The three-dimensional effects of turbulence cannot be neglected when the spanwise wavelength of the incident turbulence is not effectively infinite with respect to the chord, which may invalidate the strip assumption. Based on three-dimensional theory, a general approach, expressed in terms of a two-dimensional Fourier transform of the correlation of the buffeting force, is proposed to identify the two-wavenumber spectrum and aerodynamic admittance of the lift force on an aerofoil. It is essential that the approach presented can be validated in wind tunnel experiments. The coherence of the lift force on an aerofoil in grid-generated turbulence is obtained by simultaneous measurements of unsteady surface pressures around several chordwise strips on a stiff sectional model, which controls the accuracy of results. For the purpose of the Fourier transform, three empirical coherence models of the lift force are presented to fit the experimental results. Compared with the linearized theory, the two-wavenumber aerodynamic admittance can describe well the pressure distribution and the pattern of energy transition in an isotropic turbulence field. Thus, the failure mechanism of the traditional strip assumption can be demonstrated explicitly. In addition, the results obtained also validate the theory proposed by Graham (Aeronaut. Q., vol. 21, 1970, pp. 182–198;Aeronaut. Q., vol. 22, 1971, pp. 83–100). The present approach can be extended to study the three-dimensionality of the buffeting force on line-like structures with arbitrary cross-configurations, such as long-span bridges and high-rise buildings.

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.