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.
In this paper, with consideration of the nonlinear and non-stationary properties of the temperature time series, we employ the Hilbert-Huang Transform, based on the empirical mode decomposition(EMD), to analyze the temperature time series from 1959 to 2012 in the Fengxian district of Shanghai, obtained from a certain monitoring station. The oscillating mode is drawn from the data, and its characteristics of the time series are investigated. The results show that the intrinsic modes of 1, 2 and 6 represent the periodic properties of 1 year, 2.5 years, and 27 years. The mean temperature shows periodic variations, but the main trend of this fluctuation is the rising of the temperature in the recent 50 years. The analysis of the reconstructed modes with the wave pattern shows that the variations are quite large from 1963 to 1964, from 1977 to 1982 and from 2003 to 2006, which indicates that the temperature rises and falls dramatically in these periods. The volatility from 1993 to 1994 is far more dramatic than in other periods. And the volatility is the most remarkable in recent 50 years. The log-linear plots of the mean time scales T and M show that each mode associated with a time scale almost twice as large as the time scale of the preceding mode. The Hilbert spectrum shows that the energy is concentrated in the range of low frequency from 0.05 to 0.1 Hz, and a very small amount of energy is distributed in the range of higher frequency over 0.1 Hz. In conclusion, the HHT is better than other traditional signal analysis methods in processing the nonlinear signals to obtain the periodic variation and volatility's properties of different time scales.
In this paper orthogonal wavelet transformations are applied to decompose experimental velocity signals in fully developed channel flows with varying pressure gradient into scales.We analyze the time series from turbulent data,to obtain the statistical characteristics,correlations between the adjacent scales and the principal scale of coherent structures in different scales by wavelet transformations.The results show that,in the counter gradient transport(CGT)region,skewness factors and flatness factors deviate strongly from the corresponding values of Gaussian distribution on certain scales.PDFs on each scale confirm this observation.Scale-scale correlations show further that the fluctuations on some certain special scales are more intermittent than nearby.Principal scale of coherent structure is coincident with the scales on which the statistical properties depart from Gaussian distribution.These features are the same for different families of wavelets,and it also shows some different features in the region between favorable pressure gradient and adverse pressure gradient.
