TY - JOUR

T1 - Scaling of maximum probability density function of velocity increments in turbulent Rayleigh-Bénard convection

AU - Qiu, X.

AU - Huang, Y.

AU - Zhou, Q.

AU - Sun, Chao

PY - 2014

Y1 - 2014

N2 - 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−αpmax(τ)=maxΔuτp(Δuτ)−τ−α, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re λ≈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.

AB - 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−αpmax(τ)=maxΔuτp(Δuτ)−τ−α, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re λ≈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.

KW - IR-94893

KW - METIS-304677

U2 - 10.1016/S1001-6058(14)60040-8

DO - 10.1016/S1001-6058(14)60040-8

M3 - Article

VL - 26

SP - 351

EP - 362

JO - Journal of hydrodynamics

JF - Journal of hydrodynamics

SN - 1001-6058

IS - 3

ER -