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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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Abstract
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).
| Item URL in elib: | https://elib.dlr.de/18895/ | |||||||||
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| Document Type: | Article | |||||||||
| Additional Information: | LIDO-Berichtsjahr=2005, | |||||||||
| Title: | The unstable spectrum of swirling gas flows | |||||||||
| Authors: |
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| Date: | 2005 | |||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | |||||||||
| Refereed publication: | Yes | |||||||||
| Open Access: | No | |||||||||
| Gold Open Access: | No | |||||||||
| In SCOPUS: | No | |||||||||
| In ISI Web of Science: | Yes | |||||||||
| Volume: | 537 | |||||||||
| Page Range: | pp. 433-442 | |||||||||
| Status: | Published | |||||||||
| 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 (old) | |||||||||
| DLR - Research area: | Aeronautics | |||||||||
| DLR - Program: | L RR - Rotorcraft Research | |||||||||
| DLR - Research theme (Project): | L - Flight Physics (old) | |||||||||
| Location: | Köln-Porz , Braunschweig , Göttingen | |||||||||
| Institutes and Institutions: | Institute of Aerodynamics and Flow Technology | |||||||||
| Deposited By: | Grant, Claudia | |||||||||
| Deposited On: | 10 Jan 2006 | |||||||||
| Last Modified: | 14 Jan 2010 19:54 |
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