Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T02:41:11.388Z Has data issue: false hasContentIssue false
  • English
  • Français

The propagation of gravity currents in a circular cross-section channel: experiments and theory

Published online by Cambridge University Press:  09 January 2015

S. Longo Open the ORCID record for S. Longo [Opens in a new window] ,
M. Ungarish ,
V. Di Federico ,
L. Chiapponi  and
A. Maranzoni
S. Longo*
Affiliation:
Dipartimento di Ingegneria Civile, Ambiente Territorio e Architettura (DICATeA), Università di Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
M. Ungarish
Affiliation:
Department of Computer Science, Technion, Israel Institute of Technology, Haifa 32000, Israel
V. Di Federico
Affiliation:
Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali (DICAM), Università di Bologna, Viale Risorgimento, 2, 40136 Bologna, Italy
L. Chiapponi
Affiliation:
Dipartimento di Ingegneria Civile, Ambiente Territorio e Architettura (DICATeA), Università di Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
A. Maranzoni
Affiliation:
Dipartimento di Ingegneria Civile, Ambiente Territorio e Architettura (DICATeA), Università di Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

High-Reynolds number gravity currents (GC) in a horizontal channel with circular/semicircular side walls are investigated by comparing experimental data and shallow-water (SW) theoretical results. We focus attention on a Boussinesq system (salt water in fresh water): the denser fluid, occupying part of the depth or the full depth of the ambient fluid which fills the remaining part of the channel, is initially at rest in a lock separated by a gate from the downstream channel. Upon the rapid removal of the gate (‘dam break’), the denser ‘current’ begins propagating into the downstream channel, while a significant adjustment motion propagates upstream in the lock as a bore or rarefaction wave. Using an experimental channel provided by a tube of 19 cm diameter and up to 615 cm length, which could be filled to various levels, we investigated both full-depth and part-depth releases, considered the various stages of inertial-buoyancy propagation (in particular, the initial ‘slumping’ with constant speed, and the transition to the late self-similar propagation with time to the power $3/4$), and detected the transition to the viscous-buoyancy regime. A first series of tests is focused on the motion in the lock while a second series of tests is focused on the evolution of the downstream current. The speed of propagation of the current in the slumping stage is overpredicted by the theory, by about the same amount (typically 15 %) as observed in the classical flat bottom case. The length of transition to viscous regime turns out to be ${\sim}[\mathit{Re}_{0}(h_{0}/x_{0})]^{{\it\alpha}}$ ($\mathit{Re}_{0}=(g^{\prime }h_{0})^{1/2}h_{0}/{\it\nu}_{c}$ is the initial Reynolds number, $g^{\prime }$ is the reduced gravity, ${\it\nu}_{c}$ is the kinematic viscosity of the denser fluid, $h_{0}$ and $x_{0}$ are the height of the denser current and the length of the lock, respectively), with the theoretical ${\it\alpha}=3/8$ and experimental ${\it\alpha}\approx 0.27$.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 513 - 537
Check for updates
Copyright
© 2015 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

Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Bonometti, T., Ungarish, M. & Balachandar, S. 2011 A numerical investigation of constant-volume non-Boussinesq gravity currents in deep ambient. J. Fluid Mech. 673, 574–602.Google Scholar
Constantinescu, G. 2014 LES of lock-exchange compositional gravity currents: a brief review of some recent results. Environ. Fluid Mech. 14, 295–317.Google Scholar
Huppert, H. E. 2006 Gravity currents: a personal perspective. J. Fluid Mech. 554, 299–322.Google Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.Google 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, 101–124.Google Scholar
Marino, B. M. & Thomas, L. P. 2011 Dam-break release of a gravity current in a power-law channel section. J. Phys.: Conf. Ser. 296, 012008.Google Scholar
Mériaux, C. A. & Kurz-Besson, C. B. 2012 Sedimentation from binary suspensions in a turbulent gravity current along a V-shaped valley. J. Fluid Mech. 712, 624–645.Google Scholar
Monaghan, J. J., Mériaux, C., Huppert, H. & Mansour, J. 2009a Particulate gravity currents along V-shaped valleys. J. Fluid Mech. 631, 419–440.Google Scholar
Monaghan, J. J., Mériaux, C., Huppert, H. & Monaghan, J. M. 2009b High Reynolds number gravity currents along V-shaped valleys. Eur. J. Mech. (B/Fluids) 28 (5), 651–659.Google Scholar
Nasr-Azadani, M. M. & Meiburg, E. 2014 Turbidity currents interacting with three-dimensional seaflor topography. J. Fluid Mech. 745, 409–443.Google Scholar
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous releases. J. Fluid Mech. 135, 95–110.Google Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.Google Scholar
Simpson, J. E. 1997 Gravity Currents in the Environment and the Laboratory. Cambridge University Press.Google Scholar
Takagi, D. & Huppert, H. E. 2007 The effect of confining boundaries on viscous gravity currents. J. Fluid Mech. 577, 495–505.Google Scholar
Ungarish, M. 2009 An Introduction to Gravity Currents and Intrusions. CRC Press.Google Scholar
Ungarish, M. 2012 A general solution of Benjamin-type gravity current in a channel of non-rectangular cross-section. Environ. Fluid Mech. 12 (3), 251–263.Google Scholar
Ungarish, M. 2013 Two-layer shallow-water dam-break solutions for gravity currents in non-rectangular cross-area channels. J. Fluid Mech. 732, 537–570.Google Scholar
Ungarish, M., Mériaux, C. A. & Kurz-Besson, C. B. 2014 The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory. J. Fluid Mech. 754, 232–249.Google Scholar
Zemach, T. & Ungarish, M. 2013 Gravity currents in non-rectangular cross-section channels: analytical and numerical solutions of the one-layer shallow-water model for high-Reynolds-number propagation. Phys. Fluids 25, 026601.Google Scholar
Supplementary material: PDF

Longo et al. supplementary material

Supplementary material and figs

Download Longo et al. supplementary material(PDF)
PDF 361.8 KB

Longo et al. supplementary movie file

Flow in the lock and downstream, Re=4100

Download Longo et al. supplementary movie file(Video)
Video 19.2 MB

Longo et al. supplementary movie file

Flow in the lock and downstream, test Re=20500

Download Longo et al. supplementary movie file(Video)
Video 27.1 MB