Instabilities arising due to the interaction of a circular jet with a bounding rigid circular shell

Author: Green, MR

Source: Quarterly Journal of Mechanics and Applied Mathematics, Volume 52, Number 1, February 1999 , pp. 141-160(20)

Publisher: Oxford University Press

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Abstract:

A circular jet of uniform axial velocity, in inviscid incompressible flow, is placed within a bounding rigid circular shell, resulting in a strongly interacting field. A given wavenumber in the axial direction is taken and a dispersion relation relating the frequency and wavenumber for a given mode, along with velocity potentials, are found for the case of a centred and a displaced jet. The centred jet problem can be solved exactly, however, when displaced it is necessary to invoke a long-wave assumption which allows a formulation in terms of bipolar coordinates. Asymptotic forms are derived for the dispersion relation for small displacements and large shell radius and compared with the results for a centred jet and with those of a free jet.

Document Type: Research article

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