O'Reilly, G. and Pullin, D. I. (2003) Structure and stability of the compressible Stuart vortex. Journal of Fluid Mechanics, 493 . pp. 231254. ISSN 00221120. http://resolver.caltech.edu/CaltechAUTHORS:20111025105659702

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Abstract
The structure and two and threedimensional stability properties of a linear array of compressible Stuart vortices (CSV; Stuart 1967; Meiron et al. 2000) are investigated both analytically and numerically. The CSV is a family of steady, homentropic, twodimensional solutions to the compressible Euler equations, parameterized by the freestream Mach number M_∞, and the mass flux _ inside a single vortex core. Known solutions have 0 < M_∞ < 1. To investigate the normalmode stability of the generally spatially nonuniform CSV solutions, the linear partialdifferential equations describing the time evolution of small perturbations to the CSV base state are solved numerically using a normalmode analysis in conjunction with a spectral method. The effect of increasing M_∞ on the two main classes of instabilities found by Pierrehumbert & Widnall (1982) for the incompressible limit M_∞ → 0 is studied. It is found that both two and threedimensional subharmonic instabilities cease to promote pairing events even at moderate M_∞. The fundamental mode becomes dominant at higher Mach numbers, although it ceases to peak strongly at a single spanwise wavenumber. We also find, over the range of ε investigated, a new instability corresponding to an instability on a parallel shear layer. The significance of these instabilities to experimental observations of growth in the compressible mixing layer is discussed. In an Appendix, we study the CSV equations when ε is small and M_∞ is finite using a perturbation expansion in powers of ε. An eigenvalue determining the structure of the perturbed vorticity and density fields is obtained from a singular Sturm–Liouville problem for the streamfunction perturbation at O(ε). The resulting smallamplitude steady CSV solutions are shown to represent a bifurcation from the neutral point in the stability of a parallel shear layer with a tanhvelocity profile in a compressible inviscid perfect gas at uniform temperature.
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Additional Information:  © 2003 Cambridge University Press. Received 30 December 2002 and in revised form 20 May 2003. This work was supported by the Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (ASCI/ASAP) under subcontract no. B341492 of DOE contract W7405ENG48.  
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Record Number:  CaltechAUTHORS:20111025105659702  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20111025105659702  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  27406  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  26 Oct 2011 15:54  
Last Modified:  26 Dec 2012 14:19 
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