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SUMMARY:On a question posed by G.I. Taylor. - Dr Harsha Hutridurga (DPMMS)
DTSTART:20141203T160000Z
DTEND:20141203T170000Z
UID:TALK55350@talks.cam.ac.uk
CONTACT:Eavan Gleeson
DESCRIPTION:In this talk\, we shall look into a question raised by G.I. Ta
 ylor with regard to the study of the spreading (usually referred to as 'Di
 spersion') of dissolved solutes in a fluid medium. The interplay between m
 olecular diffusion and the variations in fluid velocity were studied by G.
 I. Taylor. Neither a simple molecular diffusion nor a simple convection ca
 n account for the effective mixing of solutes. The main question raised by
  Taylor was to find an expression for the Dispersion tensor in terms of th
 e molecular diffusion and the convective field. We shall try to answer thi
 s question of Taylor in case of heterogeneous flow fields and molecular di
 ffusion. Our approach is via the theory of Homogenization. We shall discus
 s a complete solution to the question of Taylor when the convective field 
 is purely periodic in space. We shall also present some recent calculation
 s which give an expression for the 'Taylor Dispersion' when the convective
  field is locally periodic i.e.\, when the fluid velocity has macroscopic 
 modulations. These results are obtained via the study of integral curves a
 ssociated with an ODE. We shall discuss a new notion of convergence in mov
 ing coordinates which might be helpful in the study of various problems in
  fluid dynamics. We shall also try to discuss the difficulties that are pr
 esent in giving a complete solution to the original question raised by G.I
 . Taylor.
LOCATION:MR14\, Centre for Mathematical Sciences
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