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Structure and stability of the compressible Stuart vortex

O'Reilly, G. and Pullin, D. I. (2003) Structure and stability of the compressible Stuart vortex. ASCI Technical Report, ASCI-TR166. . (Unpublished)

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The structure and two- and three-dimensional 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, two-dimensional solutions to the compressible Euler equations, parameterized by the free-stream Mach number M_∞, and the mass flux _ inside a single vortex core. Known solutions have 0 < M_∞ < 1. To investigate the normal-mode stability of the generally spatially non-uniform CSV solutions, the linear partial-differential equations describing the time evolution of small perturbations to the CSV base state are solved numerically using a normal-mode 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 three-dimensional 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 stream-function perturbation at O(ε). The resulting small-amplitude steady CSV solutions are shown to represent a bifurcation from the neutral point in the stability of a parallel shear layer with a tanh-velocity profile in a compressible inviscid perfect gas at uniform temperature.

Item Type:Report or Paper (Technical Report)
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Additional Information: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 W-7405-ENG-48.
Group:Accelerated Strategic Computing Initiative, GALCIT
Funding AgencyGrant Number
Department of Energy (DOE)B341492
Department of Energy (DOE)W-7405-ENG-48
Series Name:ASCI Technical Report
Issue or Number:ASCI-TR166
Record Number:CaltechAUTHORS:20230210-513731000.1
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119222
Deposited By: George Porter
Deposited On:11 Feb 2023 22:11
Last Modified:11 Feb 2023 22:11

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