Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T03:47:32.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Inclined gravity currents filling basins: the impact of peeling detrainment on transport and vertical structure

Published online by Cambridge University Press:  05 May 2017

Charlie A. R. Hogg Open the ORCID record for Charlie A. R. Hogg [Opens in a new window] ,
Stuart B. Dalziel ,
Herbert E. Huppert  and
Jörg Imberger
Charlie A. R. Hogg*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University, CambridgeCB3 0WA, UK Bob and Norma Street Environmental Fluid Mechanics Laboratory, Stanford University, Stanford, CA, 94305, USA
Stuart B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University, CambridgeCB3 0WA, UK
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University, CambridgeCB3 0WA, UK School of Mathematics, University of New South Wales, Kensington NSW 2052, Australia Faculty of Science, University of Bristol, Bristol BS2 6BB, UK
Jörg Imberger
Affiliation:
Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL, 33149, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Transport of dense fluid by an inclined gravity current can control the vertical density structure of the receiving basin in many natural and industrial settings. A case familiar to many is a lake fed by river water that is dense relative to the lake water. In laboratory experiments, we pulsed dye into the basin inflow to visualise the transport pathway of the inflow fluid through the basin. We also measured the evolving density profile as the basin filled. The experiments confirmed previous observations that when the turbulent gravity current travelled through ambient fluid of uniform density, only entrainment into the dense current occurred. When the gravity current travelled through the stratified part of the ambient fluid, however, the outer layers of the gravity current outflowed from the current by a peeling detrainment mechanism and moved directly into the ambient fluid over a large range of depths. The prevailing model of a filling box flow assumes that a persistently entraining gravity current entrains fluid from the basin as the current descends to the deepest point in the basin. This model, however, is inconsistent with the transport pathway observed in visualisations and poorly matches the stratifications measured in basin experiments. The main contribution of the present work is to extend the prevailing filling box model by incorporating the observed peeling detrainment. The analytical expressions given by the peeling detrainment model match the experimental observations of the density profiles more closely than the persistently entraining model. Incorporating peeling detrainment into multiprocess models of geophysical systems, such as lakes, will lead to models that better describe inflow behaviour.

