Analytical Invcstlgations in Tubulent and IVIlID Tttdmlent Flow

Abstract

The thesis entitled "Analytical Investigations in Turbulent and MHD Turbulent Flow" is being presented for the award of the degree of Doctor of Philosophy in Mathematics. It is the outcome of my research conducted in the Department of Mathematics, Rajshahi University during the year 1994-1998 under the guidance of Dr. M. Shamsul Alam Sarker, Department of Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh. The whole thesis has been divided into six chapters. The first is an introductory chapter and gives the general idea of turbulence, magnetohydrodynamic turbulence and its principal concepts. Throughout the work we have considered the flow of fluids to be isotropic and homogeneous. The notions generally adopted are those used by Batchelor, Chandrasekhar and Deissler in their research papers. Number inside brackets [ ] refer to the references which are arranged alphabetical at the end of the thesis. In the second chapter, we have derived the equation for tl1e rate of change of magnetic field covariance in MHD turbulent flow. 111e result shows that the defming scalars of the magnetic field covariance depend on the defining scalar H of two point magnetic field correlation. In tl1e third chapter, the decay of turbulence at ti.mes before the final period in presence of dust particles is studied. Two and three point correlation equation is used to obtain a relation for tl1e triple correlations and the equation is made detenninate by neglecting the quadruple correlations. Finally, we obtained tl1e energy decay law of dusty fluid turbulence before tl1e final period. In the fourth chapter, we have studied the decay of dusty fluid MHD turbulence before the final period. Tirree point correlation equation is used to obtain a relation for the triple correlations applicable at times before the final period. In this case the equation is made determinate by neglecting tl1e quadrnple correlations. Finally, we obtain the energy decay law of dusty fluid MHD turbulence at times before the final period.-------