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Vortex-ring-induced stratified mixing

  • Jason Olsthoorn (a1) and Stuart B. Dalziel (a1)

Abstract

There is tantalizing evidence that some mechanically driven stratified flows tend towards a state of constant mixing efficiency. We provide insight into the energy balance leading to the constant mixing efficiency and isolate the responsible mechanism. The work presented demonstrates an important mixing efficiency regime for periodically forced externally driven stratified flows. Externally forced stratified turbulent mixing is often characterized by the associated eddies within the flow, which are the dominant mixing mechanism (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431–471). Here, we study mixing induced by vortex rings in order to characterize the mixing induced by an individual eddy. By generating a long sequence of independent vortex-ring mixing events in a density-stratified fluid with a sharp interface, we determine the mixing efficiency of each ring. After an initial adjustment phase, we find that the mixing efficiency of each vortex ring is independent of the Richardson number. By studying the mixing mechanism here, we demonstrate consistent features of a volumetrically confined, periodically forced external mixing regime.

Copyright

Corresponding author

Email address for correspondence: jo344@cam.ac.uk

References

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Bethke, N. & Dalziel, S. B. 2012 Resuspension onset and crater erosion by a vortex ring interacting with a particle layer. Phys. Fluids 24, 063301.
Dahm, W. J. A., Scheil, C. M. & Tryggvason, G. 1989 Dynamics of vortex interaction with a density interface. J. Fluid Mech. 205, 143.
Davies Wykes, M. S. & Dalziel, S. B. 2014 Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification. J. Fluid Mech. 756, 10271057.
Gayen, B., Hughes, G. O. & Griffiths, R. W. 2013 Completing the mechanical energy pathways in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 111, 124301.
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467480.
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13 (1), 323.
Moore, M. J. & Long, R. R. 1971 An experimental investigation of turbulent stratified shearing flow. J. Fluid Mech. 49, 635655.
Munro, R. J., Bethke, N. & Dalziel, S. B. 2009 Sediment resuspension and erosion by vortex rings. Phys. Fluids 21 (4), 046601.
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57, 417431.
Oglethorpe, R. L. F., Caulfield, C. P. & Woods, A. W. 2013 Spontaneous layering in stratified turbulent Taylor–Couette flow. J. Fluid Mech. 721, R3.
Park, Y.-G., Whitehead, J. A. & Gnanadeskian, A. 1994 Turbulent mixing in stratified fluids: layer formation and energetics. J. Fluid Mech. 279, 279311.
Peltier, W. R. & Caulfield, C. P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35 (1), 135167.
Prastowo, T., Griffiths, R. W., Hughes, G. O. & Hogg, A. McC. 2008 Mixing efficiency in controlled exchange flows. J. Fluid Mech. 600, 235244.
Prastowo, T., Griffiths, R. W., Hughes, G. O. & Hogg, A. McC. 2009 Effects of topography on the cumulative mixing efficiency in exchange flows. J. Geophys. Res. 114, C08008.
Scotti, A. & White, B. 2011 Is horizontal convection really non-turbulent? Geophys. Res. Lett. 38 (21), 121609.
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235279.
Shravat, A., Cenedese, C. & Caulfield, C. P. 2012 Entrainment and mixing dynamics of surface-stress-driven stratified flow in a cylinder. J. Fluid Mech. 691, 498517.
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639656.
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431471.
Worster, M. G. & Huppert, H. E. 1983 Time-dependent density profiles in a filling box. J. Fluid Mech. 132, 457466.
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