Spatial-temporal harmonic resolvent analysis of asymmetric bluff-body wakes

We extend the use of resolvent analysis for base flows that exhibit both temporal and spatial periodicity. This allows us to investigate frequency crosstalk and energy transfer across different spatial and temporal scales. We demonstrate this analysis on bluff-body wakes with the presence of periodic vortex shedding. Here, a streamwise slice of the wake downstream of the bluff body is considered as the base flow while assuming spatial periodicity in the streamwise direction, conceptually similar to the traditional parallel flow assumption. First, a transverse slice of a two-dimensional wake downstream a circular cylinder is considered, where the interaction between the fundamental frequency and its harmonics are identified. The analysis is also applied to a spanwise asymmetric wake of a finite-span wing at 10$^circ$ angle of attack, where only the frequency-wavenumber combinations that result in the same phase velocity for the perturbations are considered. This identifies the interactions between tip vortex and the wake at different time and space scales.