Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 63 tok/s
Gemini 2.5 Pro 50 tok/s Pro
GPT-5 Medium 19 tok/s Pro
GPT-5 High 29 tok/s Pro
GPT-4o 101 tok/s Pro
Kimi K2 212 tok/s Pro
GPT OSS 120B 438 tok/s Pro
Claude Sonnet 4.5 36 tok/s Pro
2000 character limit reached

One dimensional models for supercritical and subcritical transitions in rotating convection (2403.19953v1)

Published 29 Mar 2024 in physics.flu-dyn, nlin.AO, and nlin.PS

Abstract: Numerous study on natural and man made systems including rotating convection report the phenomena of supercritical and subcritical transitions from one state to another with the variation of relevant control parameters. However, the complexity of the rotating convection system even under the idealized Rayleigh-B\'enard geometry, hindered the simplest possible description of these transitions to convection. Here we present an one dimensional description of the stationary subcritical and supercritical transitions to rotating Rayleigh-B\'enard convection both for rigid and free-slip boundary conditions. The analysis of the one dimensional models and performance of three dimensional direct numerical simulations of the system show qualitatively similar results in a wide region of the parameter space. A brief discussion on time dependent convection of overstable origin is also presented.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (67)
  1. The role of the earth’s mantle in controlling the frequency of geomagnetic reversals. Nature, 401(6756):885, 1999.
  2. Oscillatory and steady convection in a magnetic field. J. Fluid Mech., 113:153–186, 1981.
  3. P. A. Davidson. Magnetohydrodynamics in materials processing. Annu. Rev. Fluid Mech., 31(1):273–300, 1999.
  4. S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. Cambridge University Press, Cambridge, 1961.
  5. M. K. Verma. Physics of Buoyant Flows: From Instabilities to Turbulence. World Scientific, 2018.
  6. Liquid to vapor phase transition in excited nuclei. Phys. Rev. Lett., 88(4):042701, 2002.
  7. Heat transfer and large scale dynamics in turbulent rayleigh-bénard convection. Rev. Mod. Phys., 81(2):503, 2009.
  8. Mechanism for direct graphite-to-diamond phase transition. Sci. Rep., 4(1):5930, 2014.
  9. Band structure evolution during the ultrafast ferromagnetic-paramagnetic phase transition in cobalt. Sci. Advances, 3(3):e1602094, 2017.
  10. J. Marshall and F. Schott. Open-ocean convection: Observations, theory, and models. Rev. Geophys., 37(1):1–64, 1999.
  11. Present understanding of mhd and heat transfer phenomena for liquid metal blankets. Fusion Eng. Des., 27:553–569, 1995.
  12. Experiments on rayleigh–bénard convection, magnetoconvection and rotating magnetoconvection in liquid gallium. J. Fluid Mech., 430:283–307, 2001.
  13. Subcritical thermal convection of liquid metals in a rapidly rotating sphere. Phys. Rev. Lett., 119(9):094501, 2017.
  14. D. T. J. Hurle. Hydrodynamics, convection and crystal growth. J. of Cryst. Growth, 13:39–43, 1972.
  15. First-order phase transitions in superconductors and smectic-a liquid crystals. Phys. Rev. Lett., 32(6):292, 1974.
  16. Recent developments in rayleigh-bénard convection. Annu. Rev. Fluid Mech., 32(1):709–778, 2000.
  17. On the onset of low-prandtl-number convection in rotating spherical shells: non-slip boundary conditions. J. Fluid Mech., 601:317–337, 2008.
  18. Phenomenology of buoyancy-driven turbulence: recent results. N. J. Phys., 19(2):025012, 2017.
  19. On heat transport and energy partition in thermal convection with mixed boundary conditions. Phys. Fluids, 31(6):066601, 2019.
  20. Subcritical dynamos in rapidly rotating planar convection. Phys. Rev. Fluids, 5:113702, Nov 2020.
  21. Transitions near the onset of low prandtl-number rotating convection in presence of horizontal magnetic field. Phys. Fluids, 32(2):024110, 2020.
  22. Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom. Phys. Fluids, 34(10):104117, 2022.
  23. Effect of horizontal magnetic field on küppers–lortz instability. Phys. Fluids, 35(7), 2023.
  24. Instabilities of convection rolls in a high prandtl number fluid. J. Fluid Mech., 47(2):305–320, 1971.
  25. Convection at very low prandtl numbers. Phys. Fluids A, 2(3):334–339, 1990.
  26. H. K. Pharasi and K. Kumar. Oscillatory instability and fluid patterns in low-prandtl-number rayleigh-bénard convection with uniform rotation. Phys. Fluids, 25(10):104105, 2013.
  27. Low-prandtl-number rayleigh-bénard convection with stress-free boundaries. Eur. Phys. J. B, 87(11):278, 2014.
  28. Pattern formation outside of equilibrium. Rev. Mod. Phys., 65(3):851, 1993.
  29. R. Hoyle and R. B. Hoyle. Pattern formation: an introduction to methods. Cambridge University Press, 2006.
  30. Pattern dynamics near inverse homoclinic bifurcation in fluids. Phys. Rev. E, 87(2):023001, 2013.
  31. Transitions to chaos in two-dimensional double-diffusive convection. J. Fluid Mech., 166:409–448, 1986.
  32. Bifurcations and chaos in large-prandtl number rayleigh–bénard convection. Int. J. Non-Linear Mech., 46(5):772–781, 2011.
  33. Y. Nandukumar and P. Pal. Oscillatory instability and routes to chaos in rayleigh-bénard convection: Effect of external magnetic field. Europhys. Lett., 112(2):24003, 2015.
  34. Rumford C. Of the propagation of heat in fluids. Complete Works, 1:239, 1870.
  35. O. Thual. Zero-prandtl-number convection. J. Fluid Mech., 240:229–258, 1992.
  36. P. Manneville. Instabilities, chaos and turbulence, volume 1. World Scientific, 2010.
  37. R. E. Ecke and O. Shishkina. Turbulent rotating rayleigh-bénard convection. Annu. Rev. Fluid Mech., 55:603–638, 2023.
  38. S. H. Strogatz. Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering. Westview Press, 2001.
  39. M. Evonuk and G. A. Glatzmaier. The effects of rotation rate on deep convection in giant planets with small solid cores. Planet. Space Sci., 55(4):407–412, 2007.
  40. Phylotranscriptomic analysis of the origin and early diversification of land plants. PNAS, 111(45):E4859–E4868, 2014.
  41. M. S. Miesch. The coupling of solar convection and rotation (invited review). In Helioseismic Diagnostics of Solar Convection and Activity, pages 59–89. Springer, 2000.
  42. H. T. Rossby. A study of bénard convection with and without rotation. J. Fluid Mech., 36(2):309–335, 1969.
  43. Y. Nakagawa. An experiment on the inhibition of thermal convection by a magnetic field. Nature, 175(4453):417, 1955.
  44. D. Fultz and Y. Nakagawa. Experiments on over-stable thermal convection in mercury. Proc. R. Soc. London, Ser. A, 231(1185):211–225, 1955.
  45. G. Veronis. Cellular convection with finite amplitude in a rotating fluid. J. Fluid Mech., 5(3):401–435, 1959.
  46. I. A. Eltayeb. Hydromagnetic convection in a rapidly rotating fluid layer. Proc. R. Soc. Lond. A, 326(1565):229–254, 1972.
  47. T. Clune and E. Knobloch. Pattern selection in rotating convection with experimental boundary conditions. Phys. Rev. E, 47(4):2536, 1993.
  48. K. Julien and E. Knobloch. Fully nonlinear three-dimensional convection in a rapidly rotating layer. Phys. Fluids, 11(6):1469–1483, 1999.
  49. Rapidly rotating turbulent rayleigh-bénard convection. J. Fluid Mech., 322:243–273, 1996.
  50. Heat flux intensification by vortical flow localization in rotating convection. Phys. Rev. E, 74(5):056306, 2006.
  51. Model of convective taylor columns in rotating rayleigh-bénard convection. Phys. Rev. Lett., 104(22):224501, 2010.
  52. Homoclinic bifurcations in low-prandtl-number rayleigh-bénard convection with uniform rotation. Europhys. Lett., 103(6):64003, 2013.
  53. P. Maity and K. Kumar. Zero-prandtl-number convection with slow rotation. Phys. Fluids, 26(10):104103, 2014.
  54. S. Sakai. The horizontal scale of rotating convection in the geostrophic regime. J. Fluid Mech., 333:85–95, 1997.
  55. P. Vorobieff and R. E. Ecke. Turbulent rotating convection: an experimental study. J. Fluid Mech., 458:191–218, 2002.
  56. Rayleigh-bénard convection with rotation at small prandtl numbers. Phys. Rev. E, 65(5):056309, 2002.
  57. Rotation suppresses giant-scale solar convection. PNAS, 118(31), 2021.
  58. G. Veronis. Motions at subcritical values of the rayleigh number in a rotating fluid. J. Fluid Mech., 24(3):545–554, 1966.
  59. Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis. J. Fluid Mech., 94(4):609–627, 1979.
  60. A. Oberbeck. Über die wärmeleitung der flüssigkeiten bei berücksichtigung der strömungen infolge von temperaturdifferenzen. Ann. Phys. Chem., 243(6):271–292, 1879.
  61. J. Boussinesq. Théorie analytique de la chaleur, volume 2. Gauthier-Villars, 1903.
  62. Application of spectral collocation techniques to the stability of swirling flows. J. of Comput. Phys., 81(1):206–229, 1989.
  63. Imperfect homoclinic bifurcations. Phys. Rev. E, 64(3):036208, 2001.
  64. Supercriticality to subcriticality in dynamo transitions. Phys. Plasmas, 20(7), 2013.
  65. B. Ermentrout. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. SIAM, 2002.
  66. nek5000 web page, 2008.
  67. Benchmarking and scaling studies of pseudospectral code tarang for turbulence simulations. Pramana, 81(4):617–629, 2013.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 1 post and received 1 like.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up to View