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Gravity currents in the cabbeling regime

Andrew P. Grace*, Marek Stastna, and Kevin G. Lamb

K. Andrea Scott

  • Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

  • Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

  • *andrew.grace@uwaterloo.ca
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Phys. Rev. Fluids 8, 014502 – Published 5 January, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.014502

Abstract

In this study, we present a series of simulations of gravity currents where ambient and intruding temperatures are on opposite sides of the temperature of maximum density. We use these simulations to describe how cabbeling (mixing of parcels of fluid that leads to a parcel of fluid that is denser) affects the evolution of gravity currents. We show that initially buoyant currents (called hypopycnal currents) undergo mixing in the body and tail region of the gravity current, which generates dense water from cabbeling. We investigate the maximum distance that the initial current progresses as a function of a parameter controlling the nonlinearity of the equation of state (referred to as Θ). We find that the maximum distance that the current progresses is a nonlinear function of Θ. For low Θ hypopycnal currents reverse direction after they begin flowing, and cabbeling occurs over a limited spatial extent. As Θ is increased, currents achieve a larger maximum distance of propagation, allowing the dense water formed by cabbeling to sink and form a secondary current along the bottom of the domain (called a hyperpycnal current). As we increase the parameter controlling the nonlinearity of the equation of state, the hyperpycnal current becomes much larger in scale. We discuss some general characteristics of the hyperpycnal current and highlight that once it forms, larger values of Θ lead to a larger spatial extent of the current but narrower distributions of density and temperature.

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synopsis

How Freshwater Mixes in a Winter Lake

Published 5 January, 2023

An influx of warmer water mixing with a colder ambient volume can create a dense parcel that drives bottom currents and determines the resulting circulation patterns.

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Article Text

References (41)

