ECCOMAS 2024

Dynamical System analysis of irregular flow around two square cylinders

  • Sahu, Sidhartha (Imperial College London)
  • Papadakis, George (Imperial College London)

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We investigate the dynamics of the irregular flow over two side-by-side square cylinders at a Reynolds Number of 200, and a gap ratio of 1. For this set of parameters, the flow is chaotic, see [1]. More specifically, we linearise the Navier-Stokes equations around the unsteady chaotic trajectory of the system and study the tangent space. We identify the characteristic Lyapunov exponents (LEs) of the flow using a Gram-Schmidt-based periodic orthonormalization algorithm [2]. Furthermore, we also obtain the Covariant Lyapunov Vectors (CLVs) of the flow using the dynamical algorithm proposed by Ginelli et al [3]. The CLVs correspond to the eigenvalues and eigenvectors of a typical linear stability analysis; the latter however is performed on a steady base flow, but in our analysis, we have a time-varying base flow. For unsteady flows, analysis of a time-varying tangent space is physically more meaningful than performing linear stability analysis on a time-average base flow.