title: Roughness as a Route to the Ultimate Regime of Thermal Convection.
abstract: We use highly resolved numerical simulations to study turbulent Rayleigh-Bénard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr=1 and Ra=[4×10^{6},3×10^{9}]. By varying the wavelength λ at a fixed amplitude, we find an optimal wavelength λ_{opt} for which the Nusselt-Rayleigh scaling relation is (Nu-1∝Ra^{0.483}), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech. 804, 370 (2016)JFLSA70022-112010.1017/jfm.2016.528] who prove that Nu can grow no faster than O(Ra^{1/2}) as Ra→∞, and thus with the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When λ≪λ_{opt} and λ≫λ_{opt}, the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each Ra, we choose the maximum Nu among all λ, thus optimizing over all λ, to find Nu_{opt}-1=0.01×Ra^{0.444}.
authors.affiliation: Yale University, New Haven, Connecticut 06520, USA.
authors.forename: Srikanth
authors.initials: S
authors.lastname: Toppaladoddi
authors.affiliation: Istituto per le Applicazioni del Calcolo "Mauro Picone" (C.N.R.), 00185 Rome, Italy.
authors.forename: Sauro
authors.initials: S
authors.lastname: Succi
authors.affiliation: Yale University, New Haven, Connecticut 06520, USA.|Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.|Nordita, Royal Institute of Technology and Stockholm University, 114 28 Stockholm, Sweden.
authors.forename: John S
authors.initials: JS
authors.lastname: Wettlaufer