Physical reduced model for the flow past a circular cylinder for $47<$\bf{\emph{Re}}$<100$

The \emph{Reynolds} ($Re=\frac{U.D}{\nu}$) range considered for this study lies within the time-periodic bidimensional r\'{e}gime where any experiment started by its stationary solution should evolve to a stable limit-cycle. This transient oscilatiory ramp starts with the exponential growth of the linear unstable eigenmode and finishes bounded by nonlinear effects with multi-harmonics extra dissipation. The steady solution and the leading eigenmode are numerically obtained using FEM discretization (\emph{Taylor-Hood P2/P1 elements}) and \emph{Arnoldi} iterations, then the nonlinear evolution operator is employed to generate new modes complementing the linear eigenmode up to a given order. The full NSE is then projected onto this physical base (\emph{nonlinear Galerkin projection}) leading to a physical reduced system. This reduced model has a simple framework to track many nonlinear features like meanflow evolution and energy changes between the harmonics, clarifying the nonlinear mechanisms that takes this system to a periodic orbit. Numerical and experimental (\emph{Particle Image Velocimetry}) evidences will be presented at the time of the meeting.