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On the interaction between oncoming internal waves and a dense gravity current in a two-layer stratification

Published online by Cambridge University Press:  06 December 2021

Yukinobu Tanimoto Open the ORCID record for Yukinobu Tanimoto [Opens in a new window] ,
Nicholas T. Ouellette Open the ORCID record for Nicholas T. Ouellette [Opens in a new window]  and
Jeffrey R. Koseff Open the ORCID record for Jeffrey R. Koseff [Opens in a new window]
Yukinobu Tanimoto*
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Nicholas T. Ouellette
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Jeffrey R. Koseff
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: ytanimoto@stanford.edu
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alahyari, A. & Longmire, E.K. 1994 Particle image velocimetry in a variable density flow: application to a dynamically evolving microburst. Exp. Fluids 17 (6), 434–440.CrossRefGoogle Scholar
Baines, P.G. 2005 Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech. 538, 245–267.CrossRefGoogle Scholar
Baines, P.G. 2008 Mixing in downslope flows in the ocean - plumes versus gravity currents. Atmosphere 46 (4), 405–419.Google Scholar
Barrett, T.K. & Van Atta, C.W. 1991 Experiments on the inhibition of mixing in stably stratified decaying turbulence using laser Doppler anemometry and laser–induced fluorescence. Phys. Fluids A 3 (5), 1321–1332.CrossRefGoogle Scholar
Benjamin, T.B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209–248.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
Britter, R.E. & Simpson, J.E. 1978 Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88 (2), 223–240.CrossRefGoogle Scholar
Britter, R.E. & Simpson, J.E. 1981 A note on the structure of the head of an intrusive gravity current. J. Fluid Mech. 112, 459–466.CrossRefGoogle Scholar
Cenedese, C. & Adduce, C. 2010 A new parameterization for entrainment in overflows. J. Phys. Oceanogr. 40 (8), 1835–1850.CrossRefGoogle Scholar
Charonko, J.J. & Vlachos, P.P. 2013 Estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio. Meas. Sci. Technol. 24 (6).CrossRefGoogle Scholar
Cheong, H.B., Kuenen, J.J.P. & Linden, P.F. 2006 The front speed of intrusive gravity currents. J. Fluid Mech. 552, 1–11.CrossRefGoogle Scholar
Clément, S.A., Guillemain, A., McCleney, A.B. & Bardet, P.M. 2018 Options for refractive index and viscosity matching to study variable density flows. Exp. Fluids 59 (2), 1–15.CrossRefGoogle Scholar
Cortés, A., Rueda, F.J. & Wells, M.G. 2014 Experimental observations of the splitting of a gravity current at a density step in a stratified water body. J. Geophys. Res. 119 (2), 1038–1053.CrossRefGoogle Scholar
Cortés, A., Wells, M.G., Fringer, O.B., Arthur, R.S. & Rueda, F.J. 2015 Numerical investigation of split flows by gravity currents into two-layered stratified water bodies. J. Geophys. Res. C 120 (7), 5254–5271.CrossRefGoogle Scholar
Cotte, G. & Vennemann, T.W. 2020 Mixing of Rhône river water in lake Geneva: seasonal tracing using stable isotope composition of water. J. Great Lakes Res. 46 (4), 839–849.CrossRefGoogle Scholar
Cowen, E.A. & Monismith, S.G. 1997 A hybrid digital particle tracking velocimetry technique. Exp. Fluids 22 (3), 199–211.CrossRefGoogle Scholar
Crimaldi, J.P. 2008 Planar laser induced fluorescence in aqueous flows. Exp. Fluids 44 (6), 851–863.CrossRefGoogle Scholar
Crimaldi, J.P. & Koseff, J.R. 2001 High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume. Exp. Fluids 31 (1), 90–102.CrossRefGoogle Scholar
Daviero, G.J., Roberts, P.J.W. & Maile, K. 2001 Refractive index matching in large-scale stratified experiments. Exp. Fluids 31 (2), 119–126.CrossRefGoogle Scholar
Dossmann, Y., Bourget, B., Brouzet, C., Dauxois, T., Joubaud, S. & Odier, P. 2016 Mixing by internal waves quantified using combined PIV/PLIF technique. Exp. Fluids 57 (8), 132.CrossRefGoogle Scholar
Ellison, T.H. & Turner, J.S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423–448.CrossRefGoogle Scholar
