On the interaction between oncoming internal waves and a dense gravity current in a two-layer stratification. (English) Zbl 07442572

Summary: A series of laboratory experiments was conducted to investigate the dynamics of a dense gravity current flowing down an inclined slope into a two-layer stratification in the presence of oncoming internal interfacial waves. The experiment is set up such that the gravity current propagates towards a wave maker emitting interfacial waves such that the current and waves propagate in opposite directions. The results were compared with the case of gravity current without oncoming waves. The gravity current splits into a portion that inserts itself into the pycnocline as an interflow and another that propagates down the slope as an underflow, with the proportionality depending on the characteristics of the gravity current and the oncoming waves when they are present. The interflow is shown to arise from a combination of detrainment and the preferential insertion of fluid with density greater than the upper layer and less than lower layer along the pycnocline. The mass flux of the interflow is observed to be reduced by the oncoming waves, as waves act to decrease the interflow velocity. The internal waves also increase the path length that the interflow must travel. A combination of reduced velocities and increased path length explains the observed reduction in cumulative flux. The trend of the final cumulative flux is consistent with the mass change observed by comparing density profiles obtained before and after the experiment.


76-XX Fluid mechanics
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[1] Alahyari, A. & Longmire, E.K.1994Particle image velocimetry in a variable density flow: application to a dynamically evolving microburst. Exp. Fluids17 (6), 434-440.
[2] Baines, P.G.2005Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech.538, 245-267. · Zbl 1108.76302
[3] Baines, P.G.2008Mixing in downslope flows in the ocean - plumes versus gravity currents. Atmosphere46 (4), 405-419.
[4] Barrett, T.K. & Van Atta, C.W.1991Experiments on the inhibition of mixing in stably stratified decaying turbulence using laser Doppler anemometry and laser-induced fluorescence. Phys. Fluids A3 (5), 1321-1332.
[5] Benjamin, T.B.1968Gravity currents and related phenomena. J. Fluid Mech.31 (2), 209-248. · Zbl 0169.28503
[6] Britter, R.E. & Linden, P.F.1980The motion of the front of a gravity current travelling down an incline. J. Fluid Mech.99 (3), 531-543.
[7] Britter, R.E. & Simpson, J.E.1978Experiments on the dynamics of a gravity current head. J. Fluid Mech.88 (2), 223-240.
[8] Britter, R.E. & Simpson, J.E.1981A note on the structure of the head of an intrusive gravity current. J. Fluid Mech.112, 459-466.
[9] Cenedese, C. & Adduce, C.2010A new parameterization for entrainment in overflows. J. Phys. Oceanogr.40 (8), 1835-1850.
[10] Charonko, J.J. & Vlachos, P.P.2013Estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio. Meas. Sci. Technol.24 (6).
[11] Cheong, H.B., Kuenen, J.J.P. & Linden, P.F.2006The front speed of intrusive gravity currents. J. Fluid Mech.552, 1-11. · Zbl 1087.76022
[12] Clément, S.A., Guillemain, A., Mccleney, A.B. & Bardet, P.M.2018Options for refractive index and viscosity matching to study variable density flows. Exp. Fluids59 (2), 1-15.
[13] Cortés, A., Rueda, F.J. & Wells, M.G.2014Experimental observations of the splitting of a gravity current at a density step in a stratified water body. J. Geophys. Res.119 (2), 1038-1053.
[14] Cortés, A., Wells, M.G., Fringer, O.B., Arthur, R.S. & Rueda, F.J.2015Numerical investigation of split flows by gravity currents into two-layered stratified water bodies. J. Geophys. Res. C120 (7), 5254-5271.
[15] Cotte, G. & Vennemann, T.W.2020Mixing of Rhône river water in lake Geneva: seasonal tracing using stable isotope composition of water. J. Great Lakes Res.46 (4), 839-849.
[16] Cowen, E.A. & Monismith, S.G.1997A hybrid digital particle tracking velocimetry technique. Exp. Fluids22 (3), 199-211.
[17] Crimaldi, J.P.2008Planar laser induced fluorescence in aqueous flows. Exp. Fluids44 (6), 851-863.
[18] Crimaldi, J.P. & Koseff, J.R.2001High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume. Exp. Fluids31 (1), 90-102.
[19] Daviero, G.J., Roberts, P.J.W. & Maile, K.2001Refractive index matching in large-scale stratified experiments. Exp. Fluids31 (2), 119-126.
[20] Dossmann, Y., Bourget, B., Brouzet, C., Dauxois, T., Joubaud, S. & Odier, P.2016Mixing by internal waves quantified using combined PIV/PLIF technique. Exp. Fluids57 (8), 132.
[21] Ellison, T.H. & Turner, J.S.1959Turbulent entrainment in stratified flows. J. Fluid Mech.6 (3), 423-448. · Zbl 0086.40706
[22] Ferrier, A.J., Funk, D.R. & Roberts, P.J.W.1993Application of optical techniques to the study of plumes in stratified fluids. Dyn. Atmos. Oceans20 (1), 155-183.
