyancy contribution at the integral level. It appears that the baroclinic torque is a mechanism that might explain higher values of the entrainment coefficient in spatial plumes compared with jets.

JFM classification

Convection: Convection Convection: Plumes/thermals Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 222 - 250
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Copyright
© 2016 Cambridge University Press 

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