Relating Skewness and Fourier Harmonics in Low Reynolds Number Wake Flow*

In the study of simple, laminar wake flows, it is observed that multiple Fourier modes are necessary to accurately describe the wake's dynamics, even though these flows exhibit perfect periodicity with a single period. The spatial configuration of these modes shows distinct patterns: odd harmonics exhibit a peak at the wake center, while even harmonics display a zero crossing at the same location. Our research reveals that these harmonic structures are intrinsically linked to the skewness present in the wake's vorticity field. By employing simple mathematical models and analyzing laminar wake flow data, we establish that data with non-zero skewness require multiple Fourier modes to represent the flow dynamics, even for signals that are perfectly periodic. Furthermore, we elucidate the mathematical relationship between the skewness of the vorticity field and the phases of the corresponding Fourier modes, demonstrating how these phase shifts influence the spatial distribution of the Fourier modes. This work provides new insights into the fundamental mechanisms governing wake flows and underscores the significance of skewness in fluid dynamics analysis.