Physics of Traveling Waves in Shallow Water Environment

We present a study of the physical characteristics of traveling waves at shallow and intermediate water depths. The main subject of study is to the influence of nonlinearity on the dispersion properties of waves, their limiting heights and steepness, the shape of solitary waves, etc. A fully nonlinear Serre–Green–Naghdi-type model, a classical weakly nonlinear Boussinesq model and fifth-order Stokes wave solutions were chosen as models for comparison. The analysis showed significant, if not critical, differences in the effect of nonlinearity on the properties of traveling waves for these models. A comparison with experiments was carried out on the basis of the results of a joint Russian–Taiwanese experiment, which was carried out in 2015 at the Tainan Hydraulic Laboratory, and on available experimental data. A comparison with the experimental results confirms the applicability of a completely nonlinear model for calculating traveling waves over the entire range of applicability of the model in contrast to the Boussinesq model, which shows contradictory and unrealistic wave properties for moderate wavelengths.

Extreme wave statistics of random waves propagating over a 3D varying bathymetry

<p>Non-uniform bathymetry may modify the wave statistics for both surface elevation and velocity field.<br>Laboratory evidence reported by Trulsen et al. (2012) shows that for a relatively long unidirectional<br>waves propagating over a sloping bottom, from deep to shallower water, there can be a local maximum<br>of kurtosis and skewness in surface elevation near the edge of the shallower side of the slope. Recent<br>laboratory experiments of long-crested irregular waves propagating over a shoal by Trulsen et al. (2020)<br>reported that the kurtosis of horizontal velocity field have different behaviour from the kurtosis of surface<br>elevation where the local maximum of kurtosis in surface elevation and horizontal velocity occur at<br>different location.<br>In present work, we utilize numerical simulation to study the evolution of skewness and kurtosis for<br>irregular waves propagating over a three-dimensional varying bathymetry. Numerical simulations are<br>based on High Order Spectral Method (HOSM) for variable depth as described in Gouin et al. (2017)<br>for wave evolution and Variational Boussinesq model (VBM) as described in Lawrence et al. (2021) for<br>velocity field calculation.</p><p> </p><p>References</p><p>GOUIN, M., DUCROZET, G. & FERRANT, P. 2017 Propagation of 3D nonlinear waves over an elliptical<br>mound with a High-Order Spectral method. Eur. J. Mech. B Fluids 63, 9–24.<br>LAWRENCE, C., GRAMSTAD, O. & TRULSEN, K. 2021 Variational Boussinesq model for kinematics<br>calculation of surface gravity waves over bathymetry. Wave Motion 100, 102665.<br>TRULSEN, K., RAUSTØL, A., JORDE, S. & RYE, L. 2020 Extreme wave statistics of long-crested<br>irregular waves over a shoal. J. Fluid Mech. 882, R2.<br>TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by<br>non-uniform bathymetry. Phys. Fluids 24, 097101.</p>

New High-Resolution Modeling of the 2018 Palu Tsunami, Based on Supershear Earthquake Mechanisms and Mapped Coastal Landslides, Supports a Dual Source

The Mw 7.5 earthquake that struck Central Sulawesi, Indonesia, on September 28, 2018, was rapidly followed by coastal landslides and destructive tsunami waves within Palu Bay. Here, we present new tsunami modeling that supports a dual source mechanism from the supershear strike-slip earthquake and coastal landslides. Up until now the tsunami mechanism: earthquake, coastal landslides, or a combination of both, has remained controversial, because published research has been inconclusive; with some studies explaining most observations from the earthquake and others the landslides. Major challenges are the numerous different earthquake source models used in tsunami modeling, and that landslide mechanisms have been hypothetical. Here, we simulate tsunami generation using three published earthquake models, alone and in combination with seven coastal landslides identified in earlier work and confirmed by field and bathymetric evidence which, from video evidence, produced significant waves. To generate and propagate the tsunamis, we use a combination of two wave models, the 3D non-hydrostatic model NHWAVE and the 2D Boussinesq model FUNWAVE-TVD. Both models are nonlinear and address the physics of wave frequency dispersion critical in modeling tsunamis from landslides, which here, in NHWAVE are modeled as granular material. Our combined, earthquake and coastal landslide, simulations recreate all observed tsunami runups, except those in the southeast of Palu Bay where they were most elevated (10.5 m), as well as observations made in video recordings and at the Pantoloan Port tide gauge located within Palu Bay. With regard to the timing of tsunami impact on the coast, results from the dual landslide/earthquake sources, particularly those using the supershear earthquake models are in good agreement with reconstructed time series at most locations. Our new work shows that an additional tsunami mechanism is also necessary to explain the elevated tsunami observations in the southeast of Palu Bay. Using partial information from bathymetric surveys in this area we show that an additional, submarine landslide here, when simulated with the other coastal slides, and the supershear earthquake mechanism better explains the observations. This supports the need for future marine geology work in this area.

Comparison of models for the simulation of landslide generated Tsunamis

In this paper, we analyze the relevance of the use of the shallow water model and the Boussinesq model to simulate tsunamis generated by a landslide. In a first part, we determine if the two models are able to reproduce waves generated by a landslide. Each model has drawbacks but it seems that it is possible to use them together to improve the simulations. In a second part we try to recover the landslide displacement from the generated wave. This problem is formulated as a minimization problem and we limit the number of parameters to determine assuming that the bottom can be well described by an empirical law.

Granular impacts: how far the Boussinesq model can go?

A key problem on granular impacts deals with the determination of the mechanical response of the grains due to the impact of the intruder. This topic has been poorly addressed in the literature so far, a gap to which this study aims to contribute by measuring the pressure distribution at the bottom of a loose and dry sandy bed, impacted by a heavy sphere of fixed diameter. Exploring different bed thicknesses and intruder’s dropping height, we have found that the structure of this distribution is very similar to the Boussinesq model, initially proposed for a static point-force acting over an isotropic-elastic medium. This surprising result opens up many challenging questions that could help validate or refute this model in other scenarios.