Pure and Applied Geophysics

, Volume 175, Issue 10, pp 3639–3652 | Cite as

Correct Boundary Conditions for the High-Resolution Model of Nonlinear Acoustic-Gravity Waves Forced by Atmospheric Pressure Variations

  • Yu. A. Kurdyaeva
  • S. P. KshevetskiiEmail author
  • N. M. Gavrilov
  • S. N. Kulichkov


Currently, an international network of operating high-resolution microbarographs was established to record wave-induced pressure variations at the Earth’s surface. Based on these measurements, simulations are performed to analyze the characteristics of waves corresponding to the observed variations of atmospheric pressure. Such a mathematical problem involves a set of primitive nonlinear hydrodynamic equations considering lower boundary conditions in the form of pressure variations at the Earth’s surface. Selection of upward propagating acoustic-gravity waves (AGWs) generated or reflected at the Earth’s surface requires the Neumann boundary conditions involving the vertical gradients of vertical velocity at the lower boundary. To analyze the correctness of the mathematical problem, linearized equations are used for small-surface wave amplitudes excited near the ground. Using the relation for wave energy, it is proven that the solution of the boundary problem based on the nondissipative approximation is uniquely determined by the variable pressure field at the Earth’s surface. The respective dissipative problem has also a unique solution with the appropriate choice of lower boundary conditions for temperature and velocity components. To test the numerical algorithm, solutions of the linearized equations for AGW modes are used. Developed boundary conditions are implemented into the model describing acoustic-gravity wave propagation from the surface atmospheric pressure source. Atmospheric waves propagating from the observed surface pressure variations to the upper atmosphere are simulated using the obtained algorithms and the computer codes.



Numerical simulations of the project were supported by the Russian Basic Research Foundation (Grant 17-05-00574) and the microbarograph surface pressure measurements by the Russian Scientific Foundation (Grant 14-47-00049). N. Gavrilov and S. Kshevetskii formulated the problem. Yu. Kurdyaeva and S. Kshevetskii proved the main theorems. S. Kshevetskii and N. Gavrilov developed the model for simulations. Yu. Kurdyaeva performed simulations. S. Kulichkov obtained the experimental data of the pressure variations with high-sensitive microbarographs.

Supplementary material

24_2018_1906_MOESM1_ESM.docx (26 kb)
Supplementary material 1 (DOCX 25 kb)


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Physical-Mathematical Sciences and Information TechnologiesBaltic Federal UniversityKaliningradRussia
  2. 2.Atmospheric Physics DepartmentSaint Petersburg State UniversitySt. PetersburgRussia
  3. 3.Obukhov Institute of Atmospheric PhysicsRussian Academy of ScienceMoscowRussia

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