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

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 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 is found to be linearly increasing with the wall distance with an exponent 0.65±0.05.