Ferrier, A.J., Funk, D.R. & Roberts, P.J.W. 1993 Application of optical techniques to the study of plumes in stratified fluids. Dyn. Atmos. Oceans 20 (1), 155–183.CrossRefGoogle Scholar
Fischer, H.B. & Smith, R.D. 1983 Observations of transport to surface waters from a plunging inflow to Lake Mead. Limnol. Oceanogr. 28 (2), 258–272.CrossRefGoogle Scholar
Flynn, M.R. & Sutherland, B.R. 2004 Intrusive gravity currents and internal gravity wave generation in stratified fluid. J. Fluid Mech. 514, 355–383.CrossRefGoogle Scholar
Fringer, O.B. & Street, R.L. 2003 The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494 (494), 319–353.CrossRefGoogle Scholar
Hallworth, M.A., Huppert, H.E., Phillips, J.C. & Sparks, R.S.J. 1996 Entrainment into two-dimensional and axisymmetric turbulent gravity currents. J. Fluid Mech. 308, 289–311.CrossRefGoogle Scholar
Hass, M. & Davisson, J.W. 1977 Absorption coefficient of pure water at 488 and 541.5 nm by adiabatic laser calorimetry*. J. Opt. Soc. Am. 67 (5), 622–624.CrossRefGoogle Scholar
Hogg, C.A.R., Dalziel, S.B., Huppert, H.E. & Imberger, J. 2017 Inclined gravity currents filling basins: the impact of peeling detrainment on transport and vertical structure. J. Fluid Mech. 820, 400–423.CrossRefGoogle Scholar
Hogg, C.A.R., Egan, G.C., Ouellette, N.T. & Koseff, J.R. 2018 Shoaling internal waves may reduce gravity current transport. Environ. Fluid Mech. 18 (2), 383–394.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
Howard, L.N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10 (04), 509–512.CrossRefGoogle Scholar
Hult, E.L., Troy, C.D. & Koseff, J.R. 2009 The breaking of interfacial waves at a submerged bathymetric ridge. J. Fluid Mech. 637, 45–71.CrossRefGoogle Scholar
Johnson, B.A. & Cowen, E.A. 2018 Turbulent boundary layers absent mean shear. J. Fluid Mech. 835, 217–251.CrossRefGoogle Scholar
Jones, E., Qadir, M., van Vliet, M.T.H., Smakhtin, V. & Kang, S. 2019 The state of desalination and brine production: a global outlook. Sci. Total Environ. 657, 1343–1356.CrossRefGoogle ScholarPubMed
Koochesfahani, M.M. & Dimotakis, P.E. 1985 Laser-induced fluorescence measurements of mixed fluid concentrationin a liquid plane shear layer. AIAA J. 23 (11), 1700–1707.CrossRefGoogle Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2015 The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech. 765, 303–324.CrossRefGoogle Scholar
Larsen, L.G. & Crimaldi, J.P. 2006 The effect of photobleaching on PLIF. Exp. Fluids 41 (5), 803–812.CrossRefGoogle Scholar
Liao, Q. & Cowen, E.A. 2005 An efficient anti-aliasing spectral continuous window shifting technique for PIV. Exp. Fluids 38 (2), 197–208.CrossRefGoogle Scholar
Linden, P.F. & Simpson, J.E. 1986 Gravity-driven flows in a turbulent fluid. J. Fluid Mech. 172 (1980), 481–497.CrossRefGoogle Scholar
Lowe, R.J., Linden, P.F. & Rottman, J.W. 2002 A laboratory study of the velocity structure in an intrusive gravity current. J. Fluid Mech. 456, 33–48.CrossRefGoogle Scholar
Maroto, J.A., de Dios, J. & de las Nieves, F.J. 2002 Use of a Mariotte bottle for the experimental study of the transition from laminar to turbulent flow. Am. J. Phys. 70 (7), 698–701.CrossRefGoogle Scholar
Martin, A., Negretti, M.E., Ungarish, M. & Zemach, T. 2020 Propagation of a continuously supplied gravity current head down bottom slopes. Phys. Rev. Fluids 5 (5), 54801.CrossRefGoogle Scholar
Maurer, B.D. & Linden, P.F. 2014 Intrusion-generated waves in a linearly stratified fluid. J. Fluid Mech. 752, 282–295.CrossRefGoogle Scholar
McDougall, T.J. 1979 On the elimination of refractive-index variations in turbulent density-stratified liquid flows. J. Fluid Mech. 93 (1), 83–96.CrossRefGoogle Scholar
Mellor, G.L. & Yamada, T. 1982 Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. 20 (4), 851–875.CrossRefGoogle Scholar
Miles, J.W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10 (4), 496–508.CrossRefGoogle Scholar
Monaghan, J.J. 2007 Gravity current interaction with interfaces. Annu. Rev. Fluid Mech. 39, 245–261.CrossRefGoogle Scholar
