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    • Aa
    • Aa
  • Journal of Fluid Mechanics, Volume 524
  • February 2005, pp. 197-206

Smooth transonic flow in an array of counter-rotating vortices

  • G. K. O'REILLY (a1) and D. I. PULLIN (a1)
  • DOI:
  • Published online: 01 February 2005

Numerical solutions to the steady two-dimensional compressible Euler equations corresponding to a compressible analogue of the Mallier & Maslowe (Phys. Fluids, vol. A 5, 1993, p. 1074) vortex are presented. The steady compressible Euler equations are derived for homentropic flow and solved using a spectral method. A solution branch is parameterized by the inverse of the sound speed at infinity, $c_{\infty}^{-1}$, and the mass flow rate between adjacent vortex cores of the corresponding incompressible solution, $\epsilon$. For certain values of the mass flux, the solution branches followed numerically were found to terminate at a finite value of $c_{\infty}^{-1}$. Along these branches numerical evidence for the existence of extensive regions of smooth steady transonic flow, with local Mach numbers as large as 1.276, is presented.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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