Taylor’s hypothesis and two-point coherence measurements

Abstract

Experimentally obtained time coherence has traditionally been interpreted as streamwise one-dimensional spatial coherence through Taylor’s hypothesis. We calculate corrections to the highwavenumber part of the coherence to account for the errors caused by the deviation from Taylor’s hypothesis in high-intensity turbulent flows. The small-scale turbulence is assumed to be frozen and convected by a fluctuating convection velocity. Both Lumley’s two-term approximation and the Gaussian approximation are used in the calculations. In general, we find that the coherence for crossstream separations is significantly overestimated by the direct use of Taylor’s hypothesis, the error increasing with wavenumber; that for streamwise separations is underestimated. The analyses are compared with cross-stream coherence measurements in the atmospheric surface layer. Our results indicate that predictions from Lumley’s approximation yield better agreement with experimental data for cross-stream separations than those from the Gaussian model. Our study suggests that reliable measurement of two-point spatial coherence can be achieved only for scales not too small compared to the sensor separation.