  1. S. M. Powers and S. E. Hampton, Winter limnology as a new frontier, Limnol. Oceanogr. Bull. 25, 103 (2016).
  2. G. Kirillin, M. Leppäranta, A. Terzhevik, N. Granin, J. Bernhardt, C. Engelhardt, T. Efremova, S. Golosov, N. Palshin, P. Sherstyankin, G. Zdorovennova, and R. Zdorovennov, Physics of seasonally ice-covered lakes: A review, Aquatic Sci. 74, 659 (2012).
  3. J. Jansen, S. MacIntyre, D. C. Barrett, Y.-P. Chin, A. Cortés, A. L. Forrest, A. R. Hrycik, R. Martin, B. C. McMeans, M. Rautio, and R. Schwefel, Winter limnology: How do hydrodynamics and biogeochemistry shape ecosystems under ice? J. Geophys. Res.: Biogeosci. 126, 1 (2021).
  4. B. Boehrer and M. Schultze, Stratification of lakes, Rev. Geophys. 46, RG2005 (2008).
  5. T. D. Foster, An analysis of the cabbeling instability in sea water, J. Phys. Oceanogr. 2, 294 (1972).
  6. T. D. Foster and E. C. Carmack, Tempearture and salinity structure in the Weddell Sea, J. Phys. Oceanogr. 6, 36 (1976).
  7. T. J. McDougall, Thermobaricity, cabbeling, and water-mass conversion, J. Geophys. Res. 92, 5448 (1987).
  8. S. Groeskamp, R. P. Abernathey, and A. Klocker, Water mass transformation by cabbeling and thermobaricity, Geophys. Res. Lett. 43, 10,835–10,845 (2016).
  9. C. J. Shakespeare and L. N. Thomas, A new mechanism for mode water formation involving cabbeling and frontogenetic strain at thermohaline fronts. Part II: Numerical simulations, J. Phys. Oceanogr. 47, 1755 (2017).
  10. J. E. Simpson, Gravity currents in the laboratory, atmosphere, and ocean. Annu. Rev. Fluid Mech. 14, 213 (1982).
  11. J. E. Simpson, Gravity Currents: In the Environment and the Laboratory, 2nd ed. (Cambridge University Press, Cambridge, 1999).
  12. M. G. Wells and R. M. Dorrell, Turbulence processes within turbidity currents, Annu. Rev. Fluid Mech. 53, 59 (2021).
  13. E. Meiburg and B. Kneller, Turbidity currents and their deposits, Annu. Rev. Fluid Mech. 42, 135 (2010).
  14. C. Härtel, F. Carlsson, and M. Thunblom, 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 (2000).
  15. C. Härtel, E. H. Meiburg, and F. Necker, 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 (2000).
  16. R. Ouillon, E. Meiburg, and B. R. Sutherland, Turbidity currents propagating down a slope into a stratified saline ambient fluid, Environ. Fluid Mech. 19, 1143 (2019).
  17. H. E. Huppert and J. E. Simpson, The slumping of gravity currents, J. Fluid Mech. 99, 785 (1980).
  18. P. Linden, Gravity currents - theory and laboratory experiments, Buoyancy-Driven Flows, edited by E. Chassignet, C. Cenedese, and J. Verron, Vol. 13 (Cambridge University Press, Cambridge, 2012), Chap. 1, p. 51.
  19. A. P. Grace, M. Stastna, K. G. Lamb, and K. A. Scott, Asymmetries in gravity currents attributed to the nonlinear equation of state, J. Fluid Mech. 915, A18 (2021).
  20. K. D. Stewart, T. W. N. Haine, A. McC. Hogg, and F. Roquet, On cabbeling and thermobaricity in the surface mixed layer, J. Phys. Oceanogr. 47, 1775 (2017).
  21. E. C. Carmack, Combined influence of inflow and lake temperatures of spring circulation in a riverine lake, J. Phys. Oceanogr. 9, 422 (1979).
  22. E. C. Carmack, B. J. Gray, H. Pharo, and R. J. Daley, Importance of lake-river interaction on seasonal patterns in the general circulation of Kamloops Lake, British Columbia, Limnol. Oceanogr. 24, 634 (1979).
  23. P. R. Holland and A. Kay, A review of the physics and ecological implications of the thermal bar circulation, Limnologica 33, 153 (2003).
  24. M. N. Shimaraev, N. G. Granin, and A. A. Zhdanov, Deep ventilation of Lake Baikal waters due to spring thermal bars, Limnol. Oceanogr. 38, 1068 (1993).
  25. M. Schmid, N. M. Budnev, N. G. Granin, M. Sturm, M. Schurter, and A. Wüest, Lake Baikal deepwater renewal mystery solved, Geophys. Res. Lett. 35, L09605 (2008).
  26. G. Kirillin, T. Shatwell, and P. Kasprzak, Consequences of thermal pollution from a nuclear plant on lake temperature and mixing regime, J. Hydrol. 496, 47 (2013).
  27. A. Gaudard, C. Weber, T. J. Alexander, S. Hunziker, and M. Schmid, Impacts of using lakes and rivers for extraction and disposal of heat, WIREs Water 5, 1 (2018).
  28. B. O. Tsydenov, A. Kay, and A. V. Starchenko, Numerical modeling of the spring thermal bar and pollutant transport in a large lake, Ocean Model. 104, 73 (2016).
  29. D. C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models, AIAA J. 26, 1299 (1988).
  30. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
  31. P. R. Holland, A. Kay, and V. Botte, A numerical study of the dynamics of the riverine thermal bar in a deep lake, Environ. Fluid Mech. 1, 311 (2001).
  32. C. J. Subich, K. G. Lamb, and M. Stastna, Simulation of the Navier-Stokes equations in three dimensions with a spectral collocation method, Int. J. Numer. Methods Fluids 73, 103 (2013).
  33. B. R. Sutherland, M. K. Gingras, C. Knudson, L. Steverango, and C. Surma, Particle-bearing currents in uniform density and two-layer fluids, Phys. Rev. Fluids 3, 023801 (2018).
  34. S. Davarpanah Jazi and M. G. Wells, Dynamics of settling-driven convection beneath a sediment-laden buoyant overflow: Implications for the length-scale of deposition in lakes and the coastal ocean, Sedimentology 67, 699 (2020).
  35. J. Olsthoorn, E. W. Tedford, and G. A. Lawrence, Diffused-interface Rayleigh-Taylor instability with a nonlinear equation of state, Phys. Rev. Fluids 4, 094501 (2019).
  36. A. P. Grace, M. Stastna, K. G. Lamb, and K. A. Scott, Numerical simulations of the three-dimensionalization of a shear flow in radiatively forced cold water below the density maximum, Phys. Rev. Fluids 7, 023501 (2022).
  37. M. I. Cantero, S. Balachandar, M. H. García, and D. Bock, Turbulent structures in planar gravity currents and their influence on the flow dynamics, J. Geophys. Res.: Oceans 113, C8 (2008).
  38. T. Maxworthy, The dynamics of sedimenting surface gravity currents, J. Fluid Mech. 392, 27 (1999).
  39. H. E. Huppert, J. S. Turner, S. N. Carey, R. S. J. Sparks, and M. A. Hallworth, A laboratory simulation of pyroclastic flows down slopes, J. Volcanol. Geotherm. Res. 30, 179 (1986).
  40. A. W. Woods and M. I. Bursik, A laboratory study of ash flows, J. Geophys. Res. 99, 4375 (1994).
  41. C. Gladstone, L. J. Ritchie, R. S. J. Sparks, and A. W. Woods, An experimental investigation of density-stratified inertial gravity currents, Sedimentology 51, 767 (2004).

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Information

Phys. Rev. Fluids 8, 014502– Published 5 January, 2023
  • Received 12 August 2022
  • Accepted 9 November 2022
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