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Absolute and convective instability character of slender viscous vortices

Phys. Fluids 12, 1062 (2000); doi:10.1063/1.870361

Issue Date: May 2000

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Xie-Yuan Yin, De-Jun Sun, and Ming-Jun Wei
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China

Jie-Zhi Wu
University of Tennessee Space Institute, Tullahoma, Tennessee 37388
State Key Laboratory for Turbulence Research, Peking University, Beijing 100871, People's Republic of China
Motivated by the need for effective vortex control, the character of absolute and convective instabilities (AI/CI) of incompressible and high-Mach number slender vortices with axial-velocity deficit is studied. Attention is focused on the disturbance modes which lead to the maximum absolute growth rate, and their dependence on flow conditions such as axial-flow profile, Reynolds number, and Mach number. A significant difference between the AI/CI and temporal-instability characters of the vortices occurs as the axial velocity deficit reduces. These theoretical results are applied to the flow region where vortex breakdown happens. It is found that the breakdown region is absolutely unstable, where waves are dominated by the spiral disturbance with lowest azimuthal wave number, in reasonable agreement with measurement. ©2000 American Institute of Physics.
History: Received 3 February 1999; accepted 28 December 1999
Permalink: http://link.aip.org/link/?PHFLE6/12/1062/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.20.-k
    Fluid dynamics Hydrodynamic stability
  • 47.32.Cc
    Fluid dynamics Rotational flow and vorticity Vortex dynamics
  • 47.27.Te
    Fluid dynamics Turbulent flows, convection, and heat transfer Convection and heat transfer
  • 47.40.-x
    Fluid dynamics Compressible flows; shock and detonation phenomena
  • YEAR: 2000

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ISSN:
1070-6631 (print)   1089-7666 (online)
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