[23] Fischer, H.B. & Smith, R.D.1983Observations of transport to surface waters from a plunging inflow to Lake Mead. Limnol. Oceanogr.28 (2), 258-272.
[24] Flynn, M.R. & Sutherland, B.R.2004Intrusive gravity currents and internal gravity wave generation in stratified fluid. J. Fluid Mech.514, 355-383. · Zbl 1067.76020
[25] Fringer, O.B. & Street, R.L.2003The dynamics of breaking progressive interfacial waves. J. Fluid Mech.494 (494), 319-353. · Zbl 1063.76013
[26] Hallworth, M.A., Huppert, H.E., Phillips, J.C. & Sparks, R.S.J.1996Entrainment into two-dimensional and axisymmetric turbulent gravity currents. J. Fluid Mech.308, 289-311.
[27] Hass, M. & Davisson, J.W.1977Absorption coefficient of pure water at 488 and 541.5 nm by adiabatic laser calorimetry*. J. Opt. Soc. Am.67 (5), 622-624.
[28] Hogg, C.A.R., Dalziel, S.B., Huppert, H.E. & Imberger, J.2017Inclined gravity currents filling basins: the impact of peeling detrainment on transport and vertical structure. J. Fluid Mech.820, 400-423. · Zbl 1387.86013
[29] Hogg, C.A.R., Egan, G.C., Ouellette, N.T. & Koseff, J.R.2018Shoaling internal waves may reduce gravity current transport. Environ. Fluid Mech.18 (2), 383-394.
[30] Holyer, J.Y. & Huppert, H.E.1980Gravity currents entering a two- layer fluid. J. Fluid Mech.100 (4), 739-767. · Zbl 0444.76086
[31] Howard, L.N.1961Note on a paper of John W. Miles. J. Fluid Mech.10 (04), 509-512.
[32] Hult, E.L., Troy, C.D. & Koseff, J.R.2009The breaking of interfacial waves at a submerged bathymetric ridge. J. Fluid Mech.637, 45-71. · Zbl 1183.76023
[33] Johnson, B.A. & Cowen, E.A.2018Turbulent boundary layers absent mean shear. J. Fluid Mech.835, 217-251. · Zbl 1421.76117
[34] Jones, E., Qadir, M., Van Vliet, M.T.H., Smakhtin, V. & Kang, S.2019The state of desalination and brine production: a global outlook. Sci. Total Environ.657, 1343-1356.
[35] Koochesfahani, M.M. & Dimotakis, P.E.1985Laser-induced fluorescence measurements of mixed fluid concentrationin a liquid plane shear layer. AIAA J.23 (11), 1700-1707.
[36] Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A.2015The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech.765, 303-324.
[37] Larsen, L.G. & Crimaldi, J.P.2006The effect of photobleaching on PLIF. Exp. Fluids41 (5), 803-812.
[38] Liao, Q. & Cowen, E.A.2005An efficient anti-aliasing spectral continuous window shifting technique for PIV. Exp. Fluids38 (2), 197-208.
[39] Linden, P.F. & Simpson, J.E.1986Gravity-driven flows in a turbulent fluid. J. Fluid Mech.172 (1980), 481-497.
[40] Lowe, R.J., Linden, P.F. & Rottman, J.W.2002A laboratory study of the velocity structure in an intrusive gravity current. J. Fluid Mech.456, 33-48. · Zbl 0987.76508
[41] Maroto, J.A., De Dios, J. & De Las Nieves, F.J.2002Use of a Mariotte bottle for the experimental study of the transition from laminar to turbulent flow. Am. J. Phys.70 (7), 698-701.
[42] Martin, A., Negretti, M.E., Ungarish, M. & Zemach, T.2020Propagation of a continuously supplied gravity current head down bottom slopes. Phys. Rev. Fluids5 (5), 54801.
[43] Maurer, B.D. & Linden, P.F.2014Intrusion-generated waves in a linearly stratified fluid. J. Fluid Mech.752, 282-295.
[44] Mcdougall, T.J.1979On the elimination of refractive-index variations in turbulent density-stratified liquid flows. J. Fluid Mech.93 (1), 83-96.
[45] Mellor, G.L. & Yamada, T.1982Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys.20 (4), 851-875.
[46] Miles, J.W.1961On the stability of heterogeneous shear flows. J. Fluid Mech.10 (4), 496-508. · Zbl 0101.43002
[47] Monaghan, J.J.2007Gravity current interaction with interfaces. Annu. Rev. Fluid Mech.39, 245-261. · Zbl 1296.76013
[48] Monaghan, J.J., Cas, R.A.F., Kos, A.M. & Hallworth, M.1999Gravity currents descending a ramp in a stratified tank. J. Fluid Mech.379, 39-69. · Zbl 0938.76506
[49] Moore, C.D., Koseff, J.R. & Hult, E.L.2016Characteristics of bolus formation and propagation from breaking internal waves on shelf slopes. J. Fluid Mech.791, 260-283.
