Theoretical Investigations of Turbulence and Magneto-Hydrodynamic Turbulence in Incompressible Fluid

Abstract

The thesis entitled "Theoretical investigations of turbulence and Magnetohydrodynamic turbulence in incompressible fluid" is being presented for the award of the degree of Doctor of Philosophy in Mathematics. It is the outcome of my researches conducted in the Department of Mathematics, Rajshahi University, Rajshahi, Bangladesh under the guidance of Dr. M. Shamsul Alam Sarker, Professor, Department of mathematics, Rajshahi University, Rajshahi-6205, Bangladesh. The thesis has been divided into six chnptcrs. The first is a general introductory chapter and gives the general idea of turbulence and Magneto-hydrodynamics turbulence and its principal concepts. Some results and theories, which arc needed in the subsequent chapter, have been included in this chapter. A brief review of the past researches related lo this thesis has also been given. In the second chapter we have discussed the decay of temperature 11uclualion in homogeneous turbulence before the final petiod for the case of multi-point and multi-time. Two-point, two-lime and three-point, three-time Fourier-lransfom1ed temperature equations is made detenninate by neglecting the fourth-order correlation tem1s. Finally, we have obtained the decay law of temperature iluctualion energy before the final period.-----