Convective heat transfer in the Burgers-Rayleigh-Bénard system
نویسندگان
چکیده
The dynamics of heat transfer in a model system Rayleigh-B\'enard (RB) convection reduced to its essential, here dubbed Burgers-Rayleigh-B\'enard (BRB), is studied. spatially one-dimensional, the flow field compressible and evolution described by Burgers equation forced an active temperature field. BRB shares some remarkable similarities with realistic RB thermal higher spatial dimensions: i) it has supercritical pitchfork instability for onset which solely depends on Rayleigh number $(Ra)$ not Prandlt $(Pr)$, occurring at critical value $Ra_c = (2\pi)^4$ ii) convective regime organized distinct boundary-layers bulk regions, iii) asymptotic high $Ra$ limit displays Nusselt Reynolds numbers scaling $Nu \sqrt{RaPr}/4$ $Pr\ll 1$, $Nu=\sqrt{Ra}/(4\sqrt{\pi})$ $Pr\gg1$ $Re \sqrt{Ra/Pr}/\sqrt{12}$, thus making simplest wall-bounded exhibiting so called ultimate convection. These laws, derived analytically through matched analysis are fully supported results accompanying numerical simulations. A major difference natural absence turbulence. stationary any above This feature from nonlinear saturation mechanism whose existence grasped means two-mode truncated via stability regime.
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ژورنال
عنوان ژورنال: Physical review fluids
سال: 2023
ISSN: ['2469-9918', '2469-990X']
DOI: https://doi.org/10.1103/physrevfluids.8.063502