Leblanc, S. and Le Duc, A. (2005) The unstable spectrum of swirling gas flows. Journal of Fluid Mechanics, 537, pp. 433-442.
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The asymptotic structure of the discrete spectrum of a compressible inviscid swirling flow with arbitrary radial distributions of density, pressure and velocity is described for disturbances with large wavenumbers. It is shown that discrete eigenmodes are unstable when a criterion derived by Eckhoff & Storesletten (1978) is satisfied. In general, these modes are characterized by a length scale of order exp(-3ln(m)/4) where m is the azimuthal wavenumber of the disturbance and tends to infinity. They have a spatial structure similar to the incompressible modes obtained by Leibovich & Stewartson (1983). In the particular case of solid-body rotation with a positive gradient of entropy, the unstable discrete spectrum contains modes which scale with exp(-ln(m)/2). If the modes are localized near a solid boundary, they scale with (exp(-3ln(m)/4).
|Title:||The unstable spectrum of swirling gas flows|
|Journal or Publication Title:||Journal of Fluid Mechanics|
|In ISI Web of Science:||Yes|
|Page Range:||pp. 433-442|
|Keywords:||Hydrodynamic stability, swirling, compressible, WKB, asymptotic expansion, continuous spectrum, normal modes, discrete spectrum|
|HGF - Research field:||Aeronautics, Space and Transport (old)|
|HGF - Program:||Aeronautics|
|HGF - Program Themes:||Rotorcraft|
|DLR - Research area:||Aeronautics|
|DLR - Program:||L RR - Rotorcraft Research|
|DLR - Research theme (Project):||L - Flight Physics|
|Location:||Köln-Porz , Braunschweig , Göttingen|
|Institutes and Institutions:||Institute of Aerodynamics and Flow Technology|
|Deposited By:||Claudia Grant|
|Deposited On:||10 Jan 2006|
|Last Modified:||14 Jan 2010 19:54|
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