A numerical simulation of the transition to turbulence in a two-dimensional flow

A numerical simulation of the transition to turbulence is performed using a finite element method. The unsteady Navier-Stokes equations are discretized using a standard Galerkin approximation and a loading strategy for increasing the Reynolds number. The numerical results are then analysed at different Reynolds numbers showing a transition from a steady-state solution to a weakly chaotic one. Phase space diagrams are presented showing the presence of strange attractors. The dimension and Lyapunov's exponents of these attractors are computed and compared with existing results in the literature.