Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-17T14:51:53.971Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of a downslope gravity current with an internal wave

Published online by Cambridge University Press:  28 June 2019

Raphael Ouillon Open the ORCID record for Raphael Ouillon [Opens in a new window] ,
Eckart Meiburg Open the ORCID record for Eckart Meiburg [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]
Raphael Ouillon*
Affiliation:
Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Eckart Meiburg
Affiliation:
Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Nicholas T. Ouellette
Affiliation:
Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Jeffrey R. Koseff
Affiliation:
Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the interaction of a downslope gravity current with an internal wave propagating along a two-layer density jump. Direct numerical simulations confirm earlier experimental findings of a reduced gravity current mass flux, as well as the partial removal of the gravity current head from its body by large-amplitude waves (Hogg et al., Environ. Fluid Mech., vol. 18 (2), 2018, pp. 383–394). The current is observed to split into an intrusion of diluted fluid that propagates along the interface and a hyperpycnal current that continues to move downslope. The simulations provide detailed quantitative information on the energy budget components and the mixing dynamics of the current–wave interaction, which demonstrates the existence of two distinct parameter regimes. Small-amplitude waves affect the current in a largely transient fashion, so that the post-interaction properties of the current approach those in the absence of a wave. Large-amplitude waves, on the other hand, perform a sufficiently large amount of work on the gravity current fluid so as to modify its properties over the long term. The ‘decapitation’ of the current by large waves, along with the associated formation of an upslope current, enhance both viscous dissipation and irreversible mixing, thereby strongly reducing the available potential energy of the flow.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Stratified flows Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 889 - 913
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baines, P. G. 2001 Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.Google Scholar
Baines, P. G. 2008 Mixing in downslope flows in the ocean – plumes versus gravity currents. Atmos.-Ocean 46 (4), 405–419.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209–248.Google Scholar
Biegert, E., Vowinckel, B., Ouillon, R. & Meiburg, E. 2017 High-resolution simulations of turbidity currents. Prog. Earth Planet. Sci. 4 (1), 33.Google Scholar
Borden, Z. & Meiburg, E. 2013 Circulation based models for Boussinesq gravity currents. Phys. Fluids 25 (10), 101301.Google 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.Google Scholar
Cenedese, C. & Adduce, C. 2010 A new parameterization for entrainment in overflows. J. Phys. Oceanogr. 40 (8), 1835–1850.Google Scholar
Cortés, A., Fleenor, W. E., Wells, M. G., de Vicente, I. & Rueda, F. J. 2014 Pathways of river water to the surface layers of stratified reservoirs. Limnol. Oceanogr. 59 (1), 233–250.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423–448.Google Scholar
Fernández-Torquemada, Y., Gónzalez-Correa, J. M., Loya, A., Ferrero, L. M., Díaz-Valdés, M. & Sánchez-Lizaso, J. L. 2009 Dispersion of brine discharge from seawater reverse osmosis desalination plants. Desalin. Water Treat. 5 (1–3), 137–145.Google 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.Google 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.Google 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.Google Scholar
Hodges, B. R., Furnans, J. E. & Kulis, P. S. 2011 Thin-layer gravity current with implications for desalination brine disposal. J. Hydraul. Engng 137 (3), 356–371.Google Scholar
Hogg, C. A. R.2014 The flow of rivers into lakes: experiments and models. PhD thesis, University of Cambridge.Google 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.Google Scholar
Huppert, H. & Simpson, J. 1980 The slumping of gravity currents. J. Fluid Mech. 99 (4), 785–799.Google Scholar
Kang, S.2008 An improved immersed boundary method for computation of turbulent flows with heat transfer. PhD thesis, Stanford University, CA.Google Scholar
MacIntyre, S., Flynn, K. M., Jellison, R. & Romero, J. 1999 Boundary mixing and nutrient fluxes in Mono Lake, California. Limnol. Oceanogr. 44 (3), 512–529.Google Scholar
Marques, G. M., Wells, M. G., Padman, L. & Özgökmen, T. M. 2017 Flow splitting in numerical simulations of oceanic dense-water outflows. Ocean Model. 113, 66–84.Google Scholar
Maxworthy, T., Leilich, J., Simpson, J. E. & Meiburg, E. H. 2002 The propagation of a gravity current into a linearly stratified fluid. J. Fluid Mech. 453, 371–394.Google Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42 (1), 135–156.Google Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37 (1), 239–261.Google Scholar
Monaghan, J. J. 2007 Gravity current interaction with interfaces. Annu. Rev. Fluid Mech. 39 (1), 245–261.Google Scholar
Mortimer, C. H. 1952 Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere. Phil. Trans. R. Soc. Lond. B 236 (635), 355–398.Google Scholar
Nasr-Azadani, 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.Google Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.Google Scholar
Samothrakis, P. & Cotel, A. J. 2006 Propagation of a gravity current in a two-layer stratified environment. J. Geophys. Res. 111 (C1), C01012.Google Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.Google Scholar
Simpson, J. E. 1982 Gravity currents in the laboratory, atmosphere, and ocean. Annu. Rev. Fluid Mech. 14 (1), 213–234.Google Scholar
Snow, K. & Sutherland, B. R. 2014 Particle-laden flow down a slope in uniform stratification. J. Fluid Mech. 755, 251–273.Google Scholar
Sutherland, B. R. 2010 Internal Gravity Waves. Cambridge University Press.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.Google Scholar
Ungarish, M. 2009 An Introduction to Gravity Currents and Intrusions. Chapman and Hall/CRC.Google Scholar
Winters, K. B., Lombard, P. N., Riley, J. J. & D’Asaro, E. A. 1995 Available potential energy and mixing in density stratified fluids. J. Fluid Mech. 289, 115–128.Google Scholar