Linear stability analysis of time-averaged flow past a cylinder

Abstract

Flow past a circular cylinder looses stability at a Reynolds number,$Re \sim 47$. It has been shown, in the past, that the linear stability analysis (LSA) of the steady state solution can predict not only the critical$Re$, but also the non-dimensional frequency,$St$, of the associated instability. For larger$Re$ the non-linear effects become important and the LSA of the steady-state flow does not predict the correct$St$. It is shown that, in general, the LSA applied to the time-averaged flow can result in useful information regarding its stability. This idea is applied to the$Re=100$ flow past a circular cylinder. The LSA of the time-averaged flow results in the correct value of$St$. Proper Orthogonal (POD) or Karhunen-Lo\'{e}ve (K-L) decomposition of the unsteady flow using the snapshot method is also carried out. The modes from this decomposition are compared to the unstable modes computed using the LSA.