No abstract

Oftentimes, turbulent flows exhibit a high-frequency turbulent component developing on a strong low-frequency periodic motion. In such cases, the low-frequency motion may strongly influence the spatio-temporal features of the high-frequency component. A typical example of such behaviour is the flow around bluff bodies, for which the high-frequency turbulent component, characterized by Kelvin–Helmholtz structures associated with thin shear layers, depends on the phase of the low-frequency vortex-shedding motion. In this paper, we propose extended versions of spectral proper orthogonal decomposition (SPOD) and of resolvent analysis that respectively extract and reconstruct the high-frequency turbulent fluctuation field as a function of the phase of the low-frequency periodic motion. These approaches are based on a quasi-steady (QS) assumption, which may be justified by the supposedly large separation between the frequencies of the periodic and turbulent components. After discussing their relationship to more classical Floquet-like analyses, the new tools are illustrated on a simple periodically varying linear Ginzburg–Landau model, mimicking the overall characteristics of a turbulent bluff-body flow. In this simple model, we in particular assess the validity of the QS approximation. Then, we consider the case of turbulent flow around a squared-section cylinder at a Reynolds number of $Re=22\,000$ , for which we show reasonable agreement between the extracted spatio-temporal fluctuation field and the prediction of QS resolvent analysis at the various phases of the periodic vortex-shedding motion.

The linear stability of a typical aeroelastic section, consisting in a rectangular plate mounted on flexion and torsion springs, is revisited here for low-Reynolds-number incompressible flows. By performing global stability analyses of the coupled fluid-solid equations, we find four types of unstable modes related to different physical instabilities and classically investigated with separate flow models: coupled-mode flutter, single-mode flutter, and static divergence at high reduced velocity U* and vortex-induced vibrations at low U*. Neutral curves for these modes are presented in the parameter space composed of the solid-to-fluid mass ratio and the reduced velocity. Interestingly, the flutter mode is seen to restabilize for high reduced velocities thus leading to a finite extent flutter region, delimited by low-U* and high-U* boundaries. At a particular low mass ratio, both boundaries merge such that no flutter instability is observed for lower mass ratios. The effect of the Reynolds number is then investigated, indicating that the high-U* restabilization strongly depends on viscosity. The global stability results are compared to a statically calibrated Theodorsen model: if both approaches converge in the high mass ratio limit, they significantly differ at lower mass ratios. In addition, the Theodorsen model fails to predict the high-U* restabilization of the flutter mode.