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

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.