This paper incorperates Bingham and bi-viscosity rheology models with the Navier–Stokes solver to simulate the dynamics and kinematics processes of slumps for tsunami generation. The rheology models are integrated into a computational fluid dynamics code, Splash3D, to solve the incompressible Navier–Stokes equations with volume of fluid surface tracking algorithm. The change between un-yield and yield phases of the slide material is controlled by the yield stress and yield strain rate in Bingham and bi-viscosity models, respectively. The integrated model is carefully validated by the theoretical results and laboratory data with good agreements. This validated model is then used to simulate the benchmark problem of the failure of the gypsum tailings dam in East Texas in 1966. The accuracy of predicted flood distances simulated by both models is about 73% of the observation data. To improve the prediction, a fixed large viscosity is introduced to describe the un-yield behavior of tailings material. The yield strain rate is obtained by comparing the simulated inundation boundary to the field data. This modified bi-viscosity model improves not only the accuracy of the spreading distance to about 97% but also the accuracy of the spreading width. The un-yield region in the modified bi-viscosity model is sturdier than that described in the Bingham model. However, once the tailing material yields, the material returns to the Bingham property. This model can be used to simulate landslide tsunamis.

This paper incorporates the Bingham rheology model with the Navier–Stokes solver to simulate the tsunamis excited by a slump-type landslide. The slump is modeled as the Bingham material, in which the rheological properties changing from the un-yield phase to yield phase is taken into account. The volume of fluid method is used to track the interfaces between three materials: air, water, and slump. The developed model is validated by the laboratory data of the benchmark landslide tsunami problem. A series of rheological properties analyses is performed to identify the parameter sensitivity to the tsunami generation. The results show that the yield stress plays a more important role than the yield viscosity in terms of the slump kinematics and tsunami generation. Moreover, the scale effect is investigated under the criterion of Froude number similarity and Bingham number similarity. With the same Froude number and Bingham number, the result from the laboratory scale can be applied to the field scale. If the slump material collected in the field is used in the laboratory experiments, only the result of the maximum wave height can be used, and significant errors in slump shape and moving speed are expected.

On November 15, 1994, a Mw 7.2 earthquake event occurred along the offshore extension of the dextral, NNW-SSE trending Aglubang River Fault, rupturing southerly and onshore into Mindoro Island. It produced a 35-km surface rupture, with horizontal and vertical slip amounts of up to 4 m and <1 m, respectively. Minutes after, a tsunami also hit the coastal areas around the Verde Island Passage. Post-event surveys reported run-up heights of up to 8 m in Baco, Oriental Mindoro, while recent investigations also discovered preserved 1994 tsunami overwash deposits. A total of 78 casualties resulted from both the earthquake and tsunami. Despite the close association of the 1994 Mindoro earthquake and tsunami, previous numerical modeling suggests the inadequacy of the earthquake as the tsunami’s source mechanism. Assuming a 2-m uniform fault slip, a maximum wave height of up to 0.4 m was modeled in Baco, which is too low to translate into the reported maximum run-up height of 8 m. Hence, an additional submarine mass failure (SMF) mechanism is proposed based on submarine geomorphology and numerical modeling. For the SMF component, a 400-m-wide, 15-m-high Gaussian wave was used as a conservative estimate for the initial wave, occurring over the Malaylay Canyon. The 7-km-long, NW trending Malaylay Canyon is located <1km north of Baco, with two 1-km-wide bight-shaped scarps showing evidence of possible mass movements within the last 70 years. Results of the numerical modeling using the combined earthquake and SMF source mechanism correlate well with the distribution of observed run-up heights. However, the model also suffers from underestimation of wave heights, such as that in Baco. Despite this, the model is a promising improvement from the purely earthquake-based source mechanism. A more-defined characterization of the SMF-generated initial wave will be explored in subsequent studies. 

In the 2011 Tohoku-oki earthquake, more than 92% of people were dead due to drowning. In the near future, the Nankai Trough earthquake is expected to induce huge tsunami. Because of its deep epicenter, the tsunami is expected to reach to the coast within a few minutes after the earthquake. It is difficult to predict the arrival time of tsunamis by numerical simulation after the occurrence of an earthquake. If appropriate predictions can be conducted in real time, it will be possible to take appropriate evacuation actions. Machine learning is an effective method for this. If tsunami arrival time can be output from initial tsunami waveform, evacuation from tsunami can be immediately started. In this study, we used a neural network (NN) which is a type of machine learning. The tsunami storm surge simulator Q-Wave, which is based on the nonlinear long wave equation was used for the numerical calculations. Numerical calculations were performed using tsunami source model of the Nankai Trough. A color map of water level data and tsunami arrival time was output by Q-wave. We then constructed an NN model. In this model, we input the colormap image of initial water level, then output the colormap of water level when tsunami reached to the shoreline at Shima City. Since the input format of NN is 1D, the color map images were grayscaled and converted to 1D data before training. By increasing the number of training data, the error in the 1D data of the colormap image was reduced to approx 20%. For evaluating this error, the mean squared error was used. Once this method is established, it will be possible to determine the arrival time of tsunamis approximately a few minutes after an earthquake. 

