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Under pressure: turbulent plumes in a uniform crossflow

Published online by Cambridge University Press:  15 December 2021

Owen H. Jordan Open the ORCID record for Owen H. Jordan [Opens in a new window] ,
Gabriel G. Rooney Open the ORCID record for Gabriel G. Rooney [Opens in a new window] ,
Benjamin J. Devenish Open the ORCID record for Benjamin J. Devenish [Opens in a new window]  and
Maarten van Reeuwijk Open the ORCID record for Maarten van Reeuwijk [Opens in a new window]
Owen H. Jordan
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
Gabriel G. Rooney
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK
Benjamin J. Devenish
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK
Maarten van Reeuwijk*
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: m.vanreeuwijk@imperial.ac.uk
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Abstract

Direct numerical simulation is used to investigate the integral behaviour of buoyant plumes subjected to a uniform crossflow that are infinitely lazy at the source. Neither a plume trajectory defined by the centre of mass of the plume $z_c$ nor a trajectory defined by the central streamline $z_{U}$ is aligned with the average streamlines inside the plume. Both $z_c$ and $z_{U}$ are shown to correlate with field lines of the total buoyancy flux, which implies that a model for the vertical turbulent buoyancy flux is required to faithfully predict the plume angle. A study of the volume conservation equation shows that entrainment due to incorporation of ambient fluid with non-zero velocity due to the increase in the surface area (the Leibniz term) is the dominant entrainment mechanism in strong crossflows. The data indicate that pressure differences between the top and bottom of the plume play a leading role in the evolution of the horizontal and vertical momentum balances and are crucial for appropriately modelling plume rise. By direct parameterisation of the vertical buoyancy flux, the entrainment and the pressure, an integral plume model is developed which is in good agreement with the simulations for sufficiently strong crossflow. A perturbation expansion shows that the current model is an intermediate-range model valid for downstream distances up to $100\ell _b$–$1000 \ell _b$, where $\ell _b$ is the buoyancy length scale based on the flow speed and plume buoyancy flux.

JFM classification

Convection: Plumes/thermals Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A47
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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