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Heat transport by coherent Rayleigh-Bénard convection
5.M. A. Dominguez-Lerma, G. Ahlers, and D. S. Cannell, “Marginal stability curve and linear growth rate for rotating Couette–Taylor flow and Rayleigh-Bénard convection,” Phys. Fluids (1958-1988) 27, 856–860 (1984).
7. Estimated from linear stability about the conduction state but with free “outflow” boundary conditions at the top edge of the boundary layer, that is, .
11.R. J. Stevens, E. P. van der Poel, S. Grossmann, and D. Lohse, “The unifying theory of scaling in thermal convection: The updated prefactors,” J. Fluid Mech. 730, 295–308 (2013).
13.X. Chavanne, F. Chilla, B. Castaing, B. Hebral, B. Chabaud, and J. Chaussy, “Observation of the ultimate regime in Rayleigh-Bénard convection,” Phys. Rev. Lett. 79, 3648 (1997).
14.X. Chavanne, F. Chilla, B. Chabaud, B. Castaing, and B. Hebral, “Turbulent Rayleigh-Bénard convection in gaseous and liquid He,” Phys. Fluids 13, 1300–1320 (2001).
17.J. Niemela, L. Skrbek, K. Sreenivasan, and R. Donnelly, “Turbulent convection at very high Rayleigh numbers,” Nature 404, 837–840 (2000).
23.S. Plasting and R. Kerswell, “Improved upper bound on the energy dissipation rate in plane Couette flow: The full solution to Busse’s problem and the Constantin–Doering–Hopf problem with one-dimensional background field,” J. Fluid Mech. 477, 363–379 (2003).
26.P. R. Spalart, R. D. Moser, and M. M. Rogers, “Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions,” J. Comput. Phys. 96, 297–324 (1991).
27.M. Charalambides and F. Waleffe, “Gegenbauer tau methods with and without spurious eigenvalues,” SIAM J. Numer. Anal. 47, 48–68 (2008).
29.B. Wen, G. Chini, R. R. Kerswell, and C. Doering, private communication (2015).
30.J. Wang and F. Waleffe, private communication (2004).
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Steady but generally unstable solutions of the 2D Boussinesq equations are obtained for no-slip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number Ra ≈ 1708 has been calculated up to Ra ≈ 5.106 and its Nusselt number is Nu ∼ 0.143 Ra
0.28 with a delicate spiral structure in the temperature field. Another solution that maximizes Nu over the horizontal wavenumber has been calculated up to Ra = 109 and scales as Nu ∼ 0.115 Ra
0.31 for 107 < Ra ≤ 109, quite similar to 3D turbulent data that show Nu ∼ 0.105 Ra
0.31 in that range. The optimum solution is a simple yet multi-scale coherent solution whose horizontal wavenumber scales as 0.133 Ra
0.217. That solution is unstable to larger scale perturbations and in particular to mean shear flows, yet it appears to be relevant as a backbone for turbulent solutions, possibly setting the scale, strength, and spacing of elemental plumes.
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