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Filiz Cagatay
| Speaker: |
Filiz Çağatay (Izmir Institute of Technology) |
| Date: |
Tuesday January 15, 2008
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| Title: |
Hydrodynamic
interaction in rotational flow
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Abstract
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The
interaction of water waves with arrays of vertical cylinders problem
can be solved using diffraction of water waves and addition theorem for
Bessel functions. The linear boundary value problem which is derived
from physical assumptions is used as the approximate mathematical model
for time-harmonic waves. The problem can be solved by using Addition
theorem for Bessel functions.
Limiting case, k approaches 0, known as long wave approximation, is
analyzed using limiting forms of Bessel functions. Vortex-cylinder
interaction is analyzed using a similar technique involving Laurent
series expansions of complex velocity and the Circle Theorem. Vortex
dynamics is analyzed in annular domains, which can conformally be
mapped into infinite domain with two cylinders, using the terminology
of q-calculus.
Finally, the result of vortex-cylinder interaction in annular domain is
transformed into the infinite domain with two cylinders using conformal
mapping.
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