Spectral Analysis of Chaos Transition in a Dynamic System: Application to Backward Facing Step Flow in Mixed Convection

This work focuses on the study of the transition from steady to chaotic behavior in mixed convection flow over a backward-facing step. Direct numerical simulations are performed in a two-dimensional horizontal channel of expansion ratio ER = 2 at step level. The effects of the temperature difference between the heated bottom wall and the inflow temperature are investigated by keeping constant the Richardson number at 1. The covered range of Grashof and Reynolds numbers is respectively 3.31 × 10⁴ ≤ Gr ≤ 2.72 × 10⁵ and 182.03 ≤ Re ≤ 521.34. The thermodynamic instabilities which cause the onset of unsteady flow are described in detail. A spectral and phase portrait analysis of the temperature time series allows us to observe that the transition from steady to chaotic flow occurs by period-doubling bifurcations.