Effect of shear on local boundary layers in turbulent convection

In Rayleigh Benard convection, for a range of Prandtl numbers 4.69 <= Pr <= 5.88 and Rayleigh numbers 5.52 x 10(5) <= Ra <= 1.21 x 10(9), we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers on the hot plate. The velocity distribution in a horizontal plane within the boundary layers at each Ra, at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities V-bl; (B) bimodal with the first peak between V-bl and V-L, the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately V-L. Type A distributions occur more at lower Ra, while type C occur more at higher Ra, with type B occurring more at intermediate Ra. We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as V-L scales with Ra. We then show that the areas of such regions that have velocities of the order of VL increase exponentially with increase in Ra and then saturate. The velocities in the remaining regions, which contribute to the first peak of the bimodal type B distributions and the single peak of type A distributions, are also affected by the shear. We show that the Reynolds number based on these velocities scale as Re-bs, the Reynolds number based on the boundary layer velocities forced externally by the shear due to the LSF, which we obtained as a perturbation solution of the scaling relations derived from integral boundary layer equations. For Pr = 1 and aspect ratio Gamma = 1, Re-bs similar to Ra-0.375 for small shear, similar to the observed flux scaling in a possible ultimate regime. The velocity at the edge of the natural convection boundary layers was found to increase with Ra as Ra-0.35; since V-bl similar to Ra-1/3, this suggests a possible shear domination of the boundary layers at high Ra. The effect of shear, however, decreases with increase in Pr and with increase in Gamma, and becomes negligible for Pr >= 100 at Gamma = 1 or for Gamma >= 20 at Pr = 1, causing Re-bs similar to Ra-w(1/3) .