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., 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 comparabl...
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| Published in | Journal of hydrodynamics. Series B Vol. 26; no. 3; pp. 351 - 362 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Elsevier Ltd
01.07.2014
Springer Singapore |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1001-6058 1878-0342 |
| DOI | 10.1016/S1001-6058(14)60040-8 |
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| Summary: | 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. |
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| Bibliography: | 31-1563/T QIU Xiang, HUANG Yong-xiang , ZHOU Quan,SUN Chao （School of Science, Shanghai Institute of Technology, Shanghai 200235, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China ; Physics of Fluids Group, University of Twente, AE Enschede, The Netherlands） 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. Rayleigh-Bénard convection,scaling,probability density function（pdf） ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1001-6058 1878-0342 |
| DOI: | 10.1016/S1001-6058(14)60040-8 |