Publication: Effect of shear on local boundary layers in turbulent convection
Date
01-05-2023
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Abstract
In Rayleigh Bénard convection, for a range of Prandtl numbers and Rayleigh numbers, 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, at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities; (B) bimodal with the first peak between and, the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately. Type A distributions occur more at lower, while type C occur more at higher, with type B occurring more at intermediate. We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as scales with. We then show that the areas of such regions that have velocities of the order of increase exponentially with increase in 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, 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 and aspect ratio, 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 as; since, this suggests a possible shear domination of the boundary layers at high. The effect of shear, however, decreases with increase in and with increase in, and becomes negligible for at or for at, causing.
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Bénard convection, turbulent boundary layers, turbulent convection