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Slumping regime in lock-release turbidity currents

Published online by Cambridge University Press:  23 October 2023

Cyril Gadal Open the ORCID record for Cyril Gadal [Opens in a new window] ,
M.J. Mercier Open the ORCID record for M.J. Mercier [Opens in a new window] ,
M. Rastello Open the ORCID record for M. Rastello [Opens in a new window]  and
L. Lacaze Open the ORCID record for L. Lacaze [Opens in a new window]
Cyril Gadal*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
M.J. Mercier
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
M. Rastello
Affiliation:
Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France
L. Lacaze
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
*
†Email address for correspondence: cyril.gadal@imft.fr
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Abstract

Most gravitational currents occur on sloping topographies, often in the presence of particles that can settle during the current propagation. Yet an exhaustive exploration of associated parameters in experimental studies is still lacking. Here, we present an extensive experimental investigation of the slumping regime of turbidity (particle-laden) currents in two lock-release (dam-break) systems with inclined bottoms. We identify three regimes controlled by the ratio between settling and current inertia. (i) For negligible settling, the turbidity current morphodynamics corresponds to that of saline homogeneous gravity currents, in terms of velocity, slumping (constant-velocity) regime duration and current morphology. (ii) For intermediate settling, the slumping regime duration decreases to become fully controlled by a particle settling characteristic time. (iii) When settling overcomes the current initial inertia, the slumping (constant-velocity) regime is no longer detected. In the first two regimes, the current velocity increases with the bottom slope, of approximately $35\,\%$ between $0^\circ$ and $15^\circ$. Finally, our experiments show that the current propagates during the slumping regime with the same shape in the frame of the moving front. Strikingly, the current head is found to be independent of all experimental parameters covered in the present study. We also quantify water entrainment coefficients $E$ and compare them with previous literature, hence finding that $E$ increases rather linearly with the current Reynolds number.

