Tsunami-Launched Acoustic Wave in the Layered Atmosphere: Explicit Formulas Including Electron Density Disturbances

Abstract

The problem of the propagation of acoustic wave disturbance initiated by a boundary condition is used to simulate a disturbance of atmospheric gas caused by a rise of water masses. The boundary condition is a function of a dynamic variable that is defined on the border of the problem domain. In this work, it is chosen in such a way that its parameters and form correspond to disturbances in the gas layer produced by a tsunami wave at the air–water interface. The atmosphere is approximately described as a 1D multilayer gas media with an exponential structure of density in each layer. The boundary conditions are set at the interface between water–air and gas layers. These determine the direction of propagation and the ratio of dynamic variables characterizing an acoustic wave. The relationship between such variables (pressure, density, and velocity) is derived by means of projection operators on the subspaces of the z-evolution operator for each layer. The universal formulas for the perturbation of atmospheric variables in an arbitrary layer are obtained in frequency and time domains. As a result, explicit expressions are derived that determine the spectral composition and vertical velocity, by the stationary phase method, of the acoustic disturbance of the atmosphere at an arbitrary height, including the heights of the ionosphere. In return, this can be used to calculate the ionospheric effect. The effect is described by the explicit formula for electron density evolution, which is the solution of the diffusion equation. This forms a quick algorithm for early diagnostics of tsunami waves.