The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer

We test the applicability of the local isotropy hypothesis to surface-layer turbulent flow; turbulent velocities measured with a three-dimensional sonic anemometer are used for this purpose, and the predictions of local isotropy for the spectra, second- and third-order structure functions are assessed against measured data. Also investigated are scale interactions via the correlation between velocities and velocity increments, and the ability of isotropic spectral models to reproduce measured spectra. In general, second-order structure functions display a narrower inertial range than the corresponding spectra; both the known effects of path-averaging and the predictions of the spectral models show that the sonic anemometer is unable to resolve the whole inertial range, even at a measurement frequency of 60 Hz. We confirm previous results that unstable runs tend to be more isotropic, but find that, for third-order statistics, isotropy does not hold well for the data analysed. Turbulence intensity, and not atmospheric stability, plays a determining role on the correlation coefficient between velocities and velocity increments. The observed anisotropic behaviour has important implications for the calculation of the turbulent kinetic energy dissipation rate from Kolmogorov's four-fifths law, whose estimates are consistently smaller than those from the inertial range of the spectrum or the structure functions.