JFM classification

Geophysical and Geological Flows: Gravity currents
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 974 , 10 November 2023 , A4
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Baines, P.G. 2001 Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.CrossRefGoogle Scholar
Balasubramanian, S. & Zhong, Q. 2018 Entrainment and mixing in lock-exchange gravity currents using simultaneous velocity–density measurements. Phys. Fluids 30 (5), 056601.CrossRefGoogle Scholar
Barr, D. 1963 Densimetric exchange flow in rectangular channels. I. Definitions, review and relevance to model design. La Houille Blanche 7, 739–756.CrossRefGoogle Scholar
Beghin, P., Hopfinger, E.J. & Britter, R.E. 1981 Gravitational convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407–422.CrossRefGoogle Scholar
Benjamin, T.B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209–248.CrossRefGoogle Scholar
Birman, V.K., Battandier, B.A., Meiburg, E. & Linden, P.F. 2007 Lock-exchange flows in sloping channels. J. Fluid Mech. 577, 53–77.CrossRefGoogle Scholar
Blanchette, F., Strauss, M., Meiburg, E., Kneller, B. & Glinsky, M.E. 2005 High-resolution numerical simulations of resuspending gravity currents: conditions for self-sustainment. J. Geophys. Res. 110, C12022.Google Scholar
Bonnecaze, R.T., Hallworth, M.A., Huppert, H.E. & Lister, J.R. 1995 Axisymmetric particle-driven gravity currents. J. Fluid Mech. 294, 93–121.CrossRefGoogle Scholar
Bonnecaze, R.T., Huppert, H.E. & Lister, J.R. 1993 Particle-driven gravity currents. J. Fluid Mech. 250, 339–369.CrossRefGoogle Scholar
Bonnecaze, R.T. & Lister, J.R. 1999 Particle-driven gravity currents down planar slopes. J. Fluid Mech. 390, 75–91.CrossRefGoogle Scholar
Bonometti, T. & Ungarish, M. 2011 A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient. J. Fluid Mech. 673, 574–602.CrossRefGoogle Scholar
Borden, Z. & Meiburg, E. 2013 Circulation based models for Boussinesq gravity currents. Phys. Fluids 25 (10), 101301.CrossRefGoogle Scholar
Britter, R.E. & Linden, P.F. 1980 The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 99 (3), 531–543.CrossRefGoogle Scholar
Camenen, B. 2007 Simple and general formula for the settling velocity of particles. J. Hydraul. Engng 133 (2), 229–233.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, 1–39.CrossRefGoogle Scholar
Cantero, M.I., Shringarpure, M. & Balachandar, S. 2012 Towards a universal criteria for turbulence suppression in dilute turbidity currents with non-cohesive sediments. Geophys. Res. Lett. 39 (14), 1–5.CrossRefGoogle Scholar
Carter, L., Gavey, R., Talling, P.J. & Liu, J.T. 2014 Insights into submarine geohazards from breaks in subsea telecommunication cables. Oceanography 27 (2), 58–67.CrossRefGoogle 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.CrossRefGoogle Scholar
Cenedese, C. & Adduce, C. 2010 A new parameterization for entrainment in overflows. J. Phys. Oceanogr. 40 (8), 1835–1850.CrossRefGoogle Scholar
Chowdhury, M. & Testik, F. 2011 Laboratory testing of mathematical models for high-concentration fluid mud turbidity currents. Ocean Engng 38 (1), 256–270.CrossRefGoogle Scholar
Clare, M., et al. 2020 Lessons learned from the monitoring of turbidity currents and guidance for future platform designs. Geol. Soc. 500 (1), 605–634.CrossRefGoogle Scholar
Dai, A. 2013 Experiments on gravity currents propagating on different bottom slopes. J. Fluid Mech. 731, 117–141.CrossRefGoogle Scholar
Dai, A. 2014 Non-Boussinesq gravity currents propagating on different bottom slopes. J. Fluid Mech. 741, 658–680.CrossRefGoogle Scholar
Di Felice, R. 1995 Hydrodynamics of liquid fluidisation. Chem. Engng Sci. 50 (8), 1213–1245.CrossRefGoogle Scholar
Dobran, F., Neri, A. & Todesco, M. 1994 Assessing the pyroclastic flow hazard at Vesuvius. Nature 367 (6463), 551–554.CrossRefGoogle Scholar
Hallworth, M.A., Hogg, A.J. & Huppert, H.E. 1998 Effects of external flow on compositional and particle gravity currents. J. Fluid Mech. 359, 109–142.CrossRefGoogle Scholar
Harris, C.R., et al. 2020 Array programming with NumPy. Nature 585, 357–362.CrossRefGoogle ScholarPubMed
Harris, T.C., Hogg, A.J. & Huppert, H.E. 2001 A mathematical framework for the analysis of particle-driven gravity currents. Proc. R. Soc. Lond. A 457 (2009), 1241–1272.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, 189–212.CrossRefGoogle Scholar
van der Hoef, M.A., van Sint Annaland, M., Deen, N. & Kuipers, J. 2008 Numerical simulation of dense gas–solid fluidized beds: a multiscale modeling strategy. Annu. Rev. Fluid Mech. 40, 47–70.CrossRefGoogle Scholar
Hogg, A.J., Ungarish, M. & Huppert, H.E. 2000 Particle-driven gravity currents: asymptotic and box model solutions. Eur. J. Mech. B/Fluids 19 (1), 139–165.CrossRefGoogle Scholar
Hogg, A.J. & Woods, A.W. 2001 The transition from inertia- to bottom-drag-dominated motion of turbulent gravity currents. J. Fluid Mech. 449, 201–224.CrossRefGoogle Scholar
Hunter, J.D. 2007 Matplotlib: a 2D graphics environment. Comput. Sci. Engng 9, 90–95.CrossRefGoogle Scholar
Huppert, H.E. 1998 Quantitative modelling of granular suspension flows. Phil. Trans. R. Soc. Lond. A 356 (1747), 2471–2496.CrossRefGoogle Scholar
Huppert, H.E. & Simpson, J.E. 1980 The slumping of gravity currents. J. Fluid Mech. 99 (4), 785–799.CrossRefGoogle Scholar
Ikeda, J. & Testik, F.Y. 2021 Propagation, deposition, and suspension characteristics of constant-volume particle-driven gravity currents. Environ. Fluid Mech. 21 (1), 177–208.CrossRefGoogle Scholar