JFM classification

Convection: Buoyant boundary layers Convection: Convection Geophysical and Geological Flows: Gravity currents
Type
Papers
Information
Journal of Fluid Mechanics , Volume 820 , 10 June 2017 , pp. 400 - 423
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allgayer, D. & Hunt, G. 2012 On the application of the light-attenuation technique as a tool for non-intrusive buoyancy measurements. Exp. Therm. Fluid Sci. 38 (0), 257–261.Google Scholar
Antenucci, J. P., Brookes, J. D. & Hipsey, M. R. 2005 A simple model for quantifying cryptosporidium transport, dilution and potential risk. J. Am. Water Works Assoc. 97 (1), 86–93.CrossRefGoogle Scholar
Asaeda, T. & Imberger, J. 1993 Structure of bubble plumes in linearly stratified environments. J. Fluid Mech. 249, 35–57.CrossRefGoogle Scholar
Baines, P. G. 2001 Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.Google Scholar
Baines, P. G. 2005 Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech. 538, 245–267.CrossRefGoogle Scholar
Baines, P. G. 2008 Mixing in downslope flows in the ocean – plumes versus gravity currents. Atmos.-Ocean 46 (4), 405–419.Google Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37 (1), 51–80.CrossRefGoogle Scholar
Bensi, M., Cardin, V., Rubino, A., Notarstefano, G. & Poulain, P. M. 2013 Effects of winter convection on the deep layer of the Southern Adriatic sea in 2012. J. Geophys. Res. 118 (11), 6064–6075.Google Scholar
Carmack, E. C. 1979 Combined influence of inflow and lake temperatures on spring circulation in a riverine lake. J. Phys. Oceanogr. 9 (2), 422–434.Google Scholar
Cenedese, C. & Adduce, C. 2008 Mixing in a density-driven current flowing down a slope in a rotating fluid. J. Fluid Mech. 604, 369–388.Google Scholar
Cenedese, C. & Dalziel, S. B. 1998 Concentration and depth fields determined by the light transmitted through a dyed solution. In Proceedings of the 8th International Symposium on Flow Visualisation (ed. Carlomagno, G. M. & Grant, I.), ISBN 0953 3991 09, paper 061.Google Scholar
Cenedese, C., Whitehead, J. A., Ascarelli, T. A. & Ohiwa, M. 2004 A dense current flowing down a sloping bottom in a rotating fluid. J. Phys. Oceanogr. 34 (1), 188–203.Google Scholar
Cooper, P. & Hunt, G. R. 2010 The ventilated filling box containing a vertically distributed source of buoyancy. J. Fluid Mech. 646, 39–58.Google Scholar
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. & Knuth, D. E. 1996 On the LambertW function. Adv. Comput. Maths 5 (1), 329–359.Google Scholar
Cortés, A., Fleenor, W. E., Wells, M. G., de Vicente, I. & Rueda, F. J. 2014a Pathways of river water to the surface layers of stratified reservoirs. Limnol. Oceanogr. 59 (1), 233–250.Google Scholar
Cortés, A., Rueda, F. J. & Wells, M. G. 2014b Experimental observations of the splitting of a gravity current at a density step in a stratified water body. J. Geophys. Res. 119 (2), 1038–1053.CrossRefGoogle Scholar
Dallimore, C. J., Hodges, B. R. & Imberger, J. 2003 Coupling an underflow model to a three-dimensional hydrodynamic model. J. Hydraul. Engng 129 (10), 748–757.CrossRefGoogle Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (03), 423–448.Google Scholar
Fernandez, R. L. & Imberger, J. 2006 Bed roughness induced entrainment in a high Richardson number underflow. J. Hydraul. Res. 44 (6), 725–738.Google Scholar
Fernández-Torquemada, Y., Gónzalez-Correa, J. M., Loya, A., Ferrero, L. M., Díaz-Valdés, M. & Sánchez-Lizaso, J. L. 2009 Dispersion of brine discharge from seawater reverse osmosis desalination plants. Desalination and Water Treatment 5 (1–3), 137–145.Google Scholar
Germeles, A. E. 1975 Forced plumes and mixing of liquids in tanks. J. Fluid Mech. 71 (3), 601–623.CrossRefGoogle Scholar
Gordon, A. L., Orsi, A. H., Muench, R., Huber, B. A., Zambianchi, E. & Visbeck, M. 2009 Western Ross sea continental slope gravity currents. Deep-Sea Res. II 56 (1314), 796–817.Google Scholar
Hogg, C.2014 The flow of rivers into lakes: experiments and models. PhD thesis, Cambridge University.Google Scholar
Hogg, C. A. R., Dalziel, S. B., Huppert, H. E. & Imberger, J. 2015 Inclined gravity currents filling basins: the influence of Reynolds number on entrainment into gravity currents. Phys. Fluids 27, 096602.Google Scholar
Hughes, G. & Griffiths, R. 2006 A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Model. 12 (1–2), 46–79.Google Scholar
Hunt, G. R. & Kaye, N. G. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377–396.Google Scholar
Imberger, J. & Fandry, C. 1975 Withdrawal of a stratified fluid from a vertical two-dimensional duct. J. Fluid Mech. 70 (2), 321–332.Google Scholar
Kerr, R. C. & McConnochie, C. D. 2015 Dissolution of a vertical solid surface by turbulent compositional convection. J. Fluid Mech. 765, 211–228.Google Scholar
Killworth, P. D. & Carmack, E. C. 1979 A filling-box model of river-dominated lakes. Limnol. Oceanogr. 24 (2), 201–217.CrossRefGoogle Scholar
Lane-Serff, G. F. & Baines, P. G. 2000 Eddy formation by overflows in stratified water. J. Phys. Oceanogr. 30 (2), 327–337.Google Scholar
Legg, S., Ezer, T., Jackson, L., Briegleb, B., Danabasoglu, G., Large, W., Wu, W., Chang, Y., Özgökmen, T. M., Peters, H. et al. 2009 Improving oceanic overflow representation in climate models: the gravity current entrainment climate process team. Bull. Am. Meteorol. Soc. 90 (5), 657–670.Google Scholar
Linden, P. F. 1999 The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31 (1), 201–238.Google Scholar
Mitsudera, H. & Baines, P. 1992 Downslope gravity currents in a continuously stratified environment: a model of the Bass Strait outflow. In Proceedings of the 11th Australasian Fluid Mechanics Conference, Hobart, Australia, pp. 1017–1020.Google Scholar
Monaghan, J. J. 2007 Gravity current interaction with interfaces. Annu. Rev. Fluid Mech. 39 (1), 245–261.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 1–23.Google Scholar
Odier, P., Chen, J. & Ecke, R. E. 2014 Entrainment and mixing in a laboratory model of oceanic overflow. J. Fluid Mech. 746, 498–535.Google Scholar
Seon, T., Hulin, J.-P., Salin, D., Perrin, B. & Hinch, E. J. 2006 Laser-induced fluorescence measurements of buoyancy driven mixing in tilted tubes. Phys. Fluids 18 (4), 041701.Google Scholar
Šimek, K., Comerma, M., García, J.-C., Nedoma, J., Marcé, R. & Armengol, J. 2010 The effect of river water circulation on the distribution and functioning of reservoir microbial communities as determined by a relative distance approach. Ecosystems 14 (1), 1–14.Google Scholar
Simpson, J. E. 1987 Gravity Currents in the Environment and the Laboratory, 1st edn. Ellis Horwood and Sons.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.CrossRefGoogle Scholar
Wells, A. J. & Worster, M. G. 2008 A geophysical-scale model of vertical natural convection boundary layers. J. Fluid Mech. 609, 111–137.CrossRefGoogle Scholar
Wells, M. G. & Wettlaufer, J. S. 2005 Two-dimensional density currents in a confined basin. Geophys. Astrophys. Fluid Dyn. 99 (3), 199–218.Google Scholar
Wells, M. G. & Wettlaufer, J. S. 2007 The long-term circulation driven by density currents in a two-layer stratified basin. J. Fluid Mech. 572, 37–58.CrossRefGoogle Scholar
Wong, A. B. D., Griffiths, R. W. & Hughes, G. O. 2001 Shear layers driven by turbulent plumes. J. Fluid Mech. 434, 209–241.Google Scholar

Hogg et al. supplementary movie

Visualisation of transport during basin filling. Pulses of dye were injected into the constant buoyancy flux source.

Download Hogg et al. supplementary movie(Video)
Video 3.8 MB