Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-04T13:24:11.530Z Has data issue: false hasContentIssue false
  • English
  • Français

Gravity currents over fixed beds of monodisperse spheres

Published online by Cambridge University Press:  02 September 2020

Thomas Köllner ,
Alex Meredith Open the ORCID record for Alex Meredith [Opens in a new window] ,
Roger Nokes Open the ORCID record for Roger Nokes [Opens in a new window]  and
Eckart Meiburg Open the ORCID record for Eckart Meiburg [Opens in a new window]
Thomas Köllner
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA93106, USA CADFEM GmbH, Grafing bei München 85567, Germany
Alex Meredith*
Affiliation:
Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch 8041, New Zealand
Roger Nokes
Affiliation:
Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch 8041, New Zealand
Eckart Meiburg
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA93106, USA
*
†Email address for correspondence: alex.meredith@pg.canterbury.ac.nz
Get access Rights & Permissions [Opens in a new window]

Abstract

Laboratory experiments and direct numerical simulations are employed to investigate lock-exchange gravity currents propagating over close-packed, fixed porous beds of monodisperse spherical particles, and to quantify the mass and momentum transfer between the currents and the bed. The simulations show that the mass exchange of the current with the bed involves two separate steps that operate on different time scales. In a first step, the dense current front rapidly sweeps away the resident fluid in the exposed pore spaces between the top layer of spheres, while in a second step, a buoyancy-driven vertical exchange flow between the current and the deeper pores is set up that takes significantly longer to develop. This process depends on the permeability of the bed, which in turn is a function of the particle diameter. The momentum exchange between the current and the bed strongly depends on the ratio of the particle size to the viscous sublayer of the current. The bottom friction is moderate when the particle size is smaller than or comparable to the thickness of the viscous sublayer, but it jumps for particles that strongly protrude from the sublayer, leading to a more rapid deceleration of the flow.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A32
Check for updates
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Adduce, C., Sciortino, G. & Proietti, S. 2011 Gravity currents produced by lock exchanges: experiments and simulations with a two-layer shallow-water model with entrainment. J. Hydraul. Engng 138 (2), 111–121.CrossRefGoogle Scholar
Ardekani, M. N., Abouali, O., Picano, F. & Brandt, L. 2018 Heat transfer in laminar Couette flow laden with rigid spherical particles. J. Fluid Mech. 834, 308–334.CrossRefGoogle Scholar
Belcher, S. E., Harman, I. N. & Finnigan, J. J. 2012 The wind in the willows: flows in forest canopies in complex terrain. Annu. Rev. Fluid Mech. 44, 479–504.CrossRefGoogle Scholar
Bhaganagar, K. & Pillalamarri, N. R. 2017 Lock-exchange release density currents over three-dimensional regular roughness elements. J. Fluid Mech. 832, 793–824.CrossRefGoogle Scholar
Biegert, E., Vowinckel, B. & Meiburg, E. 2017 A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds. J. Comput. Phys. 340, 105–127.CrossRefGoogle Scholar
Bonometti, T. & Balachandar, S. 2008 Effect of Schmidt number on the structure and propagation of density currents. Theor. Comp. Fluid Dyn. 22 (5), 341–361.CrossRefGoogle Scholar
Cantero, M. I., Balachandar, S. & Garcia, M. H. 2007 High-resolution simulations of cylindrical density currents. J. Fluid Mech. 590, 437–469.CrossRefGoogle Scholar
Carman, P. C. 1997 Fluid flow through granular beds. Chem. Engng Res. Des. 75, S32–S48.CrossRefGoogle Scholar
Cenedese, C., Nokes, R. & Hyatt, J. 2018 Lock-exchange gravity currents over rough bottoms. Environ. Fluid Mech. 18 (1), 59–73.CrossRefGoogle Scholar
Doostmohammadi, A., Dabiri, S. & Ardekani, A. M. 2014 A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid. J. Fluid Mech. 750, 5–32.CrossRefGoogle Scholar
Fang, H., Han, X., He, G. & Dey, S. 2018 Influence of permeable beds on hydraulically macro-rough flow. J. Fluid Mech. 847, 552–590.CrossRefGoogle Scholar
Ferziger, J. H. & Peric, M. 2012 Computational Methods for Fluid Dynamics. Springer Science & Business Media.Google 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, 189–212.CrossRefGoogle Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99 (4), 785–799.CrossRefGoogle Scholar
Huq, P., White, L. A., Carrillo, A., Redondo, J., Dharmavaram, S. & Hanna, S. R. 2007 The shear layer above and in urban canopies. J. Appl. Meteorol. Climatol. 46 (3), 368–376.CrossRefGoogle Scholar
Jeffrey, D. J. 1973 Conduction through a random suspension of spheres. Proc. R. Soc. Lond. 335 (1602), 355–367.Google Scholar
Jiang, Y. & Liu, X. 2018 Experimental and numerical investigation of density current over macro-roughness. Environ. Fluid Mech. 18 (1), 97–116.CrossRefGoogle Scholar
Khattab, I. S., Bandarkar, F., Fakhree, M. A. A. & Jouyban, A. 2012 Density, viscosity, and surface tension of water+ethanol mixtures from 293 to 323K. Korean J. Chem. Engng 29 (6), 812–817.CrossRefGoogle Scholar
