We propose a theoretical model for spatial variations of the temperature varianceσ2(z,r)(z is the dis-tance from the sample bottom and r the radial coordinate)in turbulent Rayleigh-Bénard convection(RBC).Adaptin...We propose a theoretical model for spatial variations of the temperature varianceσ2(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”modelofshearflowtothe plumesofRBC,wederivedanequationforσ2 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,whereλth is the thermal boundary layer thickness.The equation parameters depend on r and the Prandtl number Pr,but have only an extremelyweak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for thetemperature variance profile in turbulent RBC.展开更多
基金the National Natural Science Foundation of China(Grants 11772111 and91952101)the Max Planck Partner Group.
文摘We propose a theoretical model for spatial variations of the temperature varianceσ2(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”modelofshearflowtothe plumesofRBC,wederivedanequationforσ2 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,whereλth is the thermal boundary layer thickness.The equation parameters depend on r and the Prandtl number Pr,but have only an extremelyweak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for thetemperature variance profile in turbulent RBC.
