Interaction of surface/internal water waves with a floating platform is discussed with nonlinearity of fluid motion and flexibility of oscillating structure. The set of governing equations based on a variational principle is applied to a one‐ or two‐layer fluid interacting with a horizontally very large and elastic thin plate floating on the water surface. Calculation results of surface displacements are compared with the existing experimental data, where a tsunami, in terms of a solitary wave, propagates across one‐layer water with a floating thin plate. We also simulate surface and internal waves due to a point load, such as an airplane, moving on a very large floating structure in shallow water. The wave height of the surface or internal mode is amplified when the velocity of moving point load is equal to the surface‐ or internal‐mode celerity, respectively.

Numerical simulations were generated using a nonlinear shallow-water model of velocity potential to study the fundamental processes of tsunami generation and amplification by atmospheric pressure waves. When an atmospheric pressure wave catches up with an existing tsunami that is propagating as a free wave over an abrupt change in water depth, the amplified tsunami propagates in the shallower water. An existing tsunami propagating as a free wave over a sloping seabed is also amplified by being passed by atmospheric pressure waves. When atmospheric pressure waves travel over an abrupt change in water depth, the water surface profile of tsunamis in the shallower water depends on both the interval of the atmospheric pressure waves and the phase of the tsunami-generation process over the change in water depth. Moreover, when atmospheric pressure waves travel over an abrupt change in water depth, the tsunami amplitude in the shallower water increases, as the water depth of the shallower area is decreased and the Proudman resonance is further reduced. When an atmospheric pressure wave train with positive pressure travels over a sloping seabed, the amplification of tsunami crests propagating as free waves is controlled by leaving the forced water waves following the atmospheric pressure waves. Conversely, the amplitudes of tsunami troughs propagating as free waves increase.

Three-dimensional numerical simulations were generated for tsunamis ascending processes with different river topographies. As tsunamis propagated in a narrow river, the radius of curvature around the first wave peak decreased, increasing the tsunami height with wave disintegration until the second tsunami height peak appeared. The diffracted waves also entered the river channel, causing an increase in tsunami height in the vicinity of the riverbank at the estuary. The tsunami height increased in a uniform riverbed gradient and narrower river width toward the upstream, based on the shallowing and energy concentration. As the angle between the riverbank line and coastline at the estuary was acute, the tsunami height was reduced because the diffracted waves were difficult to enter the river. The tsunami height in the rivers increased as the ratio of representative wavelength to river width was increased. The maximum tsunami height in the bore-shaped wave was larger than in the solitary wave with the same incident wave height. In the case of tsunami propagation in the compound cross-section river, multiple crestlines appeared because the tsunamis traveling diagonally in the flood channel showed multiple reflections both on the riverbank and between the flood and main channels.

Tsunami Generation Due to a Landslide or a Submarine Eruption | InTechOpen, Published on: 2016-10-12. Authors: Taro Kakinuma

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.