Three-dimensional properties of the viscous boundary layer in turbulent Rayleigh-Benard convection

We report an experimental study of the viscous boundary layer (BL) properties of turbulent Rayleigh-Benard convection in a cylindrical cell. The velocity profile with all three components was measured from the centre of the bottom plate by an integrated home-made particle image velocimetry system. The Rayleigh number Ra varied in the range 1.82 x 10(8) <= Ra <= 5.26 x 10(9) and the Prandtl number Pr was fixed at Pr = 4.34. The probability density function of the wall-shear stress indicates that using the velocity component in the mean large-scale circulation (LSC) plane alone may not be sufficient to characterise the viscous BL. Based on a dynamic wall-shear frame, we propose a method to reconstruct the measured full velocity profile which eliminates the effects of complex dynamics of the LSC. Various BL properties including the eddy viscosity are then obtained and analysed. It is found that, in the dynamic wall-shear frame, the eddy viscosity profiles along the centre line of the convection cell at different Ra all collapse on a single master curve described by nu(d)(t)/nu = 0.81 (z/delta(d)(u))(3.10 +/- 0.05) The Rayleigh number dependencies of several BL quantities are also determined in the dynamic frame, including the BL thickness delta(d)(u)(similar to Ra-0.21), the Reynolds number Re-d (similar to Ra--(0.)46) and the shear Reynolds number Re-s(d)(similar to Ra-0.24) Within the experimental uncertainty, these scaling exponents are the same as those obtained in the static laboratory frame. Finally, with the measured full velocity profile, we obtain the energy dissipation rate at the centre of the bottom plate epsilon(w), which is found to follow similar to Ra-1.25.