A Similarity Theory of the Tropospheric Turbulence Energy Spectrum

Abstract

A three-range model is proposed for the energy spectrum of tropospheric turbulence in which the range-I spectrum is governed by the cascade of eddy enstrophy, that of range-II by the cascade of eddy kinetic energy, and that of range-III by viscous dissipation. Values of the spectral densities in ranges-I and -II, as well as wavenumbers of transition from range-I to -II to -III, are determined in terms of the integrated values of the energy spectrum, V2?, and the dissipation spectrum, ?, of range-II. The resulting spectra for ranges-I and -II are shown to agree well with the recent GASP data on atmospheric spectra covering wave-lengths of from less than 3 km to 10000 km. A property of this model is that ?/V2? = f, the Coriolis parameter. This is shown to give very close agreement with the observed latitude variation of the GASP-Spectrum in range-II, to correctly indicate that this variation is much greater in range-I, and to explain why the atmosphere's eddy viscosity, K, is more variable over the globe than the energy-dissipation rate, ?. The observed seasonal variation of spectra is explained by the hemispheric variation of ? due to the seasonal change in the pole-equator temperature gradient.