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SUMMARY:The Acoustic Boundary Condition for Flow Over a Deformable Wall - 
 Ed Brambley\, DAMTP
DTSTART:20091023T150000Z
DTEND:20091023T160000Z
UID:TALK20605@talks.cam.ac.uk
CONTACT:Raymond E. Goldstein
DESCRIPTION:A common problem when considering fluid-solid interaction is t
 o consider the behaviour of small (linearized) perturbations to a steady f
 low over a deformable boundary.  The simplest way to do\nthis is to consid
 er an inviscid incompressible (and isothermal) uniform flow slipping over 
 the boundary.  Or\, if one is interested in the acoustic response\, to con
 sider an inviscid (and homentropic) uniform perfect gas flow slipping over
  the boundary.  And\, indeed\,\nthis is a very commonly studied problem.\n
 \nBecause of the slipping flow at the boundary\, difficulties arise applyi
 ng a boundary condition there.  This boundary condition should link the sm
 all motion of the boundary to the small perturbations within the fluid.  A
 fter some confusion in the 60s\nsee\, e.g. Rice 1969)\, this boundary cond
 ition was thought to have been understood in the 70s (Eversman et al 1972\
 , Tester 1973)\, and is now commonly referred to as the Myers boundary con
 dition.  The boundary condition decided on was that the normal displacemen
 t of\nthe fluid at the boundary is the same as the normal displacement of 
 the boundary.\n\nUnfortunately\, this is not the whole story.  In this tal
 k\, I aim to show why it is not the whole story\, particularly with regard
  to stability.  I will then present an analysis of the effect of a thin\nv
 iscous boundary layer over the wall\, which I hope will take the story a l
 ittle further.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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