Rajeswari Devi, M B; Dr.Jathavedan, M(Cochin University of Science and Technology, December , 2006)
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Abstract:
In this thesis an attempt is made to study vortex knots based on the work of
Keener . It is seen that certain mistakes have been crept in to the details of this
paper. We have chosen this study for an investigation as it is the first attempt to
study vortex knots. Other works had given attention to this. In chapter 2 we have
considered these corrections in detail. In chapter 3 we have tried a simple extension by introducing vorticity in the evolution of vortex knots. In chapter 4 we have introduced
a stress tensor related to vorticity. Chapter 5 is the general conclusion.Knot theory is a branch of topology and has been developed as an independent
branch of study. It has wide applications and vortex knot is one of them. As pointed
out earlier, most of the studies in fluid dynamics exploits the analogy between vorticity
and magnetic induction in the case of MHD. But vorticity is more general than magnetic
induction and so it is essential to discuss the special properties of vortex knots,
independent of MHD flows. This is what is being done in this thesis.
Description:
Dept.of Mathematics,
Cochin University of Science and Technology