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

Significance 

The impact of events such as the Deepwater Horizon oil leak and the Icelandic volcano eruption largely depend on the dispersion of contaminants within the rising buoyant plumes of oil and gas or volcanic gas and ash that form. Predicting the fate of the plume fluid and its contaminants relies on appropriate parameterisation of the turbulent entrainment by the plume. At large scales, this entrainment can be viewed as the action through which ambient fluid in the ocean or atmosphere is drawn in towards the rising plume. At small scales, it may be considered as a process through which irreversible mixing of ambient and plume fluid occurs due to molecular interactions.

This process of turbulent entrainment in a plume eventually leads to fluid being mixed irreversibly at scales where molecular diffusivity is dominant. The irreversible fluid mixing has been found to occur at significantly enhanced rates owing to stretching of surfaces by vorticity in turbulent flows. For this mixing to occur efficiently, vorticity must first be imparted to the entrained fluid. This occurs as a result of viscous stresses at the interface between the non-turbulent and turbulent fluids at a scale near the Taylor micro scale. This process is termed ‘nibbling’, and for efficient (ultimate) mixing, all the entrained fluid must undergo this process. Therefore, the significance of the nibbling process within turbulent entrained fluid should not be overlooked.

Dr. Henry Burridge at Imperial College London in collaboration with David Parker, Emily Kruger, Dr. Jamie Partridge, and Professor Paul Linden at the University of Cambridge investigated the role of the ‘engulfment’ process as part of the mechanism of entrainment by turbulent plumes. This engulfment results from transport of ambient fluid across the outer envelope of the plume by the large-scale turbulence prior to fluid being nibbled across the turbulent/non-turbulent interface (TNTI). In their study they argued that nibbling should not be emphasised at the expense of engulfment, and that engulfment is expected to be the rate limiting process within the entrainment by turbulent plumes. Their research work is published in Journal of Fluid Mechanics.

Through simultaneous measurements of the velocity field and the scalar edge of the plume, the authors demonstrated that considerable vertical velocities occur outside the instantaneous plume envelope. Velocities beyond the plume edge cannot be induced by viscous effects and must be a result of long-range pressure gradients. The authors observed that the vertical transport outside the plume, i.e. within the ambient fluid, was significant – in the mean about 5% of the total vertical transport and increasing to about 14% at heights between eddies. Moreover, they identified that the fluxes of unmixed ‘engulfed’ fluid within the plume envelope were significant and were of similar magnitude to the vertical transport of ambient fluid outside the plume. These findings indicate that the vertical acceleration of ambient fluid, at heights between large-scale eddies at the plume edge plays a significant role in the process of turbulent entrainment. Furthermore, the vertical motion imparted on this ambient fluid is likely to enable it to be efficiently engulfed across the plume envelope before being nibbled across the TNTI.

In view of these finding, the authors concluded that nearly all of the entrained fluid was first engulfed by the plume before being nibbled across the TNTI and then ultimately mixed at molecular scales.

high Péclet number turbulent plume and implications for entrainment-Advances in Engineering
FIGURE LEGEND Two typical experimental images of a plume. The small dark ‘spots’ in both images are the  50 µm particles used to obtain PIV measurements. Dense ‘plume fluid’, stained by dye, is indicated by dark regions in each image. The edges detected by both algorithms are marked by the red solid lines (7 pixels wide) and blue solid lines (3 pixels wide). Velocity vectors (red arrows) indicate the local two-dimensional velocity on the vertical central plane of the plume. Notice that where large-scale eddies are locally present the vertical velocities are small just outside and inside the plume edge (circled in green). At the locations where eddies are locally absent the vertical velocities outside the plume are significant (circled in red). The heights at which the measurement of the local width Rp indicate that large-scale coherent structures are present and absent are indicated by coloured bars (green present, red absent) on the left-hand edges of the two images. Credit with permission: Journal of Fluid Mechanics, volume 823 (2017), pages 26–56.

