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Title:  Studies of Static and Dynamic Multiscaling in Turbulence 
Authors:  Mitra, Dhrubaditya 
Advisors:  Pandit, Rahul 
Submitted Date:  Sep2004 
Publisher:  Indian Institute of Science 
Abstract:  The physics of turbulence is the study of the chaotic and irregular behaviour in driven fluids. It is ubiquitous in cosmic, terrestrial and laboratory environments. To describe the properties of a simple incompressible fluid it is sufficient to know its velocity at all points in space and as a function of time. The equation of motion for the velocity of such a fluid is the incompressible Navier–Stokes equation. In more complicated cases, for example if the temperature of the fluid also fluctuates in space and time, the Navier–Stokes equation must be supplemented by additional equations. Incompressible fluid turbulence is the study of solutions of the Navier–Stokes equation at very high Reynolds numbers, Re, the dimensionless control parameter for this problem. The chaotic nature of these solutions leads us to characterise them by their statistical properties. For example, statistical properties of fluid turbulence are characterised often by structure functions of velocity. For intermediate range of length scales, that is the inertial range, these structure functions show multiscaling. Most studies concentrate on equaltime structure functions which describe the equaltime statistical properties of the turbulent fluid. Dynamic properties can be measured by more general timedependent structure functions. A major challenge in the field of fluid turbulence is to understand the multiscaling properties of both the equaltime and timedependent structure functions of velocity starting from the Navier–Stokes equation. In this thesis we use numerical and analytical techniques to study scaling and multiscaling of equaltime and timedependent structure functions in turbulence not only in fluids but also in advection of passivescalars and passive vectors, and in randomly forced Burgers equation. 
URI:  http://etd.iisc.ernet.in/handle/2005/122 
Appears in Collections:  Physics (physics)

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