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 flow. The problem is tackled asymptotically, in the limit of large a (streamwise and azimuthal) wavenumbers, together with large Mach numbers. This problem, with Viscous effects neglected, was discussed in Stott and Duck [J. Fluid Mech. 268, 323 (1994)]. The authors found that the nature of the solution passes through different regimes as the Mach number increases, relative to the wave number. This structure persists when viscous effects are included in the analysis. In the present study, as in that mentioned above, the mode present in the incompressible case ceases to be unstable at high Mach numbers and a center mode forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find generally that viscosity has a stabilizing influence on the flow, whilst in the case of center modes, viscous effects become important at much larger Reynolds numbers than for the first class of disturbance. (C) 1995 American Institute of Physics.