THE EFFECTS OF VISCOSITY ON THE STABILITY OF A TRAILING-LINE VORTEX IN COMPRESSIBLE FLOW

We consider the effects of viscosity on the inviscid stability of the Batchelor [J. Fluid Mech. 20, 645 (1964)] vortex in a compressible flo w. The problem is tackled asymptotically, in the limit of large a (str eamwise and azimuthal) wavenumbers, together with large Mach numbers. This problem, with Viscous effects neglected, was discussed in Stott a nd Duck [J. Fluid Mech. 268, 323 (1994)]. The authors found that the n ature of the solution passes through different regimes as the Mach num ber increases, relative to the wave number. This structure persists wh en viscous effects are included in the analysis. In the present study, as in that mentioned above, the mode present in the incompressible ca se ceases to be unstable at high Mach numbers and a center mode forms, whose stability characteristics are determined primarily by condition s close to the vortex axis. We find generally that viscosity has a sta bilizing influence on the flow, whilst in the case of center modes, vi scous effects become important at much larger Reynolds numbers than fo r the first class of disturbance. (C) 1995 American Institute of Physi cs.