Publication
Lie symmetry analysis of the LundgrenMoninNovikov equations for multipoint probability density functions of turbulent flow 

Wacławczyk M., Grebenev V.N., Oberlack M. 
Publication type:

Journal of Physics A  Mathematical and Theoretical50, 2017, 175501, 10.1088/17518121/aa62f4 
Organization unit:

The problem of turbulence statistics described by the Lundgren–Monin–Novikov (LMN) hierarchy of integrodifferential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a truncated LMN chain which presents the first two equations in an infinite set of integrodifferential equations for the multipoint probability density functions (pdf's) of velocity. A complete set of point transformations is derived for the onepoint pdf's and the independent variables: sample space of velocity, space and time. For this purpose we use a direct method based on the canonical Lie–Bäcklund operator. Due to the oneway coupling of correlation equations, the present results are complete in the sense that no additional symmetries exist for the first leading equation, even if the full infinite hierarchy is considered.