A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection. Issue 2 (February 2021) - He, Xiaozhou; Bodenschatz, Eberhard; Ahlers, Guenter
Highlights: A theoretical model for temperature variance profiles in turbulent Rayleigh-Bénard convection is proposed. The derived equation for the temperature variance includes both logarithmic and power-law terms. The equation parameters are expected to have only an extremely weak dependence on Ra . Abstract: We propose a theoretical model for spatial variations of the temperature variance σ 2 ( z, r ) ( z is the distance 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 for σ 2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation includes both logarithmic and power-law dependences on z / λ t h, where λ t h 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.