Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Collision of inwardly propagating axisymmetric gravity currents

Albert Dai*

Yu-Lin Huang

  • Department of Water Resources and Environmental Engineering, Tamkang University, New Taipei City 251301, Taiwan

  • *Contact author: hdai@ntu.edu.tw

Phys. Rev. Fluids 11, 083801 – Published 12 August, 2026

DOI: https://doi.org/10.1103/sjg6-cwjl

Abstract

Collision of inwardly propagating axisymmetric gravity currents was investigated by means of three-dimensional high-resolution simulations. Our goal is to deepen our understanding of the flow structures, energy budgets, and the mean flow and turbulence characteristics in the axisymmetric collision in light of our understanding of the collision of two planar counterflowing gravity currents. The lifetime of axisymmetric collision is approximately 4H̃/ũN,max, where H̃ is the depth of heavy and ambient fluids and ũN,max is the maximum inward front speed before the collision, and the lifetime of axisymmetric collision can be divided into three phases. During Phase I, 0(t̃t̃c)ũN,max/H̃0.7, where t̃ is the time and t̃c is the time instance at which the “averaged” vertical acceleration of the density front from collision reaches its maximum value, a circular array of radially elongated vortices surrounding the center of the flow domain develop close to the bottom boundary and create strong turbulence and dissipation of turbulent kinetic energy. The radial vorticity is generated from the tilting of azimuthal vorticity due to the axisymmetric geometry and this mechanism for generation of vorticity is essentially different from the collision of two planar counterflowing gravity currents. During Phase II, 0.7(t̃t̃c)ũN,max/H̃1.26, the deflected updraught of collided heavy fluid expands radially outwards and there exists another circular array of radially elongated vortices close to the top boundary. Both baroclinic production of vorticity and diffusion of vorticity act to stabilize the flow from further intensifying radial vorticity close to the top boundary. During Phase III, 1.26(t̃t̃c)ũN,max/H̃4, the radially elongated vortices observed in Phase II break up into smaller structures while the collided heavy fluid slumps away from the center of the flow domain. In Phase I and Phase II, the primary source of turbulent kinetic energy is production of turbulent kinetic energy, while in Phase III, the primary source is due to turbulent buoyancy flux. Our space-time averaged eddy diffusivity data support the experimental data, numerical simulation data and the guide for parameterization of eddy diffusivity proposed for the collision of two planar counterflowing gravity currents of equal strengths in the literature.

Physics Subject Headings (PhySH)

Article Text

References (51)

