Can frequencies be predicted from mean flows? RZIF for thermosolutal convection (INVITED)

Abstract eng:
Motivated by studies of the cylinder wake, in which the vortex-shedding frequency can be obtained from the mean flow, we study 2D thermosolutal convection driven by opposing thermal and solutal gradients, in which branches of traveling waves (TW) and standing waves (SW) are created simultaneously by a Hopf bifurcation. We find that the TW of thermosolutal convection have the RZIF property, meaning that linearization about the mean fields of the traveling waves yields an eigenvalue whose real part is almost zero and whose imaginary part corresponds very closely to the nonlinear frequency. In contrast, this is not the case for the SW. This difference can be attributed to the fact that the temporal power spectrum for the TW is peaked, while that of the SW is broad, and we show why this is so. We demonstrate that the frequency of any quasi-monochromatic oscillation can be predicted from its temporal mean.

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