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Mixing efficiency in run-down gravity currents

  • G. O. Hughes (a1) and P. F. Linden (a2)


This paper presents measurements of mixing efficiency of the two counter-flowing gravity currents created by symmetric lock exchange in a channel. The novel feature of this work is that the buoyancy Reynolds number of the currents is higher than in previous experiments, so that the mixing is not significantly affected by viscosity. We find that the mixing efficiency asymptotes to 0.08 at high Reynolds numbers. We present a model of the mixing based on the evolution of idealized mean profiles of velocity and density at the interface between the two currents, the results of which are in good agreement with the measurements of mixing efficiency.


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Adduce, C., Sciortino, G. & Proietti, S. 2012 Gravity currents produced by lock exchanges: experiments and simulations with a two-layer shallow-water model with entrainment. J. Hydraul. Engng ASCE 138, 111121.
Batchelor, G. K. 1958 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, 113133.
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209248.
Billant, P. & Chomaz, J.-M. 2001 Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13, 16451651.
Birman, V., Martin, J. E. & Meiburg, E. 2005 The non-boussinesq lock exchange problem. Part 2. High resolution simulations. J. Fluid Mech. 537, 125144.
Corcos, G. M. & Sherman, F. S. 1976 Vorticity concentration and the dynamics of unstable free shear layers. J. Fluid Mech. 73, 241264.
Fragoso, A. T., Patterson, M. D. & Wettlaufer, J. S. 2013 Mixing in gravity currents. J. Fluid Mech. 734, R2.
Gibson, C. H. 1980 Fossil turbulence, salinity and vorticity turbulence in the ocean. Marine Turbulence. (Proc. 11th Intl Liége Conf. on Ocean Hydrodyn.) , vol. 28, pp. 221257. Elsevier.
Gibson, C. H. 1999 Fossil turbulence revisited. J. Mar. Syst. 21, 147167.
Ilıcak, M. 2014 Energetics and mixing efficiency of lock-exchange flow. Ocean Model. 83, 110.
Keulegan, G. H. 1958 The motion of saline fronts in still water. Natl Bur. Stand. Rep. 5831.
Koop, C. G. & Browand, F. K. 1979 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135159.
Lawrie, A. G. W. & Dalziel, S. B. 2011 Rayleigh–Taylor mixing in an otherwise stable stratification. J. Fluid Mech. 688, 507527.
Lindborg, E. 2006 The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207242.
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 323.
Lowe, R. J., Rottman, J. W. & Linden, P. F. 2005 The non-Boussinesq lock exchange problem. Part 1. Theory and experiments. J. Fluid Mech. 537, 101124.
Marino, B. M., Thomas, L. P. & Linden, P. F. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 4978.
Osborn, T. R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 8389.
Özgökmen, T. M., Iliescu, T. & Fischer, P. F. 2009 Large eddy simulation of stratified mixing in a three-dimensional lock-exchange system. Ocean Model. 26, 134155.
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous release of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95110.
Sher, D. & Woods, A. W. 2015 Gravity currents: entrainment, stratification and self-similarity. J. Fluid Mech. 784, 130162.
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 134.
Simpson, J. E. 1997 Gravity Currents in the Environment and the Laboratory, 2nd edn. Cambridge University Press.
Smyth, W. D. & Moum, J. N. 2000 Length scales of turbulence in stably stratified mixing layers. Phys. Fluids. 12, 13271342.
Sreenivasan, K. R. 1995 The energy dissipation in turbulent shear flows. In Symposium on Developments in Fluid Dynamics and Aerospace Engineering, pp. 159190. Interline Bangalore.
Thorpe, S. A. 1973 Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61 (04), 731751.
Waite, M. L. 2013 The vortex instability pathway in stratified turbulence. J. Fluid Mech. 716, 14.
Wygnanski, I. & Fielder, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327361.
Yih, C. S.1947 A study of the characteristics of gravity waves at a liquid interface. Master’s thesis, State University of Iowa.
Yih, C. S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.
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