Formulation of joint probability density functions of velocity for turbulent flows: an alternative approach

This work presents an alternative technique in formulating an analytical form of the joint probability density function (pdf) of velocity for turbulent flows. The technique was rigorously developed by Koehler and Symanowski (J. Multivariate Anal. 55 (1995), 261–282), by which a joint pdf is constructed based on the prescribed or given knowledge of marginal distributions and strictly conserves the original shape of each marginal density. The technique also provides flexibility in estimating parameters required in the pdf to fit a specified correlation. The scope of work is limited to the formulation for two velocity components due to less difficulty in examining correlation structures. Illustrated and discussed are a number of pdfs, with emphasis on atmospheric turbulence where the vertical velocity is assumed to be positively skew and negatively correlated with the horizontal velocity.