Scaling of maximum probability density function of velocity increments in turbulent Rayleigh-Bénard convection

Abstract

In this paper, we apply a scaling analysis of the maximum of the probability density function (pdf) of velocity increments, i.e., pmax(τ)=maxΔuτp(Δuτ)−τ−α, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Reλ≈60. The scaling exponent is comparable with that of the first-order velocity structure function, ζ(1), in which the large-scale effect might be constrained, showing the background fluctuations of the velocity field. It is found that the integral time T(x/D) scales as T(x/D)-(x/D)-β, with a scaling exponent β=0.25±0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent α(x,z) is strongly inhomogeneous in the x (horizontal) direction. The vertical-direction-averaged pdf scaling exponent α˜(x,z) obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent ξ≈0.22 within the velocity boundary layer and ξ≈0.28 near the cell sidewall. In the cell's central region, α(x,z) fluctuates around 0.37, which agrees well with ζ(1) obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade T˜I(x) is found to be linearly increasing with the wall distance with an exponent 0.65±0.05.