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SUMMARY:The role of boundary conditions on scaling laws in the Rayleigh-B
 énard convection problem - Camilla Nobili (University of Surrey)
DTSTART:20221128T140000Z
DTEND:20221128T150000Z
UID:TALK182996@talks.cam.ac.uk
CONTACT:Daniel Boutros
DESCRIPTION:Rayleigh-Bénard convection is the buoyancy-driven flow of a f
 luid heated from below and cooled from above and is a paradigm for nonline
 ar dynamics with important applications to meteorology\, oceanography and 
 engineering. We are interested in obtaining quantitative bounds on the Nus
 selt number\, the vertical heat transport enhancement factor. The Nusselt 
 number\, besides being an interesting quantity for engineering application
 s\, is the natural quantity to measure the intensity and effectiveness of 
 the motion. For this reason\, we are interested in proving (upper) bounds 
 which catch the relation between the Nusselt number and the (nondimensiona
 l control parameter) Rayleigh number\, in turbulent regimes. Despite great
  scientific developments in this field in the last 30 years\, it is still 
 not clear what role the boundary conditions play in the scaling laws for t
 he Nusselt number. In this talk we address this problem\, establishing rig
 orous bounds for the Rayleigh-Bénard convection problem with Navier-slip 
 boundary conditions for the velocity. We employ the background field metho
 d and deal with a careful PDE analysis\, due to the production of vorticit
 y at the walls. In conclusion\, we relate this result to other bounds deri
 ved for no-slip and stress-free boundary conditions and discuss open probl
 ems. This seminar is based on a joint work with T. Drivas and H. Nguyen an
 d on an ongoing project with F. Bleitner.
LOCATION:CMS\, MR13
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