Theoretical Interpretation of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft During GASP

Abstract

This paper contains a theoretical interpretation of the wavenumber spectra of wind and temperature obtained from an analysis of data from over 6900 flights during the Global Atmospheric Sampling Program. The spectra cover scales ranging from 3 km to nearly 10 000 km. Major features of the observed spectra are found to be in general agreement with expectations from theoretical models of quasi two-dimensional turbulence. Kinetic energy spectra are remarkably universal, and temperature spectra adjust as required for equipartition between the two horizontal components of kinetic energy and potential energy. The observed wavenumber spectra agree closely in magnitude and shape with frequency spectra obtained independently, and this agreement supports the validity of the Taylor transformation; conversely, because the Taylor transformation works, it suggests the disturbances are turbulence rather than dispersive waves. The GASP spectra are compared in a general way with recently proposed internal wave spectral models which have been advanced to account for the mesoscale spectrum of atmospheric motions. However, these model spectra are scaled to the frequency spectrum of horizontal velocities which must be Doppler shifted if they are indeed due to waves. It is argued that these spectral models are inconsistent with the non-Doppler shifted spectrum of waves needed to compare with the aircraft wavenumber spectrum presented here. We advocate in future studies employing a non-Doppler shifted internal wave model which could be based on the low-wind frequency spectrum of vertical motions.