[50] Münch, B., Trtik, P., Marone, F. & Stampanoni, M.2009 Stripe and ring artifact removal with combined wavelet-Fourier filtering. EMPA Activities 17 (2009-2010 EMPA Activities), 34-35.
[51] Odier, P., Chen, J. & Ecke, R.E.2012Understanding and modeling turbulent fluxes and entrainment in a gravity current. Physica D241 (3), 260-268.
[52] Odier, P., Chen, J. & Ecke, R.E.2014Entrainment and mixing in a laboratory model of oceanic overflow. J. Fluid Mech.746 (3), 498-535.
[53] Ottolenghi, L., Adduce, C., Roman, F. & La Forgia, G.2020Large eddy simulations of solitons colliding with intrusions. Phys. Fluids32 (9), 096606.
[54] Ouillon, R., Meiburg, E., Ouellette, N.T. & Koseff, J.R.2019Interaction of a downslope gravity current with an internal wave. J. Fluid Mech.873, 889-913. · Zbl 1419.76133
[55] Panagopoulos, A., Haralambous, K.-J. & Loizidou, M.2019Desalination brine disposal methods and treatment technologies - a review. Sci. Total Environ.693, 133545.
[56] Peltier, W.R. & Caulfield, C.P.2003Mixing efficiency in statified shear flows. Annu. Rev. Fluid Mech.35 (1), 135-167. · Zbl 1041.76024
[57] Petersen, K.L., Heck, N., Reguero, B.G., Potts, D., Hovagimian, A. & Paytan, A.2019Biological and physical effects of brine discharge from the Carlsbad Desalination plant and implications for future desalination plant constructions. Water11 (2), 208.
[58] Phillips, O.M.1977The Dynamics of the Upper Ocean. Cambridge University Press. · Zbl 0368.76002
[59] Rimoldi, B., Alexander, J. & Morris, S.1996Experimental turbidity currents entering density-stratified water: analogues for turbidites in Mediterranean hypersaline basins. Sedimentology43 (3), 527-540.
[60] Samothrakis, P. & Cotel, A.J.2006aFinite volume gravity currents impinging on a stratified interface. Exp. Fluids41 (6), 991-1003.
[61] Samothrakis, P. & Cotel, A.J.2006bPropagation of a gravity current in a two-layer stratified environment. J. Geophys. Res.111 (C1), C01012.
[62] Shavit, U., Lowe, R.J. & Steinbuck, J.V.2007Intensity capping: a simple method to improve cross-correlation PIV results. Exp. Fluids42 (2), 225-240.
[63] Simpson, J.E.1997Gravity Currents: In the Environment and the Laboratory. Cambridge University Press.
[64] Sinnett, G., Feddersen, F., Lucas, A.J., Pawlak, G. & Terrill, E.2018Observations of nonlinear internal wave run-up to the surfzone. J. Phys. Oceanogr.48 (3), 531-554.
[65] Tanimoto, Y., Ouellette, N.T. & Koseff, J.R2020Interaction between an inclined gravity current and a pycnocline in a two-layer stratification. J. Fluid Mech.887, A8. · Zbl 1460.76158
[66] Tanimoto, Y., Ouellette, N.T. & Koseff, J.R.2021Secondary generation of breaking internal waves in confined basins by gravity currents. J. Fluid Mech.917, A49. · Zbl 07347173
[67] Tian, X. & Roberts, P.J.W.2003A 3D LIF system for turbulent buoyant jet flows. Exp. Fluids35 (6), 636-647.
[68] Troy, C.D. & Koseff, J.R.2005The generation and quantitative visualization of breaking internal waves. Exp. Fluids38 (5), 549-562.
[69] Wallace, R.B. & Sheff, B.B.1987Two-dimensional buoyant jets in two-layer ambient fluid. J. Hydraul. Engng113 (8), 992-1005.
[70] Walter, R.K., Woodson, C.B., Arthur, R.S., Fringer, O.B. & Monismith, S.G.2012Nearshore internal bores and turbulent mixing in southern Monterey Bay. J. Geophys. Res.117 (7), 1-13.
[71] Wells, M., Cenedese, C. & Caulfield, C.P.2010The relationship between flux coefficient and entrainment ratio in density currents. J. Phys. Oceanogr.40 (12), 2713-2727.
[72] Wells, M.G. & Dorrell, R.M.2021Turbulence processes within turbidity currents. Annu. Rev. Fluid Mech.53, 59-83. · Zbl 1459.76063
[73] Wells, M.G. & Wettlaufer, J.S.2007The long-term circulation driven by density currents in a two-layer stratified basin. J. Fluid Mech.572, 37-58. · Zbl 1106.76340
[74] Westerweel, J. & Scarano, F.2005Universal outlier detection for PIV data. Exp. Fluids39 (6), 1096-1100.
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