Monaghan, J.J., Cas, R.A.F., Kos, A.M. & Hallworth, M. 1999 Gravity currents descending a ramp in a stratified tank. J. Fluid Mech. 379, 39–69.CrossRefGoogle Scholar
Moore, C.D., Koseff, J.R. & Hult, E.L. 2016 Characteristics of bolus formation and propagation from breaking internal waves on shelf slopes. J. Fluid Mech. 791, 260–283.CrossRefGoogle Scholar
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.Google Scholar
Odier, P., Chen, J. & Ecke, R.E. 2012 Understanding and modeling turbulent fluxes and entrainment in a gravity current. Physica D 241 (3), 260–268.CrossRefGoogle Scholar
Odier, P., Chen, J. & Ecke, R.E. 2014 Entrainment and mixing in a laboratory model of oceanic overflow. J. Fluid Mech. 746 (3), 498–535.CrossRefGoogle Scholar
Ottolenghi, L., Adduce, C., Roman, F. & La Forgia, G. 2020 Large eddy simulations of solitons colliding with intrusions. Phys. Fluids 32 (9), 096606.CrossRefGoogle Scholar
Ouillon, R., Meiburg, E., Ouellette, N.T. & Koseff, J.R. 2019 Interaction of a downslope gravity current with an internal wave. J. Fluid Mech. 873, 889–913.CrossRefGoogle Scholar
Panagopoulos, A., Haralambous, K.-J. & Loizidou, M. 2019 Desalination brine disposal methods and treatment technologies - a review. Sci. Total Environ. 693, 133545.CrossRefGoogle ScholarPubMed
Peltier, W.R. & Caulfield, C.P. 2003 Mixing efficiency in statified shear flows. Annu. Rev. Fluid Mech. 35 (1), 135–167.CrossRefGoogle Scholar
Petersen, K.L., Heck, N., Reguero, B.G., Potts, D., Hovagimian, A. & Paytan, A. 2019 Biological and physical effects of brine discharge from the Carlsbad Desalination plant and implications for future desalination plant constructions. Water 11 (2), 208.CrossRefGoogle Scholar
Phillips, O.M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Rimoldi, B., Alexander, J. & Morris, S. 1996 Experimental turbidity currents entering density-stratified water: analogues for turbidites in Mediterranean hypersaline basins. Sedimentology 43 (3), 527–540.CrossRefGoogle Scholar
Samothrakis, P. & Cotel, A.J. 2006 a Finite volume gravity currents impinging on a stratified interface. Exp. Fluids 41 (6), 991–1003.CrossRefGoogle Scholar
Samothrakis, P. & Cotel, A.J. 2006 b Propagation of a gravity current in a two-layer stratified environment. J. Geophys. Res. 111 (C1), C01012.CrossRefGoogle Scholar
Shavit, U., Lowe, R.J. & Steinbuck, J.V. 2007 Intensity capping: a simple method to improve cross-correlation PIV results. Exp. Fluids 42 (2), 225–240.CrossRefGoogle Scholar
Simpson, J.E. 1997 Gravity Currents: In the Environment and the Laboratory. Cambridge University Press.Google Scholar
Sinnett, G., Feddersen, F., Lucas, A.J., Pawlak, G. & Terrill, E. 2018 Observations of nonlinear internal wave run-up to the surfzone. J. Phys. Oceanogr. 48 (3), 531–554.CrossRefGoogle Scholar
Tanimoto, Y., Ouellette, N.T. & Koseff, J.R 2020 Interaction between an inclined gravity current and a pycnocline in a two-layer stratification. J. Fluid Mech. 887, A8.CrossRefGoogle Scholar
Tanimoto, Y., Ouellette, N.T. & Koseff, J.R. 2021 Secondary generation of breaking internal waves in confined basins by gravity currents. J. Fluid Mech. 917, A49.CrossRefGoogle Scholar
Tian, X. & Roberts, P.J.W. 2003 A 3D LIF system for turbulent buoyant jet flows. Exp. Fluids 35 (6), 636–647.CrossRefGoogle Scholar
Troy, C.D. & Koseff, J.R. 2005 The generation and quantitative visualization of breaking internal waves. Exp. Fluids 38 (5), 549–562.CrossRefGoogle Scholar
Wallace, R.B. & Sheff, B.B. 1987 Two-dimensional buoyant jets in two-layer ambient fluid. J. Hydraul. Engng 113 (8), 992–1005.CrossRefGoogle Scholar
Walter, R.K., Woodson, C.B., Arthur, R.S., Fringer, O.B. & Monismith, S.G. 2012 Nearshore internal bores and turbulent mixing in southern Monterey Bay. J. Geophys. Res. 117 (7), 1–13.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
Wells, M.G. & Wettlaufer, J.S. 2007 The long-term circulation driven by density currents in a two-layer stratified basin. J. Fluid Mech. 572, 37–58.CrossRefGoogle Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39 (6), 1096–1100.CrossRefGoogle Scholar