Low-frequency characteristics in the wake of a circular disk

Abstract

Numerical simulations of flow over a circular disk have been performed in this study at Re = 250, 300, 3000, and 104. The Fourier spectra analysis of the velocity at different positions suggests that together with the natural vortex-shedding frequency and the shear-layer Kelvin-Helmholtz instability frequency, several much lower frequencies are also detected when the Reynolds number (Re) increases to 300: one is fp ≈ 0.03, another one is fr ≈ 0.02, and its second harmonic is at about 0.04 and a low frequency of about 0.05. Considering the limited time length of the data, time-frequency analysis based on wavelet transform is then performed. It is found that the local frequencies of the amplitude peaks for the large-scale vortex shedding and shear-layer Kelvin-Helmholtz instability vary irregularly with time, indicating that the traditional Fourier analysis of the numerical signals would not be representative. Nevertheless, the low frequencies fp ≈ 0.03 and fr ≈ 0.02 are clearly confirmed. The frequencies of about 0.04 and 0.05 are observed to occur in some time periods but with much weaker magnitude. It is found that the low-frequency signals keep nearly invariant as Reynolds number increases. The physical origins of the low frequencies fp ≈ 0.03 and fr ≈ 0.02 are then investigated. The physical origin of fp ≈ 0.03 is due to a low-frequency pumping motion of the recirculation bubble, and the fr ≈ 0.02 signal is due to a low-frequency modulation in the rotation of the azimuthal location of large-scale vortex shedding (i.e., the changing of the rotation direction). To characterize the low-frequency unsteadiness of the recirculation bubble, the temporal evolution of the low-pass filtered flow field is investigated. It is observed that the pumping motion of the recirculation bubble is associated with the growing and shedding of the large toroidal vortices formed in the bubble, which is closely related to the behavior of the separated shear layer. The separated shear layer rolls up later in the state with longer recirculation bubble, whereas it rolls up earlier in the state with shorter bubble.