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Mixing regimes for the flow of dense fluid down slopes into stratified environments

Published online by Cambridge University Press:  17 August 2005

PETER G. BAINES
PETER G. BAINES
Affiliation:
Department of Civil and Environmental Engineering, University of Melbourne, Australia 3010 and School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
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Abstract

Downslope flows into density-stratified environments have been observed to have the character of detraining gravity currents on small slopes, and of entraining plumes on steep slopes. In this paper, observations of flows on slopes of intermediate (20$^{\circ}$–30$^{\circ}$) steepness are described, and their mixing properties quantified. Both gravity-current-like and plume-like flows are observed, and an observational boundary between these two types is identified. Theoretical models for the bulk properties of these flows are presented, and their predictions are compared with the observations. A theoretical criterion is derived for the limit of applicability of the gravity-current model in terms of the Buoyancy number, the bottom slope and the bottom drag coefficient. This provides a criterion for the boundary between the plume-like and gravity-current-like flows, which is consistent with the observations. These results have implications for the modelling of downslope flows in nature, and indicate where the appropriate dynamical model may change from one type to the other.

JFM classification

Geophysical and Geological Flows: Gravity currents Convection: Plumes/thermals Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 538 , 10 September 2005 , pp. 245 - 267
Copyright
© 2005 Cambridge University Press

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Baines supplementary movie

Figure A. Flow of a gravity current down a slope of 3 degrees into a uniformly density stratified environment, B0 = 0.055, Holmboe waves. The dense fluid is marked with green fluorescene dye, which also marks fluid that is mixed with the environment. Mixing occurs through the process of Holmboe instability (see Baines (1995, Chapter 4)), which causes wisps of dense fluid to be swept off the top of the dense downflow and mix into the overlying fluid. This causes a steady build-up of detrained fluid, made visible through the accumulating concentration of dye above the main downflow (see Baines 2001a). The fluid is illuminated by a scanning laser beam giving a thin two-dimensional vertical cross-section.

Download Baines supplementary movie(Video)
Video 788.2 KB

Baines supplementary movie

Figure A. Flow of a gravity current down a slope of 3 degrees into a uniformly density stratified environment, B0 = 0.055, Holmboe waves. The dense fluid is marked with green fluorescene dye, which also marks fluid that is mixed with the environment. Mixing occurs through the process of Holmboe instability (see Baines (1995, Chapter 4)), which causes wisps of dense fluid to be swept off the top of the dense downflow and mix into the overlying fluid. This causes a steady build-up of detrained fluid, made visible through the accumulating concentration of dye above the main downflow (see Baines 2001a). The fluid is illuminated by a scanning laser beam giving a thin two-dimensional vertical cross-section.

Download Baines supplementary movie(Video)
Video 13.6 MB

Baines supplementary movie

Figure B. Flow of dense fluid down a slope of 30 degrees into a uniformly density-stratified environment, B0 = 0.028, a turbulent plume. Here the flow has the character of a turbulent plume, which entrains environmental fluid into the descending boundary current. The plume overshoots its level of equilibrium density, and springs back to spread out around its equilbrium level. Some of this fluid is entrained into the downflow and recirculated.

Download Baines supplementary movie(Video)
Video 1.3 MB

Baines supplementary movie

Figure B. Flow of dense fluid down a slope of 30 degrees into a uniformly density-stratified environment, B0 = 0.028, a turbulent plume. Here the flow has the character of a turbulent plume, which entrains environmental fluid into the descending boundary current. The plume overshoots its level of equilibrium density, and springs back to spread out around its equilbrium level. Some of this fluid is entrained into the downflow and recirculated.

Download Baines supplementary movie(Video)
Video 20.7 MB

Baines supplementary movie

Figure C. Flow of dense fluid down a slope of 30 degrees into a uniformly density-stratified environment, B0= 0.004, a case of double outflow. For 30 degrees slopes with B0 < 0.007 the downflow was observed to have unusual structure in which the effect on the environment was outflow near the top and bottom, with inflow in between. Over much of the downflow it behaved like an entraining plume, except that partially mixed fluid leaving the boundary current at lower levels rose through the central entraining region to form the upper outflow. This film shows an example of the development of this flow. In the fully developed stage near the end of the film, the buoyant fluid is seen traversing the central gap where entrainment keeps it close to the boundary current, and upward "bubbling motion" is apparent.

Download Baines supplementary movie(Video)
Video 3 MB

Baines supplementary movie

Figure C. Flow of dense fluid down a slope of 30 degrees into a uniformly density-stratified environment, B0= 0.004, a case of double outflow. For 30 degrees slopes with B0 < 0.007 the downflow was observed to have unusual structure in which the effect on the environment was outflow near the top and bottom, with inflow in between. Over much of the downflow it behaved like an entraining plume, except that partially mixed fluid leaving the boundary current at lower levels rose through the central entraining region to form the upper outflow. This film shows an example of the development of this flow. In the fully developed stage near the end of the film, the buoyant fluid is seen traversing the central gap where entrainment keeps it close to the boundary current, and upward "bubbling motion" is apparent.

Download Baines supplementary movie(Video)
Video 57.2 MB