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SUMMARY:Multi-scale steady solutions representing classical and ultimate s
 caling in thermal convection - Shingo Motoki\, Osaka University\, Japan
DTSTART:20210528T153000Z
DTEND:20210528T163000Z
UID:TALK160486@talks.cam.ac.uk
CONTACT:virginia mullins
DESCRIPTION:Rayleigh–Bénard convection is one of the most canonical flo
 ws widely observed in nature and engineering applications. The effect of b
 uoyancy on a flow is characterised by the Rayleigh number Ra\, and the flo
 w becomes turbulent eventually as Ra increases. One of the primary interes
 ts in convective turbulence is the scaling law of the Nusselt number Nu (d
 imensionless vertical heat flux) with Ra. A one-third power law for Nu wit
 h Ra\, referred to as the 'classical' scaling\, has been reported in many 
 experiments and numerical simulations. On the other hand\, a one-half powe
 r law\, referred to as the 'ultimate' scaling\, has not been observed yet 
 in conventional Rayleigh–Bénard convection (buoyancy-driven convection 
 between horizontal impermeable walls with a constant temperature differenc
 e). In this talk\, I will first discuss a multi-scale steady solution in t
 he conventional Rayleigh–Bénard convection. It is a three-dimensional s
 teady solution to the Boussinesq equations\, found using a homotopy from t
 he wall-to-wall optimal transport solution (Motoki et al. 2018 J. Fluid Me
 ch.\, 851\, R4). The exact coherent thermal convection exhibits the classi
 cal scaling and reproduces structural and statistical properties of convec
 tive turbulence. Next\, I will draw attention to thermal convection betwee
 n permeable walls. The permeable wall is a simple model mimicking a Darcy-
 type porous wall (Jiménez et al. 2001 J. Fluid Mech. 442\, 89-117). The w
 all permeability leads to the ultimate scaling\, meaning that a wall heat 
 flux being independent of thermal conductivity\, although the heat transfe
 r on the wall is dominated by thermal conduction. Finally\, I will discuss
  the physical mechanisms of classical and ultimate scaling. 
LOCATION:GKB 100 Fluid Mechanics Webinar Series
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