Model of the three-dimensional spectrum of anisotropic temperature irregularities in a stably stratified atmosphere

A phenomenological model is proposed for the three-dimensional (3 D ) spectrum of temperature irregularities generated by internal waves in the atmosphere. This model develops a theory (Chunchuzov, 2002) based on the assumption that the field of the Lagrange displacements of the medium’s particles that are caused by a statistical ensemble of internal waves with randomly independent amplitudes and phases is stationary, homogeneous, axially symmetric in a horizontal plane, and Gaussian. To fit the model to measured spectra of fluctuations in the stratosphere and mesosphere, an additional assumption is introduced into the model that the degree of anisotropy of irregularities depends on their vertical size. An explicit expression is presented for the 3 D spectrum. The model vertical spectrum follows a power law with an exponent of −3. The horizontal spectrum has three asymptotically power portions. Two of these are characterized by an exponent of −3, whereas an intermediate portion has an exponent of −1 to −3, depending on the rate at which the degree of anisotropy decreases as the vertical size of temperature irregularities increases. Simple asymptotic formulas are obtained for the horizontal spectrum. Within the range of a few decades, the model is in good agreement with the published results of measuring the spectra in the upper troposphere, stratosphere, and mesosphere.