Preprints
https://doi.org/10.5194/gmd-2017-76
https://doi.org/10.5194/gmd-2017-76
Submitted as: development and technical paper
 | 
23 May 2017
Submitted as: development and technical paper |  | 23 May 2017
Status: this preprint was under review for the journal GMD but the revision was not accepted.

Correct boundary conditions for DNS models of nonlinear acoustic-gravity waves forced by atmospheric pressure variations

Yuliya Kurdyaeva, Sergey Kshevetskii, Nikolay Gavrilov, and Sergey Kulichkov

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.

Yuliya Kurdyaeva, Sergey Kshevetskii, Nikolay Gavrilov, and Sergey Kulichkov
Yuliya Kurdyaeva, Sergey Kshevetskii, Nikolay Gavrilov, and Sergey Kulichkov
Yuliya Kurdyaeva, Sergey Kshevetskii, Nikolay Gavrilov, and Sergey Kulichkov

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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.