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SUMMARY:Global analysis of convective instabilities in nonparallel flows -
  Mittal\, S (Indian Institute of Technology)
DTSTART:20080912T105000Z
DTEND:20080912T111000Z
UID:TALK13385@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A new scheme for the global analysis of convective instabiliti
 es in nonparallel flows is proposed. The linearized perturbation equations
  for an incompressible flow are written in a moving frame of reference tha
 t travels with the perturbation. In the moving frame\, the base flow varie
 s with time. However\, at t=0\, it is same as the one in stationary frame.
  Therefore\, this analysis\, for determining the global convective instabi
 lity\, is valid in an instantaneous sense. A stabilized finite element met
 hod is utilized to discretize these equations. A sub-space iteration proce
 dure is utilized to solve the resulting generalized eigenvalue problem. Un
 like local analysis\, the proposed method gives the global eigenmode and t
 he corresponding growth rate. The scheme is applied to assess the stabilit
 y of uniform flow past bluff bodies. For the flow past a circular cylinder
  the critical Re for the onset of convective instability is found to be 4\
 , approximately. The critical Re for the onset of the shear layer instabil
 ity has been a point of contention. Various estimates have been proposed r
 anging from Re_c=350 to 2600. The proposed method is applied to find Re_c.
  To suppress the wake mode\, that leads to Karman vortex shedding\, flow p
 ast one half of the cylinder is studied. The Re_c is found to be ~54. The 
 wake and shear layer modes for a full cylinder are compared to bring out t
 he differences between the two. Also\, the connection of the instability a
 t low Re to the shear layer modes at higher Re (=500) is presented. The re
 sults are compared with earlier work from local stability analysis. Result
 s are also computed for flow past a flat plate normal to the flow. All the
  results are in excellent agreement with the direct numerical simulation o
 f the linearized flows equations.
LOCATION:Seminar Room 1\, Newton Institute
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