Experimental studies of the viscous boundary layer properties in turbulent Rayleigh-Benard convection

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh number Ra varying from 10(9) to 10(10) and the Prandtl number Pr fixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness delta(upsilon). It is found that delta(upsilon) follows the classical Blasius-like laminar boundary layer in the present range of Ra, and it scales with the Reynolds number Re as delta(upsilon)/H = 0.64Re(-0.50 +/- 0.03) (where H is the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar for Ra < 2.0 x 10(10), two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent at Ra similar to 10(13). Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles sigma(T)(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend on Ra and varies from -0.6 to -0.77, which is much larger than the classical value of -1/3. In the same region, the measured profiles of the r.m.s. vertical velocity sigma(omega)(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several 55 wall quantities is also measured directly. These are the wall shear stress tau(omega)similar to Re-1.55, the viscous sublayer delta(omega) similar to Re-0.91, the friction velocity u(tau) similar to Re-0.80, and the skinfriction coefficient c(f) similar to Re-0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that of cf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (at z(+) = z/delta(omega) similar or equal to 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.