Taro Kakinuma

Tsunamis were widely observed when the large eruption of Hunga Tonga-Hunga Ha`apai volcano occurred in January 2022 (e.g. Tanioka et al., 2022). In the present study, numerical simulations were generated using a nonlinear shallow-water model of velocity potentials to study the fundamental processes of surface/internal wave generation and amplification by air pressure waves.

Numerical simulations were generated to investigate the response of a very large floating airport to an airplane takeoff, using the set of nonlinear shallow water equations of velocity potential for water waves interacting with a floating thin plate. We have proposed two methods to reduce persistent airport vibration: reflectance reduction by decreasing the flexural rigidity in airport edge parts and amplification reduction by decreasing the still water depth partially under airport runways. First, when the flexural rigidity is uniformly decreased in an airport edge part, the reflectance of the floating body waves due to a B737 was reduced because of the multiple reflections. However, the wave reflectance for a B747 increased, depending on the conditions. A too-long edge part was not effective in reducing the wave reflectance. Conversely, when the flexural rigidity is linearly decreased in an airport edge part, the wave reflectance was reduced for both airplanes. Second, when the still water depth under an airport runway is partially reduced at the location where floating body waves are amplified, the wave heights of floating body waves tended to decrease as the still water depth in the shallower area decreased.

Drone technology is expected to play an important role in various fields, including topographic survey, wave and current monitoring, lifesaving, etc. in the ocean. In the present paper, we propose a new method for bathymetry, with the combination of an unmanned aerial vehicle (UAV) and an unmanned surface vehicle (USV). First, the motion of the USV is evaluated using images obtained by the UAV. Second, the pixel shift values of the seabed are calculated through underwater images by the USV. Finally, based on these results, the water depth is acquired by applying triangulation. The experimental results obtained using a wave basin have shown the maximum estimation error of 1.1cm, indicating the effectiveness of the proposed method.

Numerical simulations were generated to investigate the response of a floating airport to airplane movement using the nonlinear shallow water equations of velocity potential for water waves interacting with a floating thin plate. First, in the 1D calculations, the airplanes were B747 and B737. At touch-and-go, when the airplane speed is closer to the water wave speed, even B737 produced large waves based on the resonance. The impacts due to both the touchdown and leaving of the airplanes generated other forward and backward waves. At landing, when the airplane speed approached the water wave speed, a forced wave was generated and amplified, with many free waves ahead. At takeoff, a wave clump, generated shortly after starting to run, propagated in front of the airplanes. Although the wave height increased from superposition with the reflected waves, the wave reflectance was reduced by lowering the flexural rigidity near the airport edge. Second, in the 2D calculations, B787 performed landing and takeoff. When the still water depth is shallower, a grid-like pattern was formed at the floating airport and appeared more remarkably in landing than in takeoff. The effective amplification occurred from a sufficient load applied when the airplane speed approached the water wave speed. Furthermore, the maximum upslope gradient beneath the airplane increased as the still water depth decreased, and it was larger in takeoff than in landing.

We discuss the response of the wave dissipating blocks composing a detached breakwater to the waves with various periods, based on both the experimental and numerical results. First, in the hydraulic experiments, the number of the blocks fallen by the irregular waves was the largest when the still water level is moderate, namely the HWL. When the large and long wave is incident, the overflow that lasted for a long time fell many blocks at the back of the breakwater. When the irregular waves, long wave, and irregular waves are continuously incident in this order, the first irregular wave train shifted several blocks, and the subsequent long wave dropped these shifted blocks, displacing the blocks around them, whereafter the second irregular wave train dropped many of the displaced blocks. Second, in the vertically two-dimensional calculations, when the long wave struck the breakwater, a large-scale vortex was created near the seabed in front of the breakwater and remained during the pushing wave. The overflow due to the long wave generated negative wave pressure at the top behind the breakwater. Based on both the numerical and experimental results behind the breakwater, when a large positive wave pressure is generated after a negative wave pressure that is not large in absolute value, the number of fallen blocks will reduce. When large and short waves cause overtopping, and negative wave pressure frequently appears behind a breakwater, the blocks at the back of the breakwater can gradually shift, loosening their engagement.

Tsunamis generated by atmospheric pressure waves due to a volcanic eruption were investigated based on both the proposed estimation formulas and numerical calculations. First, assuming linear shallow water conditions, estimation formulas were proposed for the maximum possible amplitude and the resonance distance. Second, the fundamental properties of tsunamis generated by atmospheric pressure waves were examined numerically using both the nondispersion and weak dispersion models. Based on the numerical results, a ridge and shelf can amplify tsunamis due to atmospheric pressure waves beyond the limits of the Proudman resonance. The estimated and numerically determined maximum possible amplitudes agreed well when the dispersion of tsunamis was not large. Third, the distribution maps of the maximum possible amplitude and the resonance distance for various traveling velocities of atmospheric pressure waves were generated using the proposed formulas. The maximum tsunami amplitude depends on both the length of the excitation area and the resonance distance along the path of atmospheric pressure waves. The worldwide distribution of both the tsunami height and the appearance time of the maximum tide level fluctuations due to the 2022 Tonga volcanic eruption and several historical eruptions were interpreted based on the distribution maps. In the historical large eruptions, the period of the atmospheric pressure waves was shorter; thus, the dispersion effect was larger, resulting in a smaller tsunami amplitude.

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.

Numerical simulations were generated to investigate the propagation processes of distant tsunamis, using a set of wave equations based on the variational principle considering both the strong nonlinearity and strong dispersion of waves. First, we proposed estimate formulae for the time variations of the tsunami height and wavelength of the first distant tsunami, by assuming that the initial tsunami profile was a long crest in a uniform bathymetry. Second, we considered the plate elasticity and upper-mantle fluidity of Earth, to examine their effects on the distant tsunami propagation. When the plate and upper mantle meet certain conditions with both a large depth and moderately large density of the upper mantle, the internal-mode tsunamis with a significant tsunami height propagated slower than the tsunamis in the corresponding one-layer problems, leading to the delay of the arrival time observed in distant tsunamis from that evaluated by the one-layer calculation.