Journal of Fluid Mechanics


Smooth transonic flow in an array of counter-rotating vortices

G. K. O'REILLY a1c1 and D. I. PULLIN a1
a1 Graduate Aeronautical Laboratories, 105-50, California Institute of Technology, Pasadena, CA 91125, USA

Article author query
o'reilly gk   [Google Scholar] 
pullin di   [Google Scholar] 


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.

(Received July 28 2004)
(Revised October 7 2004)

c1 Author to whom correspondence should be addressed: