Inner and outer scales in turbulent Rayleigh-Benard convection

As in other kinds of wall-bounded turbulence, flow and heat transport in turbulent Rayleigh-Benard convection (RBC) can be divided into an inner layer and an outer layer. This paper refines the traditional inner scales, the Townsend inner scales, by determining the Prandtl number Pr effect, and proposes new scales for the outer layer. Major findings for the inner layer include (i) the mean modified pressure peaks in the inner layer, and the peak location scales with the Townsend inner length scale l(nu) = nu /u(inner), where nu is the kinematic viscosity and u(inner) is the Townsend inner velocity. (ii) The peak value of the mean modified pressure P-max scales as Psi P rho refuinner2, where rho (ref) is the fluid density and the coefficient Psi (P) is largely independent of the Reynolds number but is strongly influenced by the Prandtl number. (iii) The thickness of the thermal inner layer scales with a thermal diffusional length scale l(alpha) = Psi (alpha)alpha /u(inner), where alpha is the thermal diffusivity and the coefficient Psi (alpha) is largely independent of the Reynolds number but is strongly influenced by the Prandtl number. Like passive scalar transport in a pressure-driven turbulent plane Poiseuille flow, the Prandtl number dependence of Psi (alpha) (and Psi (P)) can be approximated by a power law Psi (alpha) similar to Psi (P) similar to Pr-m, where m is a constant of about 0.5. In the outer layer, the vertical component of velocity fluctuation variance at the RBC midplane ww(mp) is introduced as a new governing parameter in the scaling of flow and heat transfer. The new outer velocity and temperature scales for turbulent RBC are different from the Deardorff scales, which were developed for convective atmospheric boundary layers. The new outer scales are compared with direct numerical simulation data and experimental measurements.