Abstract
Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered and applied to numerical modelling with the direct possibility to use in atmosphere monitoring especially in such strong events which follow magnetic storms and other large scale atmospheric phenomena. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on a vertical coordinate, which essentially complicates the diagnostics. The relations connecting perturbations for acoustic and entropy (stationary) modes are analytically established and led to the solvable diagnostic equations. These equations specify acoustic and entropy modes in an arbitrary stratified gas under the condition of stability. The diagnostic relations are independent of time and specify the acoustic and the entropy modes. They provide the ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts uniquely at any instant within the total accessible heights range. As a prospective model, we consider the diagnostics at the height interval 120–180 km, where the equilibrium temperature of a gas depends linearly on the vertical coordinate. For such a heights range it is possible to proceed with analytical expressions for pressure and entropy perturbations of gas variables. Individual profiles of acoustic and entropy parts for some data are illustrated by the plots for the pure numerical data against those obtained by the model. The total energy of a flow is determined for both approaches and its vertical profiles are compared.
Highlights
Theoretical and numerical models which describe dynamics of gases and liquids affected by external forces are of great interest in geophysics, meteorology, and wave theory [1,2,3,4,5,6]
That serves as a tool to predict their dynamics, and to conclude about the energy of modes. This is undoubtedly important in applications in meteorology and diagnostics of atmospheric dynamics, including the understanding of such phenomena as variations of the equilibrium temperature of the stratosphere, e.g., socalled warming [21] conventionally understood as period-average
The main result of the presented work constitutes in the diagnostic equation, which solution gives the vertical profile of the acoustic and entropy modes contribution in the total wave perturbation
Summary
Theoretical and numerical models which describe dynamics of gases and liquids affected by external forces are of great interest in geophysics, meteorology, and wave theory [1,2,3,4,5,6]. The main aim of this study is the diagnostics as decomposition of a total disturbance into wave and non-wave modes in the case of arbitrary stable stratification This is helpful in the interpretation of experimental data related to the significantly disturbed atmosphere (e.g., by storms), it may be useful in a validation of a numerical modelling [14]. This is undoubtedly important in applications in meteorology and diagnostics of atmospheric dynamics, including the understanding of such phenomena as variations of the equilibrium temperature of the stratosphere, e.g., socalled warming [21] conventionally understood as period-average Such phenomenon, named “heating”, may be explained in the framework of non-linear interaction of acoustic wave and entropy modes in the presence of dissipation [16,22]. The results, obtained by the direct application of the theory to the dataset basing on the standard atmosphere within the range of approximate linear profile, and the conclusions of a model are compared
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