 

About the author

David Parker did his MSci in Mathematics at the University of Bristol and his MSc in Aeronautics at Imperial College London. He then moved to the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, where he is currently studying for a PhD in Natural Ventilation.

His research focuses on the entrainment process in flows driven by distributed buoyancy sources, and the resulting stratification that evolves within a ventilated environment. The PhD project is an iCASE award with Arup.

About the author

Emily Kruger graduated from Keele University with a BSc in Mathematics, and from the University of Oxford with an MSc in Mathematical Modelling and Scientific Computing. She then moved the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, where she is currently studying for a PhD in the Dynamics of Downdrafts on an iCASE award with the MET Office.

She is studying the effect of the initial conditions of a finite dense release impacting a surface and spreading as an axisymmetric gravity current. She uses both laboratory and numerical experiments to verify models of the descent and gravity current phases of the flow.

About the author

Henry Burridge is a Lecturer in Environmental Fluid Mechanics in the Department of Civil and Environmental Engineering at Imperial College London. He has held postdoctoral research positions at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, and the Department of Engineering, University of Cambridge. Prior to this he was Vice President of Fund Linked Derivatives Trading at Credit Suisse.

Henry’s research focuses on fluid mechanics for the built environment. This ranges from the fundamental understanding of turbulent flows and mixing with buoyancy effects and stratification, includes the practical application of this understanding to the human-focused ventilation of buildings and encompasses the slow viscous flow of liquids in wood and timber. To this end Henry co-leads the Low-Energy Ventilation Network which received EPSRC funding from the UK Fluids Network as a Special Interest Group, collaborates widely with industrial and academic partners, and maintains active projects with the Natural Materials Innovation for Sustainable Living centre in Cambridge.

About the author

Jamie Partridge is currently a Research Associate at the University of Cambridge working in the Department of Mathematics and Theoretical Physics. He was supervised by Prof. Paul Linden for his PhD where he studied natural-ventilation flows. His broader interests include stratified turbulence and experimental techniques.

About the author

Paul Linden is Director of Research and the GI Taylor Professor Emeritus of Fluid Mechanics in the Department of Applied Mathematics and Theoretical Physics, and Professorial Fellow Emeritus of Downing College, University of Cambridge.

He is also the Blasker Distinguished Professor Emeritus of Environmental Science and Engineering in the Department of Mechanical and Aerospace Engineering at UC San Diego. While at UC San Diego he was chair of the MAE department (2004-2009), the Director of the Environment and Sustainability Initiative (2007-2009) and the founding Director of the Sustainability Solutions Institute (2009-2010). He is a Fellow of the American Physical Society, the Royal Meteorological Society, Academia Europaea, and the Royal Society.

Paul is a fluid dynamicist and his research is concerned with fluid flow in the environment and in industry. In particular, he is interested in flow and turbulence in stratified and two-phase fluids, the fluid dynamics of advanced, naturally ventilated buildings, and flows on large scales where the rotation of the Earth is important. He uses laboratory experiments and theoretical models to elucidate the relevant physical processes underlying these flows and to provide predictions of their properties that can be applied in practice. Paul is a Deputy Editor of the Journal of Fluid Mechanics and the Editor of JFM Perspectives.

He currently leads three major projects in the UK. An Engineering and Physical Sciences Research Council (EPSRC) Programme Grant on the Mathematical Underpinnings of Stratified Turbulence (MUST) from 2013-2018, an EPSRC Grand Challenge grant on Future Cities: Managing Air for Green Inner Cities (MAGIC) from 2016-2021 and an European Research Council Advanced Grant on Stratified Turbulence and Mixing Processes (STAMP) 2017-2022.

Reference

H. C. Burridge, D. A. Parker, E. S. Kruger, J. L. Partridge and P. F. Linden. Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment. Journal of Fluid Mechanics, volume 823 (2017), pages 26–56.

 

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