Nonparallel linear stability analysis of unconfined vortices

Abstract

Parabolized stability equations [F. P. Bertolotti, Th. Herbert, and P. R. Spalart, J. Fluid. Mech. 242, 441 (1992)] have been used to study the stability of a family of swirling jets at high Reynolds numbers whose velocity and pressure fields decay far from the axis as rm−2 and r2(m−2), respectively [M. Pérez-Saborid, M. A. Herrada, A. Gómez-Barea, and A. Barrero, J. Fluid. Mech. 471, 51 (2002)]; r is the radial distance and m is a real number in the interval 0<m<2. Results show that the nonparallel effects of the basic flow play an important role in the development of both axisymmetric and nonaxisymmetric unstable perturbations upstream of the vortex breakdown station. A complementary local nonparallel analysis shows the convective nature of these instabilities. Therefore, a criterion based on the transition from convective to absolute instabilities cannot be applied to predict the vortex breakdown of this kind of swirling jets. On the contrary, the failure of the quasicylindrical approximation used to compute the downstream evolution of the basic flow gives a clear breakdown criterion based on the catastrophic transition between slender and nonslender flows.