Experimental and theoretical investigation of the stability of a linear vortex with a deformed core

The study is concerned with a linear vortex deformed in such a way that the flow lines are similar in shape to ellipses with small eccentricities. The instability of such a flow with respect to the perturbations associated with the bending of the axis of rotation is identified and investigated experimentally. A mathematical model of the instability is constructed on the basis of the linear theory combined with the perturbation theory in terms of the smallness of deformation. In accordance with the model proposed here, the mechanism of the observed instability is identical to the instability of a finite-amplitude wave in the three-wave interaction.