scholarly journals Direct Numerical Simulations of the PDF's (Probability Density Functions) of a Passive Scalar in a Forced Mixing Layer,

1987 ◽  
Author(s):  
P. Givi ◽  
P. A. McMurtry
Keyword(s):  
Numerical Simulations ◽  
Probability Density ◽  
Mixing Layer ◽  
Passive Scalar ◽  
Probability Density Functions ◽  
Direct Numerical Simulations ◽  
Density Functions ◽  
Forced Mixing

Conditional Averages and Probability Density Functions in the Passive Scalar Field

1998 ◽  
Vol 67 (3) ◽  
pp. 833-841 ◽  
Author(s):  
Naoya Takahashi ◽  
Tsutomu Kambe ◽  
Tohru Nakano ◽  
Toshiyuki Gotoh ◽  
Kiyoshi Yamamoto
Keyword(s):  
Scalar Field ◽  
Probability Density ◽  
Passive Scalar ◽  
Probability Density Functions ◽  
Density Functions

scholarly journals Probability density functions in the cloud-top mixing layer

2010 ◽  
Vol 12 (8) ◽  
pp. 085010 ◽  
Author(s):  
J P Mellado ◽  
B Stevens ◽  
H Schmidt ◽  
N Peters
Keyword(s):  
Probability Density ◽  
Mixing Layer ◽  
Probability Density Functions ◽  
Density Functions

scholarly journals Turbulent mixing and entrainment in a stratified horizontal plane shear layer: joint velocity–temperature analysis of experimental data

2016 ◽  
Vol 806 ◽  
pp. 542-579 ◽  
Author(s):  
Johan Carlier ◽  
Kodjovi Sodjavi
Keyword(s):  
Shear Layer ◽  
Probability Density ◽  
Turbulent Mixing ◽  
Mixing Layer ◽  
Joint Probability ◽  
Probability Density Functions ◽  
Mixing Enhancement ◽  
Density Functions ◽  
Plane Shear ◽  
Significant Difference

Buoyancy effects on the turbulent mixing and entrainment processes were analysed in the case of a stratified plane shear layer between two horizontal air flows in conditions leading to relatively low values of the flux Richardson number ($|Ri_{f}|_{max}\simeq 0.02$). Velocity and temperature measurements were made with a single$\times$-wire probe thermo-anemometry technique, using multi-overheat sequences to deliver simultaneous velocity–temperature data at high frequency. The spatial resolution was found to be fine enough, in relation to the dissipative scale and the thermal diffusive scale, to avoid false mixing enhancement in the analysis of the physical mechanisms through velocity–temperature coupling in statistical turbulence quantities. Probability density functions (PDFs) and joint probability density functions (JPDFs) were used to distinguish between the different mechanisms involved in turbulent mixing, namely entrainment, engulfing, nibbling and mixing, and point to the contribution of entrainment in the mixing process. When comparing an unstably stratified configuration to its stably stratified equivalent, no significant difference could be seen in the PDF and JPDF quantities, but a conditional analysis based on temperature thresholding enabled a separation between mixed fluid and two distinct sets of events associated with unmixed fluid entrained from the hot and cold sides of the mixing layer into the mixing layer. This separation allowed a direct calculation of the entrainment velocities on both sides of the mixing layer. A significant increase of the total entrainment could be seen in the case of unstably stratified configuration. The entrainment ratios were compared to their prediction by the Dimotakis model and both a rather good relevance of the model and some need for improvement were found from the comparison. It was hypothesised that the improvement should come from better taking into account the distinct contributions of nibbling and engulfing inside the process of entrainment and mixing.

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

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