Scattering of moving atmospheric pressure induced tsunamis by bathymetry and coastline

Abstract

Tsunamis can be generated by a moving atmospheric pressure disturbance. The 2022 Tonga volcanic eruption and tsunami demonstrated the global relevance of such a tsunami generation mechanism. The generated locked and free waves are often scattered by bathymetric variations and coastlines, generating more free waves and resulting in a complex wave field. The physical processes involved can be described by the forced linear shallow water equations. Analytical solutions are sought after for simplified bathymetric variations and coastline configurations. In this paper, a moving atmospheric pressure front, which is uniform in the direction normal to its propagation direction, is considered. The water wave motion is assumed to start from the quiescent condition, so that the incident locked and free waves are related. However, since the wave scattering processes are linear, the solutions obtained in this paper can be used for analyzing scattering of the incident locked and free waves with uncorrelated amplitudes. For one-dimensional horizontal (1DH) problems, the water depth is either a constant or has a sudden change (i.e., a step) with or without a vertically walled coastline and the atmospheric pressure front always moves in the direction normal to the depth contours. In the case where a coastline is considered, the atmospheric pressure front can either move from the land to the sea or from the sea to the land. In the 2DH (two-dimensional horizontal) example, the wave field generated by a moving atmospheric pressure front, sweeping over the a circular island surrounded by a circular shelf, is investigated and discussed. For all the cases considered, analytical solutions in the integral form are obtained using the Fourier transform method. For the 1DH cases, analytical solutions are also presented in the form of infinite series, summing over infinite number of scattered and reflected waves from the bathymetric variations and coastlines. The new solutions reveal both the complexity of the wave scattering process and the significant differences between locked and free waves.