Undergraduate Mathematical Sciences Seminar
Thursday, 6 April, 2006, 12:30--1:50pm
Absolute and convective instability of the two-dimensional wake
Stefania Scarsoglio
University of Washington Applied Mathematics visiting Graduate Student
A linear stability study for two-dimensional non-parallel flows in the intermediate and far wake behind a circular body is here presented. The hydrodynamic stability analysis is developed within the linear theory of normal modes. Through a synthetic perturbative hypothesis, it is observed the behavior of small oscillations applied to the base flow. An analytical expression of the base flow according to Navier- Stokes model is given by an asymptotic expansion which considers non-parallelism effects. As the system is slowly evolving, a spatiotemporal multiscaling approach is applied to the base flow and then to the stability analysis. In this way, we can evaluate how weakly non-parallel flow assumption influences the behavior of the stability characteristics. An eigenfunction and eigenvalue asymptotic analysis for the far wake is then included, which is in excellent agreement with the complete problem.