Physics, mathematics, and technology

2020 Issue №3

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On asymptotic expression for velocity field of atmosphere gas perturbed by 1D acoustic wave



The problem of 1D acoustic wave initiation by a rise of water masses is formulated as a boundary problem at half space . The atmosphere is modeled as a multi-layer gas with an exponential structure of density in each layer. The boundary conditions at determine the direction of propaga­tion, by link between dynamic variables (pressure, density, and velocity) of the wave. It defines the dynamic projection operators on the subspaces of z-evolution for each layer. The universal formulas for the perturbation of atmos­pheric variables in an arbitrary layer are derived in frequency and time do­mains. The explicit expressions for vertical velocity are built by the stationary phase method considering z as large parameter. The resulting formulas can be used to calculate the ionospheric effect by the explicit formula for electron den­sity evolution. This set of explicit relations form a base for a quick algorithm for early diagnostics of tsunami waves.