On the viscous modes of instability of a trailing line vortex

Abstract

A viscous linear stability analysis of a trailing line (Batchelor) vortex is presented. Employing a staggered Chebyshev spectral collocation technique, very accurate results were obtained. The destabilising role of viscous forces has been shown to produce two types of viscous instability modes. These viscous disturbances consist of an axisymmetric mode and an asymmetric mode. Both disturbances are long-wave instabilities with maximum growth rates which are orders of magnitude smaller than the inviscid modes which have been found by others. Comparison with experimental results and condensation trail observations are found to be in good qualitative agreement with the present study.