Triadic Mode Interaction and Scaling-Law Breakdown in the Cylinder Wake: A CFD-Driven Reduced-Order Model

In the field of fluid mechanics, the classical weakly nonlinear theory that follows square-root Landau scaling law near onset predicts the amplitude of vortex shedding that occurs due to the increase of Reynolds number, where the wake behind the cylinder exhibits a periodic vortex shedding transitioned from the steady flow. However, through computational and experimental observations, the scaling law does not fully apply to situations when the Reynolds number increases beyond the weakly nonlinear regime but instead rapidly breaks down. Such discrepancy is an open problem that is yet to be solved. This report investigates the nonlinear mechanisms which are responsible for the amplitude saturation and the collapse of the classical scaling law. By combining theoretical modal analysis with the combination of CFD-derived time-series data, it allow us to observe how wake dynamics cannot be described by a single Hopf mode. The flow is governed by three fundamental modes: primary oscillatory mode, second harmonic mode, and mean-flow distortion. This study provides a new FFT-based amplitude extraction method, where we can quantitatively measure three modal components and construct a reduced-order model (ROM) that accurately captures saturation, harmonic generation, and frequency trends.