Abstract
This chapter discusses the physics underlying mixing caused by turbulent flow in a stratified fluid. The ability of the oceans to absorb and redistribute heat from the atmosphere at low latitudes is a crucial aspect of the climate system and accurate quantitative estimates of the mixing rates are critical to the development of reliable climate models. However, mixing occurs at very small scales where molecular diffusion is active and these processes cannot be calculated explicitly in climate models. Thus it is necessary to represent these rates in terms of the larger scale fields and this requires an understanding of the links between these large and small scales. We focus here on laboratory experiments that attempt to make these links and, in particular, represent transport rates in terms of a mixing efficiency. We show that insights can be obtained in this way that point to reasonable representations of mixing in geophysical flows.
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References
G.K. Batchelor, Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. general discussion and the case of small conductivity. J. Fluid Mech. 5(1), 113–133 (1958)
T.B. Benjamin, Gravity currents and related phenomena. J. Fluid Mech. 31(2), 209–248 (1968)
P. Billant, J.-M. Chomaz, Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13, 1645–1651 (2001)
G. Brethouwer, P. Billant, E. Lindborg, J.-M. Chomaz, Scaling analysis and simulation of strongly stratified turbulent flow. J. Fluid Mech. 585, 343–368 (2007)
S.B. Dalziel, M.D. Patterson, C.P. Caulfield, I.A. Coomaraswamy, Mixing efficiency in high-aspect-ratio Rayleigh-Taylor experiments. Phys. Fluids 20, 065106 (2008)
E. Deusebio, C.P. Caulfield, J.R. Taylor, The intermittency boundary in stratified plane Couette flow. J. Fluid Mech. 781, 298–329 (2015)
J.M. Holford, P.F. Linden, Turbulent mixing in a stratified fluid. Dyn. Atmos. Oceans 30(2–4), 173–198 (1999)
L.N. Howard, Note on a paper of John W. Miles. J. Fluid Mech. 10(4), 509–512 (1961)
G.O. Hughes, P.F. Linden, Mixing in run-down gravity currents. J. Fluid Mech. 809, 691–704 (2016)
G.H. Keulegan, The motion of saline fronts in still water. National Bureau of Standards Report, 5831, 1958
A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Comptes Rendus de l’Académie des sciences de l’URSS 30, 299–303 (1941a)
A.N. Kolmogorov, On the degeneration of isotropic turbulence in an incompressible viscous liquid. Comptes Rendus de l’Académie des sciences de l’URSS 31, 319–323 (1941b)
A.N. Kolmogorov, Dissipation of energy in locally isotropic turbulence. Comptes Rendus de l’Académie des sciences de l’URSS 32, 19–21 (1941c)
A.G.W. Lawrie, S.B. Dalziel, Turbulent diffusion in tall tubes. I. models for Rayleigh-Taylor instability. Phys. Fluids 23, 085109 (2011)
D.K. Lilly, Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749–761 (1983)
E. Lindborg, The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207–242 (2006)
P.F. Linden, Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3–23 (1979)
P.F. Linden, Mixing across a density interface produced by grid turbulence. J. Fluid Mech. 100, 691–703 (1980)
J.W. Miles, On the stability of heterogeneous shear flows. J. Fluid Mech. 10(4), 496–508 (1961)
O.M. Phillips, Turbulence in a strongly stratified fluid—is it unstable? Deep Sea Res. 19, 79–81 (1972)
E.S. Posmentier, The generation of salinity finestructure by vertical diffusion. J. Phys. Oceanogr. 7, 298–300 (1977)
J.O. Shin, S.B. Dalziel, P.F. Linden, Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34 (2004)
J.E. Simpson, Gravity Currents in the Environment and the Laboratory (Cambridge University Press, 1997)
S.A. Thorpe, Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61(4), 731–751 (1973)
S.A. Thorpe, Layers and internal waves in uniformly stratified fluids stirred by vertical grids. J. Fluid Mech. 793, 380–413 (2016)
J.S. Turner, The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33(4), 639–656 (1968)
J.S. Turner, Buoyancy Effects in Fluids (Cambridge University Press, 1973)
C.S. Yih, A study of the characteristics of gravity waves at a liquid interface. MSc thesis, State University of Iowa, 1947
C.S. Yih, Dynamics of Nonhomogeneous Fluids (Macmillan, 1965)
Acknowledgements
I would like to thank the organisers of this summer school for inviting me to give the lectures on which these notes are based. I would also like to acknowledge the many discussions I have had on this subject with many colleagues especially Colm Caulfield, Stuart Dalziel, Graham Hughes, Jamie Partridge, and John Taylor. This work is supported by the UK EPSRC, through the Programme Grant EP/K034529/1 and by the Royal Society.
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Linden, P.F. (2018). Turbulence and Mixing in Flows Dominated by Buoyancy. In: Clercx, H., Van Heijst, G. (eds) Mixing and Dispersion in Flows Dominated by Rotation and Buoyancy. CISM International Centre for Mechanical Sciences, vol 580. Springer, Cham. https://doi.org/10.1007/978-3-319-66887-1_2
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DOI: https://doi.org/10.1007/978-3-319-66887-1_2
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