Islam, M.A. & Imran, J. 2010 Vertical structure of continuous release saline and turbidity currents. J. Geophys. Res. 115, C08025.Google Scholar
Jacobson, M. & Testik, F. 2014 Turbulent entrainment into fluid mud gravity currents. Environ. Fluid Mech. 14 (2), 541–563.CrossRefGoogle Scholar
Keulegan, G. 1957 An experimental study of the motion of saline water from locks into fresh water channels. Tech. Rep. 5168. National Bureau of Standards.Google Scholar
Khodkar, M., Nasr-Azadani, M. & Meiburg, E. 2017 Partial-depth lock-release flows. Phys. Rev. Fluids 2 (6), 064802.CrossRefGoogle Scholar
Konopliv, N., Smith, S.G.L., McElwaine, J. & Meiburg, E. 2016 Modelling gravity currents without an energy closure. J. Fluid Mech. 789, 806–829.CrossRefGoogle Scholar
Lippert, M.C. & Woods, A.W. 2020 Experiments on the sedimentation front in steady particle-driven gravity currents. J. Fluid Mech. 889, A20.CrossRefGoogle Scholar
Longo, S., Ungarish, M., Di Federico, V., Chiapponi, L. & Petrolo, D. 2018 Gravity currents produced by lock-release: theory and experiments concerning the effect of a free top in non-Boussinesq systems. Adv. Water Resour. 121 (July), 456–471.CrossRefGoogle Scholar
Lowe, R.J., Rottman, J.W. & Linden, P. 2005 The non-Boussinesq lock-exchange problem. Part 1. Theory and experiments. J. Fluid Mech. 537, 101–124.CrossRefGoogle Scholar
Maggi, M.R., Adduce, C. & Negretti, M.E. 2022 Lock-release gravity currents propagating over roughness elements. Environ. Fluid Mech. 22, 383–402.CrossRefGoogle Scholar
Marino, B., Thomas, L. & Linden, P. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 49–78.CrossRefGoogle Scholar
Maxworthy, T. & Nokes, R.I. 2007 Experiments on gravity currents propagating down slopes. Part 1. The release of a fixed volume of heavy fluid from an enclosed lock into an open channel. J. Fluid Mech. 584, 433–453.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow 28 (2), 279–300.CrossRefGoogle Scholar
Nogueira, H.I., Adduce, C., Alves, E. & Franca, M.J. 2014 Dynamics of the head of gravity currents. Environ. Fluid Mech. 14 (2), 519–540.CrossRefGoogle Scholar
Ottolenghi, L., Adduce, C., Inghilesi, R., Armenio, V. & Roman, F. 2016 Entrainment and mixing in unsteady gravity currents. J. Hydraul. Res. 54 (5), 541–557.CrossRefGoogle Scholar
Pachitariu, M. & Stringer, C. 2022 CellPose 2.0: how to train your own model. Nat. Methods 19 (12), 1634–1641.CrossRefGoogle ScholarPubMed
Rastello, M., Ancey, C., Ousset, F., Magnard, R. & Hopfinger, E.J. 2002 An experimental study of particle-driven gravity currents on steep slopes with entrainment of particles. Nat. Hazards Earth Syst. Sci. 2 (3–4), 181–185.CrossRefGoogle Scholar
Richardson, J. & Zaki, W. 1954 The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Engng Sci. 3 (2), 65–73.CrossRefGoogle Scholar
Ross, A.N., Linden, P. & Dalziel, S.B. 2002 A study of three-dimensional gravity currents on a uniform slope. J. Fluid Mech. 453, 239–261.CrossRefGoogle Scholar
Rottman, J.W. & Simpson, J.E. 1983 Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95–110.CrossRefGoogle Scholar
Séon, T., Hulin, J.-P., Salin, D., Perrin, B. & Hinch, E.J. 2005 Buoyancy driven miscible front dynamics in tilted tubes. Phys. Fluids 17 (3), 031702.CrossRefGoogle Scholar
Sher, D. & Woods, A.W. 2015 Gravity currents: entrainment, stratification and self-similarity. J. Fluid Mech. 784, 130–162.CrossRefGoogle Scholar
Shin, J., Dalziel, S. & Linden, P. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.CrossRefGoogle Scholar
Simpson, J. & Britter, R. 1980 Experiments on the dynamics of the front of a gravity current. J. Fluid Mech. 88, 223–240.Google Scholar
Simpson, J.E. 1972 Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53 (4), 759–768.CrossRefGoogle Scholar
Stagnaro, M. & Bolla Pittaluga, M. 2014 Velocity and concentration profiles of saline and turbidity currents flowing in a straight channel under quasi-uniform conditions. Earth Surf. Dyn. 2 (1), 167–180.CrossRefGoogle Scholar
Steenhauer, K., Tokyay, T. & Constantinescu, G. 2017 Dynamics and structure of planar gravity currents propagating down an inclined surface. Phys. Fluids 29 (3), 036604.CrossRefGoogle Scholar
Stethem, C., Jamieson, B., Schaerer, P., Liverman, D., Germain, D. & Walker, S. 2003 Snow avalanche hazard in Canada – a review. Nat. Hazards 28 (2), 487–515.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, 373–382.CrossRefGoogle Scholar
Ungarish, M. 2009 An Introduction to Gravity Currents and Intrusions. Chapman and Hall/CRC.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. 675, 27–59.CrossRefGoogle Scholar
Ungarish, M. & Zemach, T. 2005 On the slumping of high Reynolds number gravity currents in two-dimensional and axisymmetric configurations. Eur. J. Mech. B/Fluids 24 (1), 71–90.CrossRefGoogle Scholar
Virtanen, P., et al. 2020 SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272.CrossRefGoogle ScholarPubMed
von Kármán, T. 1940 The engineer grapples with nonlinear problems. Bull. Am. Math. Soc. 46 (8), 615–683.CrossRefGoogle Scholar
Wells, M., Cenedese, C. & Caulfield, C.P. 2010 The relationship between flux coefficient and entrainment ratio in density currents. J. Phys. Oceanogr. 40 (12), 2713–2727.CrossRefGoogle Scholar
Wells, M.G. & Dorrell, R.M. 2021 Turbulence processes within turbidity currents. Annu. Rev. Fluid Mech. 53, 59–83.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
Xie, J., Hu, P., Zhu, C., Yu, Z. & Pähtz, T. 2023 Turbidity currents propagating down an inclined slope: particle auto-suspension. J. Fluid Mech. 954, A44.CrossRefGoogle Scholar