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Spectral analysis and coherence of aerodynamic lift on rectangular cylinders in turbulent flow

The goal of the present work is to derive the closed-form expressions of coherence and admittances to describe the spatial distribution of lift on rectangular cylinders in turbulent flow, which can be used to investigate the three-dimensional effects of turbulence. The coherence of the three-dimensional aerodynamic admittance (3D AAF), which takes into full account the spanwise variations in the vertical velocity fluctuations, is introduced to assess the validity of the strip assumption. A theoretical coherence model expressed in a double-exponential form is derived starting from the two-wavenumber spectral tensor of the lift on a thin aerofoil in Fourier space, providing us with explicit insight into the coherence of the lift force. Notably, it is an intrinsic property that the lift force on the structure is more strongly correlated than the oncoming flow and 3D AAF. This coherence model is extended to rectangular cylinders by the introduction of three floating parameters into the decay parameters of the 3D AAF. Based on theoretical and experimental investigations, it is shown that the three-dimensional effects of turbulence grow more prominent as the difference between the decay parameters of the 3D AAF and vertical velocity fluctuations decreases. A generalized approach for rapidly deriving the closed-form expressions of the admittances is proposed to study the unsteady behaviour of the lift force and the distortion of the free stream passing through the rectangular cylinders.