Thermal convection over fractal surfaces

Journal article

We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-B´enard convection in cells with a fractal boundary in two dimensions for P r = 1 and Ra ∈ [10^7 , 10^10]. The fractal boundaries are functions characterized by power spectral densities S(k) that decay with wavenumber, k, as S(k) ∼ k^p (p < 0). The degree of roughness is quantified by the exponent p with p < −3 for smooth (differentiable) surfaces and −3 ≤ p < −1 for rough surfaces with Hausdorff dimension D_f =1/2 (p + 5). By computing the exponent β in power law fits Nu ∼ Ra^β, where Nu and Ra are the Nusselt and the Rayleigh numbers for Ra ∈ [10^8, 10^10], we observe that heat transport scaling increases with roughness over the top two decades of Ra ∈ [10^8, 10^10]. For p = −3.0, −2.0 and −1.5 we find β = 0.288 ± 0.005, 0.329 ± 0.006 and 0.352 ± 0.011, respectively. We also observe that the Reynolds number, Re, scales as Re ∼ Ra^ξ , where ξ ≈ 0.57 over Ra ∈ [10^7, 10^10], for all p used in the study. For a given value of p, the averaged Nu and Re are insensitive to the specific realization of the roughness.

Authors: Toppaladoddi, S; Wells, AJ; Doering, CR; Wettlaufer, JS

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Journal of Fluid Mechanics
• Volume: 907
• Article number: A12
• Publication date: 2020-11-20
• Acceptance date: 2020-09-07
• DOI: 10.1017/jfm.2020.826
• EISSN: 1469-7645
• ISSN: 0022-1120
• Language: English
• Keywords: turbulent convection; FFR; Bénard convection; fractals