A short review of experimental findings is given, followed by a theoretical derivation, based on Taylor's hypothesis, of formulas for lateral coherences. It is assumed that the flow is stationary and homogeneous. Explicit formulas are derived assuming an energy spectrum pertaining to the inertial subrange. Even when the last assumption is not fulfilled, there are only four different types of non-zero velocity coherences. These four coherences correspond to the combinations uu, vv, ww, and uv, where u, v, and w are the longitudinal, the transversal, and the vertical component of the turbulent velocity with respect to the direction of the horizontal mean wind velocity U. In the case of small displacements relative to the scale of turbulence, the coherences are shown to be universal functions of the non-dimensional frequency nD/¦U¦, where n is the frequency and D the lateral displacement. It is shown that these theoretical formulas for spectral coherences are in good agreement with atmospheric data. Finally, the role of the scale of the turbulence is discussed.

Lateral coherence in isotropic turbulence and in the natural wind

Buffeting response of long-span cable-supported bridges under skew winds. Part 2: case study

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 lift on an aerofoil in grid-generated turbulence

Direct measurements of buffeting wind forces on bridge decks

Wind speed measurements from the test site at Rutherford Appleton Laboratory have been evaluated with respect to the spatial coherence function. The experimental arrangement provides coherence information for separation distances of 62, 80 and 102 m. These are at least three times greater than the measurement heights of 18 m and 18.7 m. Based on these experimental data and data published in the literature, different theoretical formulations are compared and a new, but simple, model for longitudinal and lateral coherence is proposed. At large separations the turbulent wind field is not isotropic, theoretical models to describe the coherence function for such distances are not available. The new model we propose builds on the classical exponential approach. It takes into account the influence of turbulence intensity and models the angular dependence of horizontal coherence. It is found that, for constant turbulence intensity, the lateral coherence decay becomes independent of the mean wind speed.

Horizontal, Two Point Coherence for Separations Greater Than the Measurement Height

For the purpose of predicting the dynamic response of structures and buildings to turbulent winds, a knowledge of the lateral coherence of the upstream velocity fluctuations is essential. For the special case of isotropic turbulence, the character of the coherence function is deduced from theoretical considerations and a simple method of computing this function from any arbitrary power spectrum is derived. Particular emphasis is placed on the range of validity of simple collapsing parameters, associated with certain spectral models. The theoretical predictions are confirmed by extensive hot-wire measurements taken in grid-generated turbulence. This result facilitates determination of the dynamic response of slender structures to wind loading.

John B. Roberts

Papers

Coherence of Grid-Generated Turbulence