Kyrousi, F., Leonardi, A., Roman, F., Armenio, V., Zanello, F., Zordan, J., Juez, C. & Falcomer, L. 2018 Large eddy simulations of sediment entrainment induced by a lock-exchange gravity current. Adv. Water Resour. 114, 102–118.CrossRefGoogle Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19 (1), 59–98.CrossRefGoogle Scholar
Leonardi, A., Pokrajac, D., Roman, F., Zanello, F. & Armenio, V. 2018 Surface and subsurface contributions to the build-up of forces on bed particles. J. Fluid Mech. 851, 558–572.CrossRefGoogle Scholar
Lide, D. R. 2003 CRC Handbook of Chemistry and Physics, vol. 53. CRC Press.Google Scholar
Manes, C., Pokrajac, D., McEwan, I. & Nikora, V. 2009 Turbulence structure of open channel flows over permeable and impermeable beds: a comparative study. Phys. Fluids 21 (12), 125109.CrossRefGoogle Scholar
Marino, B. M., Thomas, L. P. & Linden, P. F. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 49–78.CrossRefGoogle Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42, 135–156.CrossRefGoogle Scholar
Nasr-Azadani, M. M. & Meiburg, E. 2014 Turbidity currents interacting with three-dimensional seafloor topography. J. Fluid Mech. 745, 409–443.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.CrossRefGoogle Scholar
Nepf, H. M. 2012 Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44, 123–142.CrossRefGoogle Scholar
Nikuradse, J. 1931 Strömungswiderstand in rauhen Rohren. J. Appl. Math. Mech. 11 (6), 409–411.Google Scholar
Nogueira, H. I. S., Adduce, C., Alves, E. & Franca, M. J. 2013 Analysis of lock-exchange gravity currents over smooth and rough beds. J. Hydraul. Res. 51 (4), 417–431.CrossRefGoogle Scholar
Nogueira, H. I. S., Adduce, C., Alves, E. & Franca, M. J. 2014 Dynamics of the head of gravity currents. Environ. Fluid Mech. 14 (2), 519–540.CrossRefGoogle Scholar
Nokes, R. 2019 Streams 3.00 - System Theory and Design. University of Canterbury.Google Scholar
Oezgoekmen, T. M., Iliescu, T. & Fischer, P. F. 2009 Large eddy simulation of stratified mixing in a three-dimensional lock-exchange system. Ocean Model. 26 (3–4), 134–155.CrossRefGoogle Scholar
Ooi, S. K., Constantinescu, G. & Weber, L. 2009 Numerical simulations of lock-exchange compositional gravity current. J. Fluid Mech. 635, 361–388.CrossRefGoogle Scholar
Ottolenghi, L., Cenedese, C. & Adduce, C. 2017 Entrainment in a dense current flowing down a rough sloping bottom in a rotating fluid. J. Phys. Oceanogr. 47 (3), 485–498.CrossRefGoogle Scholar
Ozan, A. Y., Constantinescu, G. & Hogg, A. J. 2015 Lock-exchange gravity currents propagating in a channel containing an array of obstacles. J. Fluid Mech. 765, 544–575.CrossRefGoogle Scholar
Peters, W. D. & Venart, J. E. S. 2000 Visualization of rough-surface gravity current flows using laser-induced fluorescence. In 9th (Millennium) International Symposium on Flow Visualization.Google Scholar
Pokrajac, D. & Manes, C. 2009 Velocity measurements of a free-surface turbulent flow penetrating a porous medium composed of uniform-size spheres. Transport Porous Med. 78 (3), 367.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Prosperetti, A. & Tryggvason, G. 2009 Computational Methods for Multiphase Flow. Cambridge University Press.Google Scholar
Rocca, M. L., Adduce, C., Lombardi, V., Sciortino, G. & Hinkelmann, R. 2012 Development of a lattice Boltzmann method for two-layered shallow-water flow. Intl J. Numer. Meth. Fluids 70 (8), 1048–1072.CrossRefGoogle Scholar
Schlichting, H. 1936 Experimentelle Untersuchungen zum Rauhigkeitsproblem. Arch. Appl. Mech. 7 (1), 1–34.Google Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.CrossRefGoogle Scholar
Simpson, J. E. 1999 Gravity Currents: In the Environment and the Laboratory. Cambridge University Press.Google Scholar
Tokyay, T., Constantinescu, G. & Meiburg, E. 2011 Lock-exchange gravity currents with a high volume of release propagating over a periodic array of obstacles. J. Fluid Mech. 672, 570–605.CrossRefGoogle Scholar
Ungarish, M. 2009 An Introduction to Gravity Currents and Intrusions. Chapman and Hall/CRC.CrossRefGoogle Scholar
Wilson, R. I., Friedrich, H. & Stevens, C. 2017 Turbulent entrainment in sediment-laden flows interacting with an obstacle. Phys. Fluids 29 (3), 036603.CrossRefGoogle Scholar
Yuksel-Ozan, A., Constantinescu, G. & Nepf, H. 2016 Free-surface gravity currents propagating in an open channel containing a porous layer at the free surface. J. Fluid Mech. 809, 601–627.CrossRefGoogle Scholar
Zhang, X. & Nepf, H. M. 2011 Exchange flow between open water and floating vegetation. Environ. Fluid Mech. 11 (5), 531.CrossRefGoogle Scholar
Zhou, J., Cenedese, C., Williams, T., Ball, M., Venayagamoorthy, S. K. & Nokes, R. I. 2017 On the propagation of gravity currents over and through a submerged array of circular cylinders. J. Fluid Mech. 831, 394–417.CrossRefGoogle Scholar
Zordan, J., Juez, C., Schleiss, A. J. & Franca, M. J. 2018 Entrainment, transport and deposition of sediment by saline gravity currents. Adv. Water Resour. 115, 17–32.CrossRefGoogle Scholar
Zordan, J., Schleiss, A. & Franca, M. 2019 Potential erosion capacity of gravity currents created by changing initial conditions. Earth Surf. Dynam. 7, 377–391.CrossRefGoogle Scholar