Linear stability and optimal perturbations of a trailing vortex pair in ground effect*

The stability characteristics of a trailing vortex pair interacting with its image in the ground plane is formulated analytically and studied numerically. The theoretical framework models the inviscid interaction between a counter-rotating pair of perturbed finite-core vortices near a planar surface. The stability equations are derived by matching the Biot-Savart integrals of the vortices with their temporally-varying position vectors, which are subject to constraints that represent a ground-image system. The stability problem is then cast into an optimal perturbation analysis to deduce the maximum growth rate for a prescribed disturbance as a function of time and the induced vortex trajectories.