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

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

Publication date: 1999-02-01

More about this publication?

• The Quarterly Journal of Mechanics and Applied Mathematics publishes original research articles on the application of mathematics to the field of mechanics interpreted in its widest sense. In addition to traditional areas, such as fluid and solid mechanics, the editors welcome submissions relating to any modern and emerging areas of applied mathematics.

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