Stability Analysis of Nonlinear Fluid Flows through Mathematical and Computational Approaches

Fluid nonlinear stability is a basic problem in fluid dynamics, which has a great impact in applications to industrial, meteorological, or engineering processes. This paper studies the mathematical and computational methods to analyze the stability of fluid flows governed by the nonlinear equations like Navier-Stokes equations. The transition scenarios, bifurcations and turbulence onset are also investigated by computational simulations. It is shown that combining analytical and numerical approaches improves understanding of flow stability, and thus facilitates predictive modeling of such systems.