Vorticity waves in problems of hydrodynamic stability |
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Authors: | M N Zakharenkov |
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Institution: | (1) Department Earth and Ocean Sciences, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada |
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Abstract: | The known problem of flow transition near a circular cylinder at Re = 40 from a symmetrical form to the Karman vortex street
can be considered as the problem of vortex wave development and intensification. Development of three bundles of vortex waves
of low intensity is observed in a wake of a cylinder; these bundles are easily visualized as the structures of relative vorticity
$
\bar \Omega
$
\bar \Omega
= Ω(t
1) − Ω(t
0): difference of vorticity Ω at two time moments, t
0 being fixed. In the field of $
\bar \Omega
$
\bar \Omega
the alternating structure of quadrupoles is characterized by linear parameter l = h/d: the ratio of the width of the central bundle of vortex waves to the distance between the centers of quadrupoles of a “single
sign”. When l = 0.281 is achieved, which coincides with the value of the same parameter of a stable Karman street, the transition from
symmetrical streamlining by viscous incompressible liquid to the vortex street occurs. |
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Keywords: | |
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