A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

• 作者: Xiaozhou He Eberhard Bodenschatz Guenter Ahlers
• 来源期刊: 力学快报（英文版）
• 年，卷（期）: 2021,（2）
• 所属期刊栏目: Fluid Mechanics
• 页码范围: 102-104
• 页数: 3页
• 语种: 英文
• DOI: 10.3969/j.issn.2095-0349.2021.02.007

摘要

We propose a theoretical model for spatial variations of the temperature variance σ2 ( z, r ) ( z is the dis- tance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection (RBC). Adapting the "attached-eddy"model of shear flow to the plumes of RBC, we derived an equation forσ2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation in- cludes both logarithmic and power-law dependences on z/ λth , where λth is the thermal boundary layer thickness. The equation parameters depend on r and the Prandtl number Pr , but have only an extremely weak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for the temperature variance profile in turbulent RBC.