Hostname: page-component-65f69f4695-bj4tz Total loading time: 0 Render date: 2025-06-27T20:56:27.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex-ring-induced stratified mixing: mixing model

Published online by Cambridge University Press:  20 December 2017

Jason Olsthoorn Open the ORCID record for Jason Olsthoorn [Opens in a new window]  and
Stuart B. Dalziel
Jason Olsthoorn*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Stuart B. Dalziel
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: Jason.Olsthoorn@cantab.net
Get access Rights & Permissions [Opens in a new window]

Abstract

The study of vortex-ring-induced mixing has been significant for understanding stratified turbulent mixing in the absence of a mean flow. Renewed interest in this topic has prompted the development of a one-dimensional model for the evolution of a stratified system in the context of isolated mixing events. This model is compared to numerical simulations and physical experiments of vortex rings interacting with a stratification. Qualitative agreement between the evolution of the density profiles is observed, along with close quantitative agreement of the mixing efficiency. This model highlights the key dynamical features of such isolated mixing events.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Stratified flows

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 129 - 146
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Archer, P. J., Thomas, T. G. & Coleman, G. N. 2009 The instability of a vortex ring impinging on a free surface. J. Fluid Mech. 642, 79–94.Google Scholar
Balmforth, N. J., Llewellyn Smith, S. G. & Young, W. R. 1998 Dynamics of interfaces and layers in a stratified turbulent fluid. J. Fluid Mech. 355, 329–358.Google Scholar
Fernando, H. J. 1991 Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech. 23 (1), 455–493.Google Scholar
Ivey, G. N., Winters, K. B. & Koseff, J. R. 2008 Density stratification, turbulence, but how much mixing? Annu. Rev. Fluid Mech. 40 (1), 169–184.Google Scholar
Lawrie, A. G. W. & Dalziel, S. B. 2011 Turbulent diffusion in tall tubes. I. Models for Rayleigh–Taylor instability. Phys. Fluids 23 (8), 085109.Google Scholar
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467–480.Google Scholar
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13 (1), 3–23.Google Scholar
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57, 417–431.Google Scholar
Olsthoorn, J. & Dalziel, S. B. 2015 Vortex-ring-induced stratified mixing. J. Fluid Mech. 781, 113–126.Google Scholar
Olsthoorn, Jason & Dalziel, S. B. 2017 Three-dimensional visualization of the interaction of a vortex ring with a stratified interface. J. Fluid Mech. 820, 549–579.Google Scholar
Park, Y.-G., Whitehead, J. A. & Gnanadeskian, A. 1994 Turbulent mixing in stratified fluids: layer formation and energetics. J. Fluid Mech. 279, 279–311.Google Scholar
Shrinivas, A. B. & Hunt, G. R. 2015 Confined turbulent entrainment across density interfaces. J. Fluid Mech. 779, 116–143.Google Scholar
Subich, C. J., Lamb, K. G. & Stastna, M. 2013 Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method. Intl J. Numer. Meth. Fluids 73 (2), 103–129.Google Scholar
Tominaga, Y. & Stathopoulos, T. 2007 Turbulent schmidt numbers for {CFD} analysis with various types of flowfield. Atmos. Environ. 41 (37), 8091–8099.Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639–656.Google Scholar
Vassilicos, J. C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47 (1), 95–114.Google Scholar
Winters, K. B., Lombard, P. N., Riley, J. J. & D’Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115–128.Google Scholar