Skip to main content Accessibility help
Hostname: page-component-7f7b94f6bd-mcrbk Total loading time: 0.235 Render date: 2022-06-29T21:25:22.702Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient

Published online by Cambridge University Press:  15 March 2011

Université de Toulouse, INPT, UPS, Institut de Mécanique des Fluides de Toulouse, Allée Camille Soula, F-31400 Toulouse, France CNRS, Institut de Mécanique des Fluides de Toulouse (IMFT), F-31400 Toulouse, France
Department of Computer Science, Technion, Haifa 32000, Israel
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
Email address for correspondence:


The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h0 and length x0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ = x0/h0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λcrit), the dynamics of the current is significantly influenced by λ. We conjecture that λcrit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λcrit) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ1/4 when λ < λcrit.

Copyright © Cambridge University Press 2011

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.)


Baines, W. D., Rottman, J. W. & Simpson, J. E. 1985 The motion of constant-volume air cavities released in long horizontal tubes. J. Fluid Mech. 161, 313327.CrossRefGoogle Scholar
Benjamin, T. B. 1968 Density currents and related phenomena. J. Fluid Mech. 31, 209248.CrossRefGoogle Scholar
Birman, V., Martin, J. E. & Meiburg, E. 2005 The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations. J. Fluid Mech. 537, 125144.CrossRefGoogle Scholar
Bonometti, T. & Balachandar, S. 2010 Slumping of non-Boussinesq density currents of various initial fractional depths: a comparison between direct numerical simulations and a recent shallow-water model. Comput. Fluids 39, 729734.CrossRefGoogle Scholar
Bonometti, T., Balachandar, S. & Magnaudet, J. 2008 Wall effects in non-Boussinesq density currents. J. Fluid Mech. 616, 445475.CrossRefGoogle Scholar
Bonometti, T. & Magnaudet, J. 2007 An interface capturing method for incompressible two-phase flows: validation and application to bubble dynamics. Intl J. Multiphase Flow 33, 109133.CrossRefGoogle Scholar
Cantero, M. I., Lee, J. R., Balachandar, S. & Garcia, M. H. 2007 On the front velocity of gravity currents. J. Fluid Mech. 586, 139.CrossRefGoogle Scholar
Etienne, J., Hopfinger, E. J. & Saramito, P. 2005 Numerical simulations of high density ratio lock-exchange flows. Phys. Fluids 17, 036601.CrossRefGoogle Scholar
Fanneløp, T. K. & Jacobsen, Ø. 1984 Gravity spreading of heavy clouds instantaneously released. Z. Angew. Math. Phys. 35, 559584.CrossRefGoogle Scholar
Gardner, G. C. & Crow, I. G. 1970 The motion of large bubbles in horizontal channels. J. Fluid Mech. 43, 247255.CrossRefGoogle Scholar
Gröbelbauer, H. P., Fanneløp, T. K. & Britter, R. E. 1993 The propagation of intrusion fronts of high density ratio. J. Fluid Mech. 250, 669687.CrossRefGoogle Scholar
Grundy, R. E. & Rottman, J. 1985 The approach to self-similarity of the solutions of the shallow-water equations representing gravity current releases. J. Fluid Mech. 156, 3953.CrossRefGoogle Scholar
Hallez, Y. & Magnaudet, J. 2009 A numerical investigation of horizontal viscous gravity currents. J. Fluid Mech. 630, 7191.CrossRefGoogle Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000 Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418, 189212.CrossRefGoogle Scholar
Hogg, A. J. 2006 Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 6187.CrossRefGoogle Scholar
Huppert, H. & Simpson, J. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785799.CrossRefGoogle Scholar
Huq, P. 1996 The role of aspect ratio on entrainment rates of instantaneous, axisymmetric finite volume releases of density fluid. J. Hazard. Mater. 49, 89101.CrossRefGoogle Scholar
Keller, J. J. & Chyou, Y. P. 1991 On the hydraulic lock exchange problem. J. Appl. Math. Phys. 42, 874909.CrossRefGoogle Scholar
Klemp, J. B., Rotunno, R. & Skamarock, W. C. 1994 On the dynamics of density currents in a channel. J. Fluid Mech. 269, 169198.CrossRefGoogle Scholar
Lauber, G. & Hager, W. H. 1998 Experiments to dam-break wave: horizontal channel. J. Hydraul. Res. 36, 291307.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Marino, B., Thomas, L. & Linden, P. 2005 The front condition for density currents. J. Fluid Mech. 536, 4978.CrossRefGoogle Scholar
Martin, J. C. & Moyce, W. J. 1952 An experimental study of the collapse of liquid columns on a rigid horizontal plane. Phil. Trans. R. Soc. Lond. A 244, 312324.CrossRefGoogle Scholar
Ooi, S. K., Constantinescu, G. & Weber, L. 2009 Numerical simulations of lock-exchange compositional gravity currents. J. Fluid Mech. 635, 361388.CrossRefGoogle Scholar
Ozgökmen, T., Fischer, P., Duan, J. & Iliescu, T. 2004 Three-dimensional turbulent bottom density currents from a high-order nonhydrostatic spectral element model. J. Phys. Oceanogr. 34, 20062026.2.0.CO;2>CrossRefGoogle Scholar
Rottman, J. & Simpson, J. 1983 Density currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95110.CrossRefGoogle Scholar
Schoklitsch, A. 1917 Uber Dammbruchwellen. Sitzungsber. Akad. Wissenchaft. Wien 26, 14891514.Google Scholar
Shin, J., Dalziel, S. & Linden, P. 2004 Density currents produced by lock exchange. J. Fluid Mech. 521, 134.CrossRefGoogle Scholar
Simpson, J. E. 1982 Gravity currents in the laboratory, atmosphere and oceans. Annu. Rev. Fluid Mech. 14, 213234.CrossRefGoogle Scholar
Spicer, T. O. & Havens, J. A. 1985 Modelling the phase I Thorney Island experiments. J. Hazard. Mater. 11, 237260.CrossRefGoogle Scholar
Stansby, P. K., Chegini, A. & Barnes, T. C. D. 1998 The initial stages of dam-break flow J. Fluid Mech. 374, 407424.CrossRefGoogle Scholar
Ungarish, M. 2007 A shallow-water model for high-Reynolds-number gravity currents for a wide range of density differences and fractional depths. J. Fluid Mech. 579, 373382.CrossRefGoogle Scholar
Ungarish, M. 2009 An Introduction to Gravity Currents and Intrusions. Chapman & Hall/CRC Press.CrossRefGoogle Scholar
Ungarish, M. 2011 Two-layer shallow-water dam-break solutions for non-Boussinesq gravity currents in a wide range of fractional depth. J. Fluid Mech. (in press).Google Scholar
Wilkinson, D. L. 1982 Motion of air cavities in long horizontal ducts. J. Fluid Mech. 118, 109122.CrossRefGoogle Scholar
Zalesak, S. T. 1979 Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31, 335362.CrossRefGoogle Scholar
Zukoski, E. E. 1966 Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes. J. Fluid Mech. 25, 821840.CrossRefGoogle Scholar
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *