Variational principles are introduced In the statistical theory of turbulent two-phase flows. With the help of these, correlation functions can be calculated by means of extremizing certain functionals. We carry out a sample calculation of the mean flow profile and correlation functions of a cylindrically symmetric two-phase jet. A Rayleigh-Ritz method is used for the determination of the correlation functions. There is a reasonable agreement between the theoretical calculation and ...
A new approach to the calculation of turbulent flows is presented. Variational principles are introduced into the statistical theory of turbulence enabling the determination of correlation functions by extremizing certain functionals. To demonstrate the efficiency of the technique a sample calculation of a mean flow profile and certain two point correlation functions of a cylindrically symmetric free jet were carried out using the Rayleigh-Ritz method. A judicious choice of the ...
A description of the turbulent flow of two phase system is given in terms of a coupled system of Boltzmann and Navier Stokes equations. The use of a Boltzmann equation for the particle phase makes the description valid for low is concentrations. The Boltzmann equation is appropriately modified to account for a velocity dependent interphase interaction. Within the framework of Chapman Enskog expansion, moment equations are derived for the particle ...
There are many classical, nonlinear systems exhibiting some kind of chaotic behavior. Examples include the turbulent flow of a fluid, usually described by means of the Navier-Stokes equations, and the behavior of liquids, gases or antiferromagnets above the critical point, etc. In this paper, we reexamine and further develop and approach to the description of such systems. The statistical theory of random process is cast into a Lagrangian form. The ...
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