  1. J. Simpson, Gravity Currents, 2nd ed. (Cambridge University Press, Cambridge, UK, 1997).
  2. M. E. Nicholls, R. A. Pielke, and W. R. Cotton, A two-dimensional numerical investigation of the interaction between sea breezes and deep convection over the Florida peninsula, Mon. Weather Rev. 119, 298 (1991).
  3. A. Lapworth, Collision of two sea-breeze fronts observed in Wales, Weather 60, 316 (2005).
  4. K. Wapler and T. P. Lane, A case of offshore convective initiation by interacting land breezes near Darwin, Australia, Meteorol. Atmos. Phys. 115, 123 (2012).
  5. S. T. Gille and S. G. Llewellyn Smith, When land breezes collide: Converging diurnal winds over small bodies of water, Q. J. R. Meteorol. Soc. 140, 2573 (2014).
  6. K. K. Droegemeier and R. B. Wilhelmson, Three-dimensional numerical modeling of convection produced by interacting thunderstorm outflows. Part II: Variations in vertical wind shear, J. Atmos. Sci. 42, 2404 (1985).
  7. J. M. Intrieri, A. J. Bedard, and R. Hardesty, Details of colliding thunderstorm outflows as observed by Doppler lidar, J. Atmos. Sci. 47, 1081 (1990).
  8. L. G. Orf, J. R. Anderson, and J. M. Straka, A three-dimensional numerical analysis of colliding microbust outflow dynamics, J. Atmos. Sci. 53, 2490 (1996).
  9. R. Clarke, R. Smith, and D. Reid, The morning glory of the Gulf of Carpentaria: An atmospheric undular bore, Mon. Weather Rev. 109, 1726 (1981).
  10. J. Shin, Colliding gravity currents, Ph.D. thesis, University of Cambridge, Cambridge, UK, 2001.
  11. K. van der Wiel, S. T. Gille, S. G. Llewellyn Smith, P. F. Linden, and C. Cenedese, Characteristics of colliding sea breeze gravity current fronts: A laboratory study, Q. J. R. Meteorol. Soc. 143, 1434 (2017).
  12. C. Cafaro and G. G. Rooney, Characteristics of colliding density currents: A numerical and theoretical study, Q. J. R. Meteorol. Soc. 144, 1761 (2018).
  13. Q. Zhong, F. Hussain, and H. J. S. Fernando, Quantification of turbulent mixing in colliding gravity currents, J. Fluid Mech. 851, 125 (2018).
  14. A. Dai, Y.-L. Huang, and C.-S. Wu, Energy balances for the collision of gravity currents of equal strengths, J. Fluid Mech. 959, A20 (2023).
  15. W. Thiery, E. L. Davin, H.-J. Panitz, M. Demuzere, S. Lhermitte, and N. van Lipzig, The impact of the African Great Lakes on the regional climate, J. Clim. 28, 4061 (2015).
  16. W. Thiery, E. L. Davin, S. I. Seneviratne, K. Bedka, S. Lhermitte, and N. van Lipzig, Hazardous thunderstorm intensification over Lake Victoria, Nat. Commun. 7, 12786 (2016).
  17. B. J. Woodhams, P. A. Barrett, J. H. Marsham, C. E. Birch, C. L. Bain, J. K. Fletcher, A. J. Hartley, S. Webster, and S. Mangeni, Aircraft observations and sub-km modelling of the lake-land breeze circulation over Lake Victoria, Q. J. R. Meteorol. Soc. 148, 557 (2022).
  18. J. Gratton and F. Minotti, Self-similar viscous gravity currents: Phase-plane formalism, J. Fluid Mech. 210, 155 (1990).
  19. J. A. Diez, R. Gratton, and J. Gratton, Self-similar solution of the second kind for a convergent viscous gravity current, Phys. Fluids 4, 1148 (1992).
  20. S. B. Angenent and D. G. Aronson, Intermediate asymptotics for convergent viscous gravity currents, Phys. Fluids 7, 223 (1995).
  21. M. Hallworth, H. E. Huppert, and M. Ungarish, On inwardly propagating high-Reynolds-number axisymmetric gravity currents, J. Fluid Mech. 494, 255 (2003).
  22. A. C. Slim and H. E. Huppert, Self-similar solutions of the axisymmetric shallow-water equations governing converging inviscid gravity currents, J. Fluid Mech. 506, 331 (2004).
  23. M. D. Patterson, J. E. Simpson, S. B. Dalziel, and G. J. F. van Heijst, Vortical motion in the head of an axisymmetric gravity current, Phys. Fluids 18, 046601 (2006).
  24. C. Härtel, E. 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).
  25. F. Necker, C. Härtel, L. Kleiser, and E. Meiburg, Mixing and dissipation in particle-driven gravity currents, J. Fluid Mech. 545, 339 (2005).
  26. T. Bonometti and S. Balachandar, Effect of Schmidt number on the structure and propagation of density currents, Theor. Comput. Fluid Dyn. 22, 341 (2008).
  27. M. Cantero, S. Balachandar, and M. Garcia, High-resolution simulations of cylindrical density currents, J. Fluid Mech. 590, 437 (2007).
  28. M. Cantero, J. Lee, S. Balachandar, and M. Garcia, On the front velocity of gravity currents, J. Fluid Mech. 586, 1 (2007).
  29. A. Dai and C.-S. Wu, High-resolution simulations of cylindrical gravity currents in a rotating system, J. Fluid Mech. 806, 71 (2016).
  30. A. Dai and Y.-L. Huang, On the merging and splitting processes in the lobe-and-cleft structure at a gravity current head, J. Fluid Mech. 930, A6 (2022).
  31. A. Dai and Y.-L. Huang, The flow within the head of a gravity current, J. Fluid Mech. 997, A42 (2024).
  32. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, 1988).
  33. J. H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys. 35, 48 (1980).
  34. D. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics (Springer, Berlin, 1999).
  35. T. Cortese and S. Balachandar, High performance spectral simulation of turbulent flows in massively parallel machines with distributed memory, Int. J. Supercomput. Appl. 9, 187 (1995).
  36. C. Härtel, L. K. M. Michaud, and C. Stein, A direct numerical simulation approach to the study of intrusion fronts, J. Eng. Math. 32, 103 (1997).
  37. M. Cantero, S. Balachandar, M. Garcia, and J. Ferry, Direct numerical simulations of planar and cylindrical density currents, J. Appl. Mech. 73, 923 (2006).
  38. V. K. Birman, J. E. Martin, and E. Meiburg, The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations, J. Fluid Mech. 537, 125 (2005).
  39. P. Chakraborty, S. Balachandar, and R. Adrian, On the relationships between local vortex identification schemes, J. Fluid Mech. 535, 189 (2005).
  40. R. J. Adrian, Hairpin vortex organization in wall turbulence, Phys. Fluids 19, 041301 (2007).
  41. A. Dai and Y.-L. Huang, High-resolution simulations of non-Boussinesq downslope gravity currents in the acceleration phase, Phys. Fluids 28, 026602 (2016).
  42. K. B. Winters, P. N. Lombard, J. J. Riley, and E. A. D'Asaro, Available potential energy and mixing in density-stratified fluids, J. Fluid Mech. 289, 115 (1995).
  43. M. Ungarish and H. E. Huppert, Energy balances for axisymmetric gravity currents in homogeneous and linearly stratified ambients, J. Fluid Mech. 616, 303 (2008).
  44. R. Breidenthal, Structure in turbulent mixing layers and wakes using a chemical reaction, J. Fluid Mech. 109, 1 (1981).
  45. M. Princevac, H. J. S. Fernando, and C. D. Whiteman, Turbulent entrainment into natural gravity-driven flows, J. Fluid Mech. 533, 259 (2005).
  46. J.-Y. Grandpeix and J.-P. Lafore, A density current parameterization coupled with Emanuel's convection scheme. Part I: The models, J. Atmos. Sci. 67, 881 (2010).
  47. S. R. Freitas, G. A. Grell, A. D. Chovert, M. A. F. Silva Dias, and E. deLima Nascimento, A parameterization for cloud organization and propagation by evaporation-driven cold pool edges, J. Adv. Model Earth Syst. 16, e2023MS003982 (2024).
  48. S. U. Okon, Q. Zhong, and Z. He, Experimental study on the vertical motion of colliding gravity currents, Phys. Fluids 33, 016601 (2021).
  49. C.-S. Wu, Head-on collision of gravity currents of unequal strengths: Large eddy simulations and laboratory experiments, Phys. Fluids 36, 096610 (2024).
  50. A. Kokkinos and P. Prinos, Colliding gravity currents in a stratified environment, Phys. Fluids 37, 086637 (2025).
  51. G. G. Rooney, Negatively buoyant vortices in the Boussinesq-Euler equations, Phys. Rev. Fluids 8, 123802 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation