Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection

• DOI: 10.1017/jfm.2017.19
• Publication Date: 2017-02-03T13:36:13Z
• Authors: Yang Zhang; Quan Zhou; Chao Sun
• Keywords: Unicode

We investigate the statistical properties of kinetic $\unicode[STIX]{x1D700}_{u}$ and thermal $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}$ energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh–Bénard (RB) convection. Direct numerical simulations were carried out a box with unit aspect ratio Rayleigh number range $10^{6}\leqslant Ra\leqslant 10^{10}$ for Prandtl numbers $Pr=0.7$ 5.3. The probability density functions (PDFs) both are found to deviate significantly from log-normal distribution. PDF tails can be well described by stretched exponential function, become broader higher lower number, indicating an increasing degree small-scale intermittency Reynolds number. Our results show that ensemble averages $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle scale as $Ra^{-0.18\sim -0.20}$ , which is excellent agreement scaling estimated two global exact relations rates. By separating bulk boundary-layer contributions total dissipations, our further reveal dominated boundary layers, corresponding regimes $I_{l}$ $I_{u}$ Grossmann–Lohse (GL) theory ( J. Fluid Mech. vol. 407, 2000, pp. 27–56). To include effects plumes, plume–background partition also considered plume dominated. Moreover, boundary-layer/plume those predicted GL theory, while deviations predictions observed bulk/background contributions. possible reasons discussed.