The Kolomogorov and Taylor hypotheses revisited

Applications of Kolmogorov's universal equilibrium hypothesis and Taylor's hypothesis to sonic anemometer data spectra are examined. Significant disparities exist between theory and measurement, to include the absence of local isotropy in the atmospheric surface layer inertial subrange and lateral-to-longitudinal velocity spectrum ratio convergence towards 1.0 rather than towards 4/3. Pressure terms of the turbulent kinetic energy equation are not able to completely distribute shear and buoyant energy among the velocity components, particularly in strong diabatic conditions. Taylor's hypothesis does not lead to a correct transform from frequency to wavenumber spectra unless turbulence intensity compensation is used. The random relationship between eddy propagation velocity and mean flow at scales where the isotropy approximation is relevant causes velocity spectra convergence towards 1.0. Spectrum ratio convergence towards unity and cospectrum convergence towards zero are necessary, but not sufficient, for a state of local isotropy to exist in the atmospheric surface layer.