Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 33
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Rahmani, M. Seymour, B. R. and Lawrence, G. A. 2016. The effect of Prandtl number on mixing in low Reynolds number Kelvin-Helmholtz billows. Physics of Fluids, Vol. 28, Issue. 5, p. 054107.


    Bogoni, Manuel Canestrelli, Alberto and Lanzoni, Stefano 2015. Finite volume modelling of a stratified flow with the presence of submerged weirs. Journal of Applied Water Engineering and Research, Vol. 3, Issue. 1, p. 43.


    Garaud, Pascale Gallet, Basile and Bischoff, Tobias 2015. The stability of stratified spatially periodic shear flows at low Péclet number. Physics of Fluids, Vol. 27, Issue. 8, p. 084104.


    Meunier, Thomas Ménesguen, Claire Schopp, Richard and Le Gentil, Sylvie 2015. Tracer Stirring around a Meddy: The Formation of Layering. Journal of Physical Oceanography, Vol. 45, Issue. 2, p. 407.


    Paparella, Francesco and von Hardenberg, Jost 2014. A Model for Staircase Formation in Fingering Convection. Acta Applicandae Mathematicae, Vol. 132, Issue. 1, p. 457.


    Verhoeven, Jan and Stellmach, Stephan 2014. The compressional beta effect: A source of zonal winds in planets?. Icarus, Vol. 237, p. 143.


    Bouffard, Damien and Boegman, Leon 2013. A diapycnal diffusivity model for stratified environmental flows. Dynamics of Atmospheres and Oceans, Vol. 61-62, p. 14.


    Lozovatsky, I. D. and Fernando, H. J. S. 2012. Mixing efficiency in natural flows. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue. 1982, p. 20120213.


    Paparella, Francesco and von Hardenberg, Jost 2012. Clustering of Salt Fingers in Double-Diffusive Convection Leads to Staircaselike Stratification. Physical Review Letters, Vol. 109, Issue. 1,


    Shravat, A. Cenedese, C. and Caulfield, C. P. 2012. Entrainment and mixing dynamics of surface-stress-driven stratified flow in a cylinder. Journal of Fluid Mechanics, Vol. 691, p. 498.


    Radko, Timour and Stern, Melvin E. 2011. Finescale Instabilities of the Double-Diffusive Shear Flow*. Journal of Physical Oceanography, Vol. 41, Issue. 3, p. 571.


    WOODS, ANDREW W. CAULFIELD, C. P. LANDEL, J. R. and KUESTERS, A. 2010. Non-invasive turbulent mixing across a density interface in a turbulent Taylor–Couette flow. Journal of Fluid Mechanics, Vol. 663, p. 347.


    Dritschel, D. G. and McIntyre, M. E. 2008. Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers. Journal of the Atmospheric Sciences, Vol. 65, Issue. 3, p. 855.


    CHUDA, Takashi KIMURA, Ryuji and NIINO, Hiroshi 2007. Vertical Fine Structures of Temperature and Water Vapor in the Free Atmosphere. Journal of the Meteorological Society of Japan, Vol. 85, Issue. 5, p. 583.


    Haynes, P. H. Poet, D. A. and Shuckburgh, E. F. 2007. Transport and Mixing in Kinematic and Dynamically Consistent Flows. Journal of the Atmospheric Sciences, Vol. 64, Issue. 10, p. 3640.


    Whitehead, J. A. and Stevenson, Ian 2007. Turbulent mixing of two-layer stratified fluid. Physics of Fluids, Vol. 19, Issue. 12, p. 125104.


    Lozovatsky, I.D. Roget, E. Fernando, H.J.S. Figueroa, M. and Shapovalov, S. 2006. Sheared turbulence in a weakly stratified upper ocean. Deep Sea Research Part I: Oceanographic Research Papers, Vol. 53, Issue. 2, p. 387.


    Martin, Juan Ezequiel and Rehmann, Chris R. 2006. Layering in a Flow with Diffusively Stable Temperature and Salinity Stratification. Journal of Physical Oceanography, Vol. 36, Issue. 7, p. 1457.


    Roget, Elena Lozovatsky, Iossif Sanchez, Xavier and Figueroa, Manuel 2006. Microstructure measurements in natural waters: Methodology and applications. Progress in Oceanography, Vol. 70, Issue. 2-4, p. 126.


    MacDonald, Daniel G. 2004. Turbulent energy production and entrainment at a highly stratified estuarine front. Journal of Geophysical Research, Vol. 109, Issue. C5,


    ×
  • Journal of Fluid Mechanics, Volume 355
  • January 1998, pp. 329-358

Dynamics of interfaces and layers in a stratified turbulent fluid

  • N. J. BALMFORTH (a1) (a2), STEFAN G. LLEWELLYN SMITH (a1) (a3) and W. R. YOUNG (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112097007970
  • Published online: 01 January 1998
Abstract

This paper formulates a model of mixing in a stratified and turbulent fluid. The model uses the horizontally averaged vertical buoyancy gradient and the density of turbulent kinetic energy as variables. Heuristic ‘mixing-length’ arguments lead to a coupled set of parabolic differential equations. A particular form of mechanical forcing is proposed; for certain parameter values the relationship between the buoyancy flux and the buoyancy gradient is non-monotonic and this leads to an instability of equilibria with linear stratification. The instability results in the formation of steps and interfaces in the buoyancy profile. In contrast to previous ones, the model is mathematically well posed and the interfaces have an equilibrium thickness that is much larger than that expected from molecular diffusion.

The turbulent mixing process can take one of three forms depending on the strength of the initial stratification. When the stratification is weak, instability is not present and mixing smoothly homogenizes the buoyancy. At intermediate strengths of stratification, layers and interfaces form rapidly over a substantial interior region bounded by edge layers associated with the fluxless condition of the boundaries. The interior pattern subsequently develops more slowly as interfaces drift together and merge; simultaneously, the edge layers advance inexorably into the interior. Eventually the edge layers meet in the middle and the interior pattern of layers is erased. Any remaining structure subsequently decays smoothly to the homogeneous state. Both the weak and intermediate stratified cases are in agreement with experimental phenomenology. The model predicts a third case, with strong stratification, not yet found experimentally, where the central region is linearly stable and no steps form there. However, the edge layers are unstable; mixing fronts form and then erode into the interior.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax