Three-dimensional spectrum of temperature fluctuations in stably stratified atmosphere

Abstract

A phenomenological model is proposed for a 3-D spectrum of temperature inhomogeneities generated by internal waves in the atmosphere. This model is a development of the theory based on the assumption that a field of Lagrangian displacements of fluid particles, induced by an ensemble of internal waves with randomly independent amplitudes and phases, is statistically stationary, homogeneous, axially symmetric in horizontal plane and Gaussian. For consistency of this model with measured spectra of temperature fluctuations in the stratosphere and mesosphere the additional assumption was introduced in to the model about the anisotropy of inhomogeneities to be dependent on their vertical sizes. The analytic expressions for both the 3-D and 1-D spectra are obtained. A model vertical wave number spectrum follows a −3 power law, whereas a horizontal spectrum contains two regions with a −3 slope, and the intermediate region with the slope between −1 and −3 depending on the rate of anisotropy decrease as a function of increasing sizes of the inhomogeneities. In the range of a few decades the model showed a good agreement with the results of measurements of the spectra in the troposphere, stratosphere and mesosphere.