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Gravity currents from moving sources

Published online by Cambridge University Press:  17 August 2021

Raphael Ouillon Open the ORCID record for Raphael Ouillon [Opens in a new window] ,
Christos Kakoutas ,
Eckart Meiburg Open the ORCID record for Eckart Meiburg [Opens in a new window]  and
Thomas Peacock Open the ORCID record for Thomas Peacock [Opens in a new window]
Raphael Ouillon*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
Christos Kakoutas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
Eckart Meiburg
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
Thomas Peacock
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

Emerging technologies such as deep-sea mining and geoengineering pose fundamentally new questions regarding the dynamics of gravity currents. Such activities can continuously release dense sediment plumes from moving locations, thereafter propagating as gravity currents. Here, we present the results of idealized numerical simulations of this novel configuration, and investigate the propagation of a gravity current that results from a moving source of buoyancy, as a function of the ratio of source speed to buoyancy velocity. We show that above a certain value of this ratio, the flow enters a supercritical regime in which the source moves more rapidly than the generated current, resulting in a statistically steady state in the reference frame of the moving source. Once in the supercritical regime, the current goes through a second transition beyond which fluid in the head of the current moves approximately in the direction normal to the direction of motion of the source, and the time evolution of the front in the lateral direction is well described by an equivalent constant volume lock-release gravity current. We use our findings to gain insight into the propagation of sediment plumes released by deep-sea mining collector vehicles, and present proof-of-concept tow-tank laboratory experiments of a model deep-sea mining collector discharging dense dyed fluid in its wake. The experiments reveal the formation a wedge-shaped gravity current front which narrows as the ratio of collector-to-buoyancy velocity increases. The time-averaged front position shows good agreement with the results of the numerical model in the supercritical regime.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A43
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Aleynik, D., Inall, M.E., Dale, A. & Vink, A. 2017 Impact of remotely generated eddies on plume dispersion at abyssal mining sites in the Pacific. Sci. Rep. 7 (1), 16959.CrossRefGoogle ScholarPubMed
Benjamin, T.B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (02), 209–248.CrossRefGoogle Scholar
Bonometti, T. & Balachandar, S. 2008 Effect of Schmidt number on the structure and propagation of density currents. Theor. Comput. Fluid Dyn. 22 (5), 341–361.CrossRefGoogle Scholar
Cantero, M.I., Balachandar, S., García, M.H. & Bock, D. 2008 Turbulent structures in planar gravity currents and their influence on the flow dynamics. J. Geophys. Res. 113 (C8), C08018.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
Choi, K.W. & Lee, J.H. 2007 Distributed entrainment sink approach for modeling mixing and transport in the intermediate field. J. Hydraul. Engng ASCE 133 (7), 804–815.CrossRefGoogle Scholar
Flynn, M.R., Ungarish, M. & Tan, A.W. 2012 Gravity currents in a two-layer stratified ambient: the theory for the steady-state (front condition) and lock-released flows, and experimental confirmations. Phys. Fluids 24 (2), 026601.CrossRefGoogle Scholar
Gillard, B., Purkiani, K., Chatzievangelou, D., Vink, A., Iversen, M.H. & Thomsen, L. 2019 Physical and hydrodynamic properties of deep sea mining-generated, abyssal sediment plumes in the Clarion Clipperton Fracture zone (Eastern-Central Pacific). Elem. Sci. Anth. 7 (1), 5.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
Härtel, C., Carlsson, F. & Thunblom, M. 2000 a Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability. J. Fluid Mech. 418, 213–229.CrossRefGoogle Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000 b 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
