Mathematical and numerical treatment of instabilities of non-axisymmetric confined vortices under the Dirichlet boundary conditions

This paper is concerned with an efficient analytical and numerical method for computing instability bounds of non-axisymmetric confined vortices. We propose a new approach based on a recently mathematical method of meshless collocation, when the shifted orthogonal Chebyshev base is adapted to satisfy the boundary conditions. Appropriately modified Tollmien-Schlichting modes used for the linear stability analysis offer the main advantage of dealing with a steady perturbation model of a confined vortex that leads to a variety of information describing the behavior of the full three-dimensional unsteady flow.