Characterization of wake behind a cylinder using spectral proper orthogonal decomposition and integral bispectrum

Characterizing nonlinear interactions in unsteady flow fields is often challenging, particularly when multiple competing frequencies are present. In the present work, a combined methodology based on spectral proper orthogonal decomposition (SPOD) and integral bispectral analysis is employed to investigate nonlinear flow field dynamics in the wake of a circular cylinder subjected to periodic forcing. Two types of perturbations are considered: asymmetric forcing produced by rotational oscillation of the cylinder and symmetric forcing produced by inline oscillation. Numerical simulations are performed for Reynolds numbers in the range of 100–200, and velocity field data are analyzed using SPOD to identify dominant coherent structures and their associated frequencies. The nonlinear interactions among coherent flow structures are quantified using the integral measure of the bispectrum, which enables the identification of triadic frequency coupling in the flow field. The analysis reveals distinct differences between lock-on and non-lock-on shedding regimes. In the non-lock-on regime, triadic interactions occur primarily between the excitation frequency and the natural vortex shedding frequency, whereas in the lock-on regime, higher harmonics arise primarily through nonlinear self-interaction of the excitation frequency. For rotational oscillation, the dominant flow frequency in the lock-on region coincides with the excitation frequency, whereas for inline oscillation, the dominant response occurs at sub-harmonic frequencies. The SPOD mode shapes effectively capture the transition between lock-on and non-lock-on regimes and provide physical insight into the governing flow mechanisms. Overall, the combined SPOD-bispectral framework proves to be a powerful tool for identifying coherent structures involved in nonlinear interactions and for understanding the underlying dynamics of forced bluff-body wakes.