Hogg, A.J., Nasr-Azadani, M.M., Ungarish, M. & Meiburg, E. 2016 Sustained gravity currents in a channel. J. Fluid Mech. 798, 853–888.CrossRefGoogle Scholar
Holyer, J.Y. & Huppert, H.E. 1980 Gravity currents entering a two-layer fluid. J. Fluid Mech. 100 (4), 739–767.CrossRefGoogle Scholar
Huppert, H.E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.CrossRefGoogle Scholar
Huppert, H.E. 2006 Gravity currents: a personal perspective. J. Fluid Mech. 554, 299–322.CrossRefGoogle Scholar
Huppert, H.E. & Simpson, J.E. 1980 The slumping of gravity currents. J. Fluid Mech. 99 (4), 785–799.CrossRefGoogle Scholar
von Kármán, T. 1940 The engineer grapples with nonlinear problems. Bull. Am. Math. Soc. 46 (8), 615–684.CrossRefGoogle Scholar
Khodkar, M.A., Nasr-Azadani, M.M. & Meiburg, E. 2018 Gravity currents propagating into two-layer stratified fluids: vorticity-based models. J. Fluid Mech. 844, 994–1025.CrossRefGoogle Scholar
La Rocca, M., Adduce, C., Sciortino, G. & Pinzon, A.B. 2008 Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom. Phys. Fluids 20 (10), 106603.CrossRefGoogle Scholar
Longo, S., Ungarish, M., Di Federico, V., Chiapponi, L. & Addona, F. 2016 Gravity currents produced by constant and time varying inflow in a circular cross-section channel: experiments and theory. Adv. Water Resour. 90, 10–23.CrossRefGoogle Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42 (1), 135–156.CrossRefGoogle Scholar
Meiburg, E., Radhakrishnan, S. & Nasr-Azadani, M. 2015 Modeling gravity and turbidity currents: computational approaches and challenges. Appl. Mech. Rev. 67 (4), 040802.CrossRefGoogle Scholar
Nasr-Azadani, M.M. & Meiburg, E. 2011 TURBINS: an immersed boundary, Navier–Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies. Comput. Fluids 45 (1), 14–28.CrossRefGoogle Scholar
Nasr-Azadani, M.M., Meiburg, E. & Kneller, B. 2018 Mixing dynamics of turbidity currents interacting with complex seafloor topography. Environ. Fluid Mech. 18 (1), 201–223.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
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
Oebius, H.U., Becker, H.J., Rolinski, S. & Jankowski, J.A. 2001 Parametrization and evaluation of marine environmental impacts produced by deep-sea manganese nodule mining. Deep Sea Res. II: Top. Stud. Oceanogr. 48 (17–18), 3453–3467.CrossRefGoogle Scholar
Ouillon, R., Meiburg, E. & Sutherland, B.R. 2019 Turbidity currents propagating down a slope into a stratified saline ambient fluid. Environ. Fluid Mech. 19, 1143–1166.CrossRefGoogle Scholar
Peacock, T. & Alford, M.H. 2018 Is deep-sea mining worth it? Sci. Am. 318 (5), 72–77.CrossRefGoogle ScholarPubMed
Roberts, P.J.W. 1979 Line plume and ocean outfall dispersion. J. Hydraul. Div. ASCE 105 (4), 313–331.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
Schröder, A., Willert, C., Schanz, D., Geisler, R., Jahn, T., Gallas, Q. & Leclaire, B. 2020 The flow around a surface mounted cube: a characterization by time-resolved PIV, 3D Shake-The-Box and LBM simulation. Exp. Fluids 61 (9), 189.CrossRefGoogle 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
Taherian, M. & Mohammadian, A. 2021 Buoyant jets in cross-flows: review, developments, and applications. J. Mar. Sci. Engng 9 (1), 61.CrossRefGoogle Scholar
Tan, A.W., Nobes, D.S., Fleck, B.A. & Flynn, M.R. 2011 Gravity currents in two-layer stratified media. Environ. Fluid Mech. 11 (2), 203–223.CrossRefGoogle Scholar
Ungarish, M. 2005 Intrusive gravity currents in a stratified ambient: shallow-water theory and numerical results. J. Fluid Mech. 535, 287–323.CrossRefGoogle Scholar
Ungarish, M. 2020 Gravity Currents and Intrusions. World Scientific.CrossRefGoogle Scholar
Wells, M.G. & Dorrell, R.M. 2021 Turbulence processes within turbidity currents. Annu. Rev. Fluid Mech. 53 (1), 010719–060309.CrossRefGoogle Scholar
Zemach, T., Ungarish, M., Martin, A. & Negretti, M.E. 2019 On gravity currents of fixed volume that encounter a down-slope or up-slope bottom. Phys. Fluids 31 (9), 096604.CrossRefGoogle Scholar

Ouillon et al. supplementary movie

Video of the tow-tank experiment at $a=1.11$ showing the gravity current behaviour of the dense dyed fluid being released from the back of a model deep sea mining collector via a discharge pipe.

Download Ouillon et al. supplementary movie(Video)
Video 10.5 MB