Journal of Fluid Mechanics

Steady compressible vortex flows: the hollow-core vortex array

K.  Ardalan a1, D. I.  Meiron a1 and D. I.  Pullin a2
a1 Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
a2 Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA

Article author query
ardalan k   [Google Scholar] 
meiron di   [Google Scholar] 
pullin di   [Google Scholar] 


We examine the effects of compressiblity on the structure of a single row of hollowcore, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M[infty infinity] = q[infty infinity]/c[infty infinity], and the speed ratio, a = q[infty infinity]/qv, where qv is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M[infty infinity], is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.

(Received December 28 1994)
(Revised June 26 1995)