Papers › Convective heat transfer in the Burgers-Rayleigh-Bénard system
Convective heat transfer in the Burgers-Rayleigh-Bénard system
Enrico Calzavarini, Silvia C. Hirata
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The dynamics of heat transfer in a model system of Rayleigh-B\'enard (RB) convection reduced to its essential, here dubbed Burgers-Rayleigh-B\'enard (BRB), is studied. The system is spatially one-dimensional, the flow field is compressible and its evolution is described by the Burgers equation forced by an active temperature field. The BRB dynamics shares some remarkable similarities with realistic RB thermal convection in higher spatial dimensions: i) it has a supercritical pitchfork instability for the onset of convection which solely depends on the Rayleigh number (Ra) and not on Prandlt (Pr), occurring at the critical value Ra_c = (2π)⁴ ii) the convective regime is spatially organized in distinct boundary-layers and bulk regions, iii) the asymptotic high Ra limit displays the Nusselt and Reynolds numbers scaling regime Nu = √(RaPr)/4 for Pr≪1, Nu=√(Ra)/(4√(π)) for Pr≫1 and Re = √(Ra/Pr)/√(12), thus making BRB the simplest wall-bounded convective system exhibiting the so called ultimate regime of convection. These scaling laws, derived analytically through a matched asymptotic analysis are fully supported by the results of the accompanying numerical simulations. A major difference with realistic natural convection is the absence of turbulence. The BRB dynamics is stationary at any Ra number above the onset of convection. This feature results from a nonlinear saturation mechanism whose existence is grasped by means of a two-mode truncated equation system and via a stability analysis of the convective regime.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections