Numerical and asymptotic flow stability analysis of vortex structures

Abstract

Stability problem of an axisymmetric swirling flow of a viscous incompressible fluid with respect to nonaxisymmetric perturbations is considered. The system of ordinary differential equations for the amplitude functions is solved numerically by the Runge-Kutta method and orthogonalization procedure. Solutions of equations for perturbations at the neighborhood of singular points are obtained by the Frobenius method. The maximum of amplification coefficients and phase velocities of five unstable modes are calculated.