Local dissipation scales and integral-scale reynolds number scalings in thermally-driven turbulence

Abstract

We present direct multi-point velocity measurements of the two-dimensional velocity fields in a cylindrical Rayleigh-Benard convection cell using the particle image velocimetry (PIV) technique over the Rayleigh number range 5.9 × 109 ≲ Ra ≲ 1.1 × 1011. The longitudinal integral length scale of the horizontal and vertical velocity fields are obtained at the cell center, near the cell sidewall, and near the bottom plate of the cell, respectively. In addition, the Reynolds number based on these scales, ReLx and ReLz, are obtained. It is found that all measured ReL scales as ReL ∼ Ra β, with the exponent β ≃ 0.5, except ReLx for the horizontal velocity at the cell center, which has a β ≃ 0.75. The local dissipation scale field η at the three different places are also studied. Our results reveal two types of universality of η. The first one is that, for the same flow, the probability density functions (PDF) of η are insensitive to turbulent intensity and large-scale inhomogeneity and anisotropy of the system. The second is that the small-scale dissipation dynamics in buoyancy-driven turbulence can be described by the same models developed for homogeneous and isotropic turbulence. However, the exact functional form of the PDF of the local dissipation scale is not universal with respect to different types of flows, but depends on the integral-scale velocity boundary condition, which is found to have an exponential, not Gaussian, distribution in turbulent Rayleigh-Bénard convection.