The ratio of transverse to longitudinal turbulent velocity statistics for aircraft measurements

The classical theory of homogeneous isotropic turbulence predicts the ratio of transverse to longitudinal structure functions or power spectra equal to 4/3 in the inertial subrange. For the typical turbulence cascade in the inertial subrange, it also predicts a power law scaling with an exponent of +2/3 and −5/3 for the structure functions and the power spectra, respectively. We estimate those ratios and exponents from in-situ high-rate turbulence measurements collected by three research aircraft during four field experiments in two regimes of the marine atmospheric boundary layer: shallow trade-wind convection and subtropical stratocumulus. The results were derived by fitting power law formulas to the structure functions and power spectra computed separately for the three components of the turbulent wind velocity measured in horizontal flight segments. The variability in the results can be attributed to how the wind velocity components are measured on an individual aircraft. The differences related to environmental conditions, e.g. between characteristic levels and regimes of the boundary layer, are of secondary importance.Experiment-averaged transverse-to-longitudinal ratios are 23–46 % smaller than predicted by the theory. The deviations of average scaling exponents with respect to the theoretical values range from −35 to +47 % for structure functions and from −25 to +22 % for power spectra, depending on experiment and velocity component. The reason for the disagreement in transverse-to-longitudinal ratios between the observations and the theory remains uncertain.