An Enhanced Framework to Quantify the Shape of Impulse Waves Using Asymmetry

Abstract

The shape of a wave generated by a landslide, snow avalanche, or fluid flow greatly influences its size and speed as it propagates away from the source region, which are critical parameters needed to estimate the impacts of these waves on coastal communities. In this study, laboratory data are produced from waves generated by the impact of water into a wave flume akin to the impact of a fluidized, highly mobile, and neutrally buoyant slide into a reservoir. Water surface observations are made using wave probes that remain at fixed positions, while the water depths and source volumes of slide material are varied. The wave shape is quantified by calculating the asymmetry about the vertical axis at each wave probe. The experimental results indicate that waves with positive or near-zero asymmetry in the near field have a small influence on the maximum wave amplitude along the flume. However, waves with negative asymmetry in the near field change rapidly in shape and amplitude due to breaking until a stable state with symmetrical shape and wave breaking limit of 0.6 is reached. The length scale at which the breaking waves reach this state is quantified based on the initial asymmetry. An enhanced mathematical framework is developed using horizontal-scale coefficients to modify the solitary wave equation such that it can be used to generate asymmetrical waves. This new method might be used in combination with predictions of the maximum wave amplitude to create time series needed to