Multiscale Characterization of the Probability Density Functions of Velocity and Temperature Increment Fields
Document ID: 326
Doctoral Dissertation
North Carolina State University
Marine, Earth, and Atmospheric Sciences
Raleigh, North Carolina
Abstract
The turbulent motions with the atmospheric boundary layer exist over a wide range of spatial and temporal scales and are very difficult to characterize. Tims, to explore the behavior of such complex flow enviroments, it is customary to examine their properties from a statistical perspective. Utilizing the probability density functions of velocity and temperature increments, δu and δT, respectively, this work investigates their multiscale behavior to uncover the unique traits that have yet to be thoroughly studied. Utilizing diverse datasets, including idealized, wind tunnel experiments, atmospheric turbulence field measurements, multi-year ABL tower observations, and mesoscale models simulations, this study reveals remarkable similiarities (and sorne differences) between the srnall and !arger scale components of the probability density functions incrernents fields.
This comprehensive analysis also utilizes a set of statistical distributions to showcase their ability to capture features of increments probability density functions (pdfs) across multiscale atrnospheric rnotions. Also, an approach is proposed for estimating their pdfs utilizing the maximum likelihood estimation (MLE) technique, which has never been conducted utilizing atmospheric data. Using this approach, we reveal the ability to estimate higher order moments accurately with a limited sample size, which has been a persistent concern for atmospheric turbulence research. With the use robust Goodness of Fit (GoF) metrics, we quantitatively reveal the accuracy of the distributions to the diverse dataset. Through this analysis, it is shown that the normal inverse Gaussian (NIG) distribution is a prime candidate to be used as an estimate of the increment pdfs fields. Therefore, using the NIG model and its parameters, we display the variations in the increments over a range of scales revealing some unique scaledependent qualities under various stability and flow conditions. This novel approach can provide a method of characterizing increment fields with the sole use of only four pdf parameters. Also, we investigate the capability of the current state-of-the-art mesoscale atmospheric models to predict the features and highlight the potential for use for future model development. With the knowledge gained in this study, a number of applications can benefit by using our approach, including the wind energy and optical wave propagation fields.
| Citation: | A. W. DeMarco, "Multiscale Characterization of the Probability Density Functions of Velocity and Temperature Increment Fields", North Carolina State University, Raleigh, NC, United States, Doctoral Dissertation, 2017, 222 pages |