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Instability of rectangular jets

Published online by Cambridge University Press:  26 April 2006

Christopher K. W. Tam  and
Andrew T. Thies
Christopher K. W. Tam
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, USA
Andrew T. Thies
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, USA
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Abstract

The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. The stability equation for jets of this geometry is non-separable so that the traditional methods of analysis are not applicable. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a centre mode with maximum fluctuations concentrated in the central portion of the jet flow. The centre mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the centre mode would emerge as the dominant instability of the jet.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 425 - 448
Copyright
© 1993 Cambridge University Press

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