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.
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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