In this paper, we apply a scaling analysis of the maximum of the probability density function（pdf） of velocity increments, i.e., max（） = max（）up p u, for a velocity field of turbulent Rayleigh-Bénard convec...In this paper, we apply a scaling analysis of the maximum of the probability density function（pdf） of velocity increments, i.e., max（） = max（）up p u, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re60. The scaling exponent is comparable with that of the first-order velocity structure function, （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）, with a scaling exponent =0.25 0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent （x, z） is strongly inhomogeneous in the x（horizontal） direction. The vertical-direction-averaged pdf scaling exponent （x） obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent 0.22 within the velocity boundary layer and 0.28 near the cell sidewall. In the cell＇s central region, （x, z） fluctuates around 0.37, which agrees well with （1） obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade（）IT x is found to be linearly increasing with the wall distance x with an exponent 0.65 0.05.展开更多
基金supported by the Natural Science Foundation of China(Grant Nos.11102114,11202122 and 11222222)the Innovation Program of Shanghai Municipal Education Commission(Grant No.13YZ008,13YZ124)+1 种基金the Shanghai Shuguang Project(Grant No.13SG40)the Program for New Century Excellent Talents in University(Grant No.NCET-13-0)
文摘In this paper, we apply a scaling analysis of the maximum of the probability density function（pdf） of velocity increments, i.e., max（） = max（）up p u, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re60. The scaling exponent is comparable with that of the first-order velocity structure function, （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）, with a scaling exponent =0.25 0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent （x, z） is strongly inhomogeneous in the x（horizontal） direction. The vertical-direction-averaged pdf scaling exponent （x） obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent 0.22 within the velocity boundary layer and 0.28 near the cell sidewall. In the cell＇s central region, （x, z） fluctuates around 0.37, which agrees well with （1） obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade（）IT x is found to be linearly increasing with the wall distance x with an exponent 0.65 0.05.
