The instability of a vortex tube in a weak external shear and strain

Abstract

We investigate the stability of a straight vortex tube of constant vorticity in the presence of external shearing and straining flows orthogonal to the axis of the vortex tube. We find that the tube is unstable at degenerate wavenumbers (i.e., wavenumbers at which two Kelvin wavemodes have the same frequency). The maximum growth rate of the instability is weighted by the sum of the shear magnitude and the strain magnitude. The presence of the shear also shifts the wavenumber of the instability. © 1998 American Institute of Physics.