Stability of the Stationary Flow of an Incompressible Liquid

Abstract

The work presents four methods for assessing the stability of stationary vortex structures in multiple continuous regions. First one is based on linearized Navier - Stokes equations using modal analysis. The second method considers non-linear equations and is focused on the stability of the stationary flow at the inner point of the region. The third method is focused on the qualitative analysis of the dependence of an input power, performance and dissipation function. The fourth method is based on the analysis of the potential energy of the flowing liquid. Each of the mentioned methods will be described by a mathematical model, from which it will be possible to assess the influence of boundary conditions and the shape of the area on the mentioned stability.