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Title: Bounds on heat flux for Rayleigh–Bénard convection between Navier-slip fixed-temperature boundaries
We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number R a , this estimate interpolates between the Whitehead–Doering bound by R a 5 12 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106 , 244501) and the classical Doering–Constantin R a 1 2 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53 , 5957–5981). This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.  more » « less
Award ID(s):
2106233
NSF-PAR ID:
10327733
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume:
380
Issue:
2225
ISSN:
1364-503X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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