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Time evolution equation for advective heat transport as a constraint for optimal bounds in Rayleigh-Bénard convection

A. Tilgner

  • Institute of Geophysics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

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Phys. Rev. Fluids 4, 014601 – Published 14 January, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.014601

Abstract

Upper bounds on the heat transport and other quantities of interest in Rayleigh-Bénard convection are derived in previous work from constraints resulting from the equations of time evolution for kinetic energy, the root mean square of temperature, and the temperature averaged over horizontal planes. Here we investigate the effect of a constraint derived from the time evolution equation for the advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.

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References (18)

  1. L. Howard, Heat transport by turbulent convection, J. Fluid Mech. 17, 405 (1963).
  2. F. Busse, On Howard's upper bound for heat transport by turbulent convection, J. Fluid Mech. 37, 457 (1969).
  3. C. R. Doering and P. Constantin, Variational bounds on energy dissipation in incompressible flows: III. Convection, Phys. Rev. E 53, 5957 (1996).
  4. C. Plasting and G. Ierley, Infinite-Prandtl-number convection. Part 1. Conservative bounds, J. Fluid Mech. 542, 343 (2005).
  5. C. Seis, Scaling bounds on dissipation in turbulent flows, J. Fluid Mech. 777, 591 (2015).
  6. I. Tobasco, D. Goluskin, and C. Doering, Optimal bounds and extremal trajectories for time averages in dynamical systems, Phys. Lett. A 382, 382 (2018).
  7. N. K. Vitanov and F. H. Busse, Bounds on the convective heat transport in a rotating layer, Phys. Rev. E 63, 016303 (2000).
  8. A. Tilgner, Bounds on poloidal kinetic energy in plane layer convection, Phys. Rev. Fluids 2, 123502 (2017).
  9. D. Goluskin, Bounding averages rigorously using semidefinite programming: Mean moments of the Lorenz system, J. Nonlinear Sci. 28, 621 (2018).
  10. S. Chernyshenko, P. Goulart, D. Huang, and Papachristodoulou, Polynomial sum of squares in fluid dynamics: A review with a look ahead, Philos. Trans. R. Soc. A 372, 20130350 (2014).
  11. G. Fantuzzi, A. Pershin, and A. Wynn, Bounds on heat transfer for Bénard-Marangoni convection at infinite Prandtl number, J. Fluid Mech. 837, 562 (2018).
  12. N. Balmforth, S. Ghadge, A. Kettapun, and S. Mandre, Bounds on double-diffusive convection, J. Fluid Mech. 569, 29 (2006).
  13. C. Doering and C. Foias, Energy dissipation in body-forced turbulence, J. Fluid Mech. 467, 289 (2002).
  14. S. Childress, R. Kerswell, and A. Gilbert, Bounds on dissipation for Navier-Stokes flow with Kolmogorov forcing, Physica D 158, 105 (2001).
  15. B. Rollin, Y. Dubief, and C. Doering, Variations on Kolmogorov flow: Turbulent energy dissipation and mean flow profiles, J. Fluid Mech. 670, 204 (2011).
  16. A. Tilgner, Scaling laws and bounds for the turbulent G. O. Roberts dynamo, Phys. Rev. Fluids 2, 024606 (2017).
  17. S. Chernyshenko, Relationship between the methods of bounding time averages, arXiv:1704.02475.
  18. J. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

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Phys. Rev. Fluids 4, 014601– Published 14 January, 2019
  • Received 12 October 2018
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