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SUMMARY:Scattering by a periodic array of slits with complex boundaries vi
 a the Wiener--Hopf method - Peter Baddoo (University of Cambridge)
DTSTART:20190823T143000Z
DTEND:20190823T150000Z
UID:TALK128989@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The interaction of a plane wave with a periodic array of slits
  is an important problem in fluid dynamics\, electromagnetism and solid me
 chanics. In particular\, such an arrangement is commonly used as a model f
 or turbomachinery noise. Previous work has been restricted to the case whe
 re the slits possess a Neumann (no-flux) boundary condition.   Consequentl
 y\, in this work we consider "complex" boundary conditions including Robin
  (e.g. compliance)\, oblique derivatives (porosity) and generalised Cauchy
  conditions (impedance). We employ generalised derivatives and Fourier tra
 nsforms to recast the Helmholtz equation as an integral equation amenable 
 to the Wiener--Hopf method. Although the slits are of finite length\, we a
 re able to avoid a true matrix Wiener--Hopf problem by assuming the struct
 ure of the scattered field.   Since the Wiener--Hopf kernel is meromorphic
 \, the Fourier transform may be inverted analytically to obtain the scatte
 red field. The Wiener--Hopf analysis shows that an effect of modifying the
  boundary conditions is to perturb the zeros of the kernel function\, whic
 h correspond to the "duct modes" in the near field. In aeroacoustic applic
 ations\, this result shows that blade porosity can dramatically reduce the
  unsteady lift\, which has implications for turbomachinery design.  <br><b
 r><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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