The scaling arguments presented by [J. Fluid Mech. 204 (1989) 1] to justify the Nu ˜ Ra2/7 power law observed in high Rayleigh number thermal convection also have implications regarding the distribution of velocity and temperature fluctuations within the turbulent layer. Asymptotic matching of the inner scaling law and the outer scaling law implies that the root-mean-square (r.m.s.) vertical velocity fluctuation varies as σw ˜ ln z, and the r.m.s. temperature fluctuation varies as σθ ˜ ln z or σθ ˜ z-1/2 depending on the details of the modeling assumptions [Exp. Fluids 4 (1986) 121]. These results differ markedly from the Priestley similarity theory [Turbulent Transport in the Lower Atmosphere, 1959], in which σw ˜ z1/3 and σθ ˜ z-1/3. Consequently, the r.m.s. velocity and temperature profiles offer the possibility to distinguish between the two theories. We present measurements in wide-aspect-ratio convection over the range Ra = 107-109 that support the logarithmic variation for both the temperature and velocity.
ASJC Scopus subject areas
- Chemical Engineering(all)
- Nuclear Energy and Engineering
- Aerospace Engineering
- Mechanical Engineering
- Fluid Flow and Transfer Processes