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Compressible Vortices and Shock-Vortex Interactions


O'Reilly, Gerard Kieran (2004) Compressible Vortices and Shock-Vortex Interactions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FGJD-0Z31.


Secondary instabilities on the organized, spanwise, vortical structures in incompressible shear layers, play an important role in generating the onset of three-dimensional turbulence in such flows. The effect of increasing compressibility on these instabilities is examined by using the compressible Stuart vortex as a model for a compressible shear layer. It is found that both two- and three-dimensional subharmonic instabilities cease to promote pairing events even at moderate free stream Mach numbers. The fundamental mode becomes dominant as the free stream Mach number is increased, and a new instability corresponding to an instability on a parallel shear layer is observed. The interaction of a shock with a compressible vortex may be viewed as a simplified model of the general interaction of a shock with the coherent structures in a turbulent flow field. An approximate theory for computing shock-compressible-vortex interactions is developed, based on Ribner (1954). The problem of convection of a frozen patern of vorticity, dilatation, temperature and entropy through a planar shock wave is considered. The refraction and modification of the upstream disturbances into the three basis modes permitted by the linear Euler equations is derived, as well as the perturbation to the shock wave. This theory is used to compute approximate post-shock states corresponding to shock-CSV interactions, a model for shock shear layer interactions. The method is verified by comparing its approximate post-shock fields with those computed explicitly using AMROC, a finite difference, AMR-WENO code. Finally, numerical solutions corresponding to a compressible analogue of the Mallier and Maslowe vortex (a periodic array of counter-rotating vortices) are presented. These solutions admit the existence of large regions of smooth supersonic flow, and could potentially be used to model the counter-rotating vortices arising from the single- and multi-mode Richtmyer-Meshkov instability.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:compressible turbulence
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Pullin, Dale Ian
Thesis Committee:
  • Pullin, Dale Ian (chair)
  • Leonard, Anthony
  • Meiron, Daniel I.
  • Hornung, Hans G.
  • Shepherd, Joseph E.
Defense Date:30 April 2004
Record Number:CaltechETD:etd-05262004-145030
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2082
Deposited By: Imported from ETD-db
Deposited On:27 May 2004
Last Modified:04 Feb 2021 00:00

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