Abstract
Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. As example we pick the canonical Rayleigh-Bénard geometry, but now with the bottom plate temperature , the top plate temperature , and the density maximum around in between, resulting in penetrative turbulence. Next to the Rayleigh number Ra, the crucial new control parameter as compared to standard Rayleigh-Bénard convection is the density inversion parameter . The crucial response parameters are the relative mean midheight temperature and the overall heat transfer (i.e., the Nusselt number Nu). We numerically show (for Ra up to ) and theoretically derive that and are universally(i.e., independently of ) determined only by the density inversion parameter and succeed to derive these universal dependences. In particular, , which holds for below a -dependent critical value, beyond which sharply decreases and drops down to at . This critical density inversion parameter can be precisely predicted by a linear stability analysis. Finally, we numerically identify and discuss rare transitions between different turbulent flow states for large .
- Received 15 December 2020
- Accepted 7 June 2021
DOI:https://doi.org/10.1103/PhysRevFluids.6.063502
©2021 American Physical Society