A note on the effects of viscosity on the stability of a trailing-line vortex

The linear stability of the Batchelor (1964) vortex is investigated. Particular emphasis is placed on modes found recently in a numerical study by Khorrami (1991). These modes have a number of features very distinct from those found previously for this vortex, including (i) exhibiting small growth rates at large Reynolds numbers and (ii) susceptibility to destabilization by viscosity. In this paper these modes are described using asymptotic techniques, producing results which compare very favourably with fully numerical results at large Reynolds numbers.