Earthquakes along the Nankai Trough, located in the South of Japan, can generate devastating tsunamis and potentially cause severe damage on the nationwide coast of Japan. The Central Disaster Management Council of the Japanese Government (CDMC) has developed 11 future scenarios based on the expert judgments, which represent different slip characteristics in terms of the number and locations of large slip areas. However, it is unlikely that the considered slip distributions comprehensively cover possible future scenarios because tsunami shows more complex behavior as it gets close to nearshore. It is necessary to understand local areas prone to an amplified tsunami on a city-scale in order to estimate the local tsunami hazards and risks. This study conducts tsunami hazard assessments for the Nankai-Tonankai earthquake tsunami, targeting multiple coasts along the Pacific coast of Japan. The considered tsunami scenarios consist of the CDMC 11 models and stochastic earthquake slip models. The stochastic tsunami scenarios are generated with a random process and slip spectra that capture the spatial slip characteristics of historical subduction earthquakes. The tsunami heights caused by the CDMC models are within the possible ranges of those by the stochastic tsunami source models. The spatial patterns of the scenarios causing the maximum tsunami heights differ by region. In addition, these spatial patterns show that the worst-case scenario varies due to local topographic effect, especially along complex coastlines. In other words, the different tsunami scenarios can cause the maximum tsunami height even among coasts of adjacent cities. These results highlight the importance of consideration of various slip distributions for the tsunami hazard assessment. 

We propose a ray-tracing method to solve the two-point boundary value problem for tsunamis based on the long-wave theory. In the long-wave theory, the tsunami wave velocity is proportional to the square root of water depth, available from global bathymetric atlases. Our method computes the global shortest travel time between two given points. By applying an explicit and non-iterative scheme, our method shows high efficiency and robust results. The wave refraction effect is considered in our algorithm. We perform synthetic tests in simple and real bathymetries. The result shows our algorithm is applicable to any tsunami-accessible locations, including positions behind a slit or inside a bay. The ray-tracing method is then applied to analyze the path of tsunamis from different directions to four important bays in Japan. The result shows that tsunami ray paths are significantly influenced by local bathymetry. Large-scale bathymetric features, such as trench and trough, behave as the primary routes off the Honshu area. Deploying stations near these routes will be most beneficial for tsunami early warning. The existing tsunami-observing system off the Honshu area works well for tsunamis from the east side but slightly deficient for tsunamis from the west side. The far-field ray tracing shows that tsunamis travel from Chile to Japan through two main routes—one reaching Japan from the east via north of Hawaii and the other running from the south via the south of Hawaii— depending on the location of the source along the Chilean coast. We further apply our method to investigate the wave reflection. The late reflected waves of the 2016 Fukushima earthquake tsunami showed wave height comparable to the leading waves. We identify the reflection area along the coast. The estimated reflected travel times are about 50 min after the leading waves, which agree with the recorded waveforms.

Intensified activities of tropical cyclones in the western North Pacific have imposed increasing threats to the coastal cities in the context of global climate change. Storm surge superimposed with astronomical tide, i.e., storm-tide, often cause severe flooding in many coastal cities in South China Sea (SCS) region. Meanwhile, the assessment of potential tsunami hazard associated with the Manila megathrust has become another urgent concern in this region. These two kinds of coastal disaster have been studied independently in the past since they are caused by different source mechanisms in nature. However, there is no scientific reason to rule out the concurrence of a storm-tide-tsunami event, which could be admittedly rare. This study simulates a group of synthetic events assuming that tsunami is generated by a M_w 9 earthquake in the Manila subduction zone during a typhoon which has the same characteristics as the 2017 Typhoon Hato. A variety of scenarios are considered where the tsunamis are superimposed on different phases of the storm-tide. Their compound impacts on Macau and Hong Kong in Pearl River Delta, China, are investigated. Specifically, the results of water level, arrival time, flow velocity, and inundation depth are discussed. The worst-case scenario has been identified, which floods more than 12.0km² of lands in Macau and 8.9km² in adjacent Kai Tak terminal region in Hong Kong. In addition, the efficacy of the linear superposition of results obtained separately from each event (i.e., typhoon and tsunamis) is also discussed. Generally speaking, the linearly superimposed solutions yield delays on the arrival times of peak flooding stage. It is concluded that simulating concurrent storm-tide-tsunami using a fully coupled model improves the reliability of the predictions, which provides insight regarding the modern coastal disaster prevention practice and the development of early warning system.