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We consider the effects of viscosity on the inviscid stability of the Batchelor vortex in a compressible flow. The problem is tackled asymptotically, in the limit of large (streamwise and azimuthal) wavenumbers, together with large Mach numbers. Previous studies, with viscous effects neglected, found that the nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumber. This structure persists when viscous effects are included in the analysis. In the present study 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, while in the case of center modes, viscous effects become important at much larger Reynolds numbers than for the first class of disturbance.

Born in Manchester, and a bookbinder by trade, Benjamin Stott was an active trade unionist and member of the Chartist movement. Songs of the Millions, a suite of seventeen short poems in which Stott experimented with a variety of forms, was his best known work. Poverty and famine, injustice and the brutality of the police and their spies, solidarity and resistance are his themes. A devout militant Christian, Stott saved some of his most powerful words for the clergy who urged the working masses to wait patiently in poverty for their reward in the next world. The miscellaneous poems that complete this collection, include Stott's long ode to the Independent Order of Oddfellows Manchester Unity, which remains the largest fraternal organization of its kind in the United Kingdom. (Phil Benson)