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.