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Gravity currents from moving sources. (English) Zbl 1480.76029

Summary: 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.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76D50 Stratification effects in viscous fluids
76M20 Finite difference methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
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[1] Aleynik, D., Inall, M.E., Dale, A. & Vink, A.2017Impact of remotely generated eddies on plume dispersion at abyssal mining sites in the Pacific. Sci. Rep.7 (1), 16959.
[2] Benjamin, T.B.1968Gravity currents and related phenomena. J. Fluid Mech.31 (02), 209-248. · Zbl 0169.28503
[3] Bonometti, T. & Balachandar, S.2008Effect of Schmidt number on the structure and propagation of density currents. Theor. Comput. Fluid Dyn.22 (5), 341-361. · Zbl 1178.76115
[4] Cantero, M.I., Balachandar, S., García, M.H. & Bock, D.2008Turbulent structures in planar gravity currents and their influence on the flow dynamics. J. Geophys. Res.113 (C8), C08018.
[5] Cantero, M.I., Lee, J.R., Balachandar, S. & Garcia, M.H.2007On the front velocity of gravity currents. J. Fluid Mech.586, 1-39. · Zbl 1178.76135
[6] Choi, K.W. & Lee, J.H.2007Distributed entrainment sink approach for modeling mixing and transport in the intermediate field. J. Hydraul. Engng ASCE133 (7), 804-815.
[7] Flynn, M.R., Ungarish, M. & Tan, A.W.2012Gravity currents in a two-layer stratified ambient: the theory for the steady-state (front condition) and lock-released flows, and experimental confirmations. Phys. Fluids24 (2), 026601.
[8] Gillard, B., Purkiani, K., Chatzievangelou, D., Vink, A., Iversen, M.H. & Thomsen, L.2019Physical 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.
[9] Hallworth, M.A., Hogg, A.J. & Huppert, H.E.1998Effects of external flow on compositional and particle gravity currents. J. Fluid Mech.359, 109-142. · Zbl 0916.76094
[10] Härtel, C., Carlsson, F. & Thunblom, M.2000aAnalysis 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. · Zbl 1103.76337
[11] Härtel, C., Meiburg, E. & Necker, F.2000bAnalysis 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. · Zbl 0985.76042
[12] Hogg, A.J., Nasr-Azadani, M.M., Ungarish, M. & Meiburg, E.2016Sustained gravity currents in a channel. J. Fluid Mech.798, 853-888. · Zbl 1422.76040
[13] Holyer, J.Y. & Huppert, H.E.1980Gravity currents entering a two-layer fluid. J. Fluid Mech.100 (4), 739-767. · Zbl 0444.76086
[14] Huppert, H.E.1982The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech.121, 43-58.
[15] Huppert, H.E.2006Gravity currents: a personal perspective. J. Fluid Mech.554, 299-322. · Zbl 1090.76022
[16] Huppert, H.E. & Simpson, J.E.1980The slumping of gravity currents. J. Fluid Mech.99 (4), 785-799.
[17] Von Kármán, T.1940The engineer grapples with nonlinear problems. Bull. Am. Math. Soc.46 (8), 615-684. · JFM 66.0985.04
[18] Khodkar, M.A., Nasr-Azadani, M.M. & Meiburg, E.2018Gravity currents propagating into two-layer stratified fluids: vorticity-based models. J. Fluid Mech.844, 994-1025. · Zbl 1429.76065
[19] La Rocca, M., Adduce, C., Sciortino, G. & Pinzon, A.B.2008Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom. Phys. Fluids20 (10), 106603. · Zbl 1182.76416
[20] Longo, S., Ungarish, M., Di Federico, V., Chiapponi, L. & Addona, F.2016Gravity currents produced by constant and time varying inflow in a circular cross-section channel: experiments and theory. Adv. Water Resour.90, 10-23.
[21] Meiburg, E. & Kneller, B.2010Turbidity currents and their deposits. Annu. Rev. Fluid Mech.42 (1), 135-156. · Zbl 1345.76104
[22] Meiburg, E., Radhakrishnan, S. & Nasr-Azadani, M.2015Modeling gravity and turbidity currents: computational approaches and challenges. Appl. Mech. Rev.67 (4), 040802.
[23] Nasr-Azadani, M.M. & Meiburg, E.2011TURBINS: an immersed boundary, Navier-Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies. Comput. Fluids45 (1), 14-28. · Zbl 1429.76018
[24] Nasr-Azadani, M.M., Meiburg, E. & Kneller, B.2018Mixing dynamics of turbidity currents interacting with complex seafloor topography. Environ. Fluid Mech.18 (1), 201-223.
[25] Necker, F., Härtel, C., Kleiser, L. & Meiburg, E.2002High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow28 (2), 279-300. · Zbl 1136.76590
[26] Necker, F., Härtel, C., Kleiser, L. & Meiburg, E.2005Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech.545, 339-372. · Zbl 1085.76559
[27] Oebius, H.U., Becker, H.J., Rolinski, S. & Jankowski, J.A.2001Parametrization 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.
[28] Ouillon, R., Meiburg, E. & Sutherland, B.R.2019Turbidity currents propagating down a slope into a stratified saline ambient fluid. Environ. Fluid Mech.19, 1143-1166.
[29] Peacock, T. & Alford, M.H.2018Is deep-sea mining worth it?Sci. Am.318 (5), 72-77.
[30] Roberts, P.J.W.1979Line plume and ocean outfall dispersion. J. Hydraul. Div. ASCE105 (4), 313-331.
[31] Rottman, J.W. & Simpson, J.E.1983Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech.135, 95-110.
[32] Schröder, A., Willert, C., Schanz, D., Geisler, R., Jahn, T., Gallas, Q. & Leclaire, B.2020The flow around a surface mounted cube: a characterization by time-resolved PIV, 3D Shake-The-Box and LBM simulation. Exp. Fluids61 (9), 189.
[33] Shin, J.O., Dalziel, S.B. & Linden, P.F.2004Gravity currents produced by lock exchange. J. Fluid Mech.521, 1-34. · Zbl 1065.76037
[34] Taherian, M. & Mohammadian, A.2021Buoyant jets in cross-flows: review, developments, and applications. J. Mar. Sci. Engng9 (1), 61.
[35] Tan, A.W., Nobes, D.S., Fleck, B.A. & Flynn, M.R.2011Gravity currents in two-layer stratified media. Environ. Fluid Mech.11 (2), 203-223.
[36] Ungarish, M.2005Intrusive gravity currents in a stratified ambient: shallow-water theory and numerical results. J. Fluid Mech.535, 287-323. · Zbl 1072.76016
[37] Ungarish, M.2020Gravity Currents and Intrusions. World Scientific. · Zbl 1182.76001
[38] Wells, M.G. & Dorrell, R.M.2021Turbulence processes within turbidity currents. Annu. Rev. Fluid Mech.53 (1), 010719-060309. · Zbl 1459.76063
[39] Zemach, T., Ungarish, M., Martin, A. & Negretti, M.E.2019On gravity currents of fixed volume that encounter a down-slope or up-slope bottom. Phys. Fluids31 (9), 096604.
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