Abstract

A state variable procedure has been developed that can be used to study the influence of non-equilibrium pressure gradient forces on the stability of axial trailing-line vortices. In addition to previously-developed modified Navier-Stokes equations, a Poisson equation governing perturbation pressure fluctuations was developed that is of the same differential order as the velocity perturbation equations. A normal mode analysis was utilized to formulate the small perturbations in the vortical flow with radially-varying amplitudes, producing a system of ordinary differential equations governing the evolution of the normal modes in the flow. This has resulted in a more-consistent approach for analyzing the stability and unsteady behavior of these axial vortices.

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