Numerical Study on the Excitation and Propagation of Surface/Internal Waves Due to Air Pressure Waves over Topography

Numerical simulations have been generated using a nonlinear shallow water model on velocity potential, to investigate the excitation and propagation of water waves due to air pressure waves with positive air pressure, over topographies in several model cases. When the Froude number is close to one in quite shallow waters, the tsunami nonlinearity caused a significant increase in tsunami height. In the one-layer problem, when the tsunami speed is larger than the air pressure wave speed in the deeper area, a generated free tsunami crest preceded the air pressure wave with a forced tsunami trough. Then, over an upslope seabed, the air pressure wave generated a new tsunami crest again, and the maximum water level increased as the overlap degree of the new tsunami crest and the preceding free tsunami crest was increased. The numbers of significant tsunami crests and troughs depended on the number of seabed slopes, as well as the number of air pressure waves that excited the tsunamis. Conversely, in the two-layer problems, water waves were excited because of the Proudman resonance when the air pressure wave speed was close to the water wave speed in each mode. When a surface mode surface wave is excited, a surface mode internal wave was also generated. However, when an internal mode internal wave is excited, no significant internal mode surface wave appeared.