The goal of this thesis is to study the stability of a vortex, which has been called the m-Shape vortex, that takes place in some Formula 1 cars. This vortex has been obtained from Computational Fluid Dynamics data. It is well known that the Navier- Stokes equations that rule the motion of uids are still unsolved analytically for arbitrary geometries. Therefore, the approach taken in this study is to discretise the geometry with an adequate mesh in order to study the hydrodynamic stability of flows performing firstly a direct numerical simulation and secondly a direct stability analysis of the linearised Navier-Stokes equations. For doing so, spectral/hp elements methods are used. Firstly, a study on the stability of the Bachelor vortex is done. As the Bachelor vortex has been studied previously, this first study validates the subsequent results and introduces the methodology that is going to be used. Moreover, the m-Shape vortex that has an important role the development of the mentioned cars is studied using the same approach.

Outgoing