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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/gmd-2017-76
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Development and technical paper
23 May 2017
Review status
This discussion paper is a preprint. It has been under review for the journal Geoscientific Model Development (GMD). The revised manuscript was not accepted.
Correct boundary conditions for DNS models of nonlinear acoustic-gravity waves forced by atmospheric pressure variations
Yuliya Kurdyaeva1, Sergey Kshevetskii1, Nikolay Gavrilov2, and Sergey Kulichkov3 1Baltic Federal University, Institute of Physical-Mathematical Sciences and Information Technologies, Kaliningrad, Russia
2Saint-Petersburg State University, Atmospheric Physics Department, Russia
3Obukhov Institute of Atmospheric Physics, Russian Academy of Science, Moscow, Russia
Abstract. Currently, international networks exist for high-resolution microbarograph recording wave pressure variations at the surface of the Earth. This increases interest in simulating propagation of waves caused by variations of atmospheric pressure. Such mathematical problem involves a set of primitive nonlinear hydrodynamic equations with lower boundary conditions in the form of wavelike pressure variations at the Earth's surface. To analyze the correctness of the problem, the linearized equations are used near the ground for small amplitudes of surface wave excitation. The method of wave energy functional shows that in nondissipative approximation the solution of the boundary problem is uniquely determined by the variable pressure field at the Earth's surface. Respective dissipative problem has also unique solution with the appropriate choice of lower boundary conditions for temperature and velocity components. To test the numerical algorithm, analytical solutions of the linearized equations for acoustic and gravity wave modes are used. Reasonable agreements of numerical and analytical solutions are obtained. Analytical studies show possibilities of sharp changes of temperature and density near the ground. Numerical simulations confirm these analytical results. Obtained algorithms and computer codes can be used for simulations of atmospheric wave propagation from the pressure variations at the Earth's surface.

Citation: Kurdyaeva, Y., Kshevetskii, S., Gavrilov, N., and Kulichkov, S.: Correct boundary conditions for DNS models of nonlinear acoustic-gravity waves forced by atmospheric pressure variations, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-76, 2017.
Yuliya Kurdyaeva et al.
Yuliya Kurdyaeva et al.

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Short summary
Various meteorological phenomena generate acoustic-gravity waves in the atmosphere and cause wave variations of atmospheric pressure. There are networks of microbarographs, which record pressure variations on the Earth's surface. The hydrodynamic problem of propagation of waves in the atmosphere from pressure variations on the Earth's surface is formulated. The problem wellposedness is proved. A supercomputer program for simulation of waves from pressure variations is developed and applied.
Various meteorological phenomena generate acoustic-gravity waves in the atmosphere and cause...
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