_____________________________________________________________________________________________________ *Corresponding author: Email: anchor@hmti.ac.by; Physical Science International Journal 9(2): 1-6, 2016, Article no.PSIJ.22455 ISSN: 2348-0130 SCIENCEDOMAIN international www.sciencedomain.org Probability Density Function of Scalar Length Scales in Turbulent Flow Andrei Chorny 1* 1 A. V. Luikov Heat and Mass Transfer Institute of NAS of Belarus, 15, P. Brovka Street, Minsk, 220072, Republic of Belarus. Author’s contribution The sole author designed, analyzed and interpreted and prepared the manuscript. Article Information DOI: 10.9734/PSIJ/2016/22455 Editor(s): (1) Igor I. Strakovsky, Center for Nuclear Studies, Department of Physics, The George Washington University Washington, DC, USA. (2) Abbas Mohammed, Blekinge Institute of Technology, Sweden. Reviewers: (1) Amaury de Souza, Federal University of Mato Grosso do Sul, Brazil. (2) Manoel F Borges, Sao Paulo State University, Brazil. (3) António Félix Flores Rodrigues, University of the Azores, Portugal. Complete Peer review History: http://sciencedomain.org/review-history/12534 Received 1 st October 2015 Accepted 5 th November 2015 Published 2 nd December 2015 ABSTRACT In this Brief Communication scalar length-scale and time-scale distributions are proposed to determine by considering the statistics of the scalar field and its gradient. For this purpose, a relationship between the scalar length-scale probability density function and the joint probability density function for the scalar field and its gradient in the form of the integral relation is established. Keywords: Turbulent flow; scalar; dissipation rate; length scale; probability density function. 1. INTRODUCTION Statistical approaches, among which is the method based on probability density functions (PDFs), find wide use for solving a variety of problems on complex turbulent flows [1]. It is known that as compared to other methods, the PDF method allows one to describe the influence of turbulent fluctuations on the mixing intensity of scalar fields of temperature or concentration and then to take into account more accurately this influence on chemical processes in reacting flows [2]. The study of turbulent mixing of reacting flows by the PDF method is based on three major approaches. First, mixing is represented in terms of the decay rate of the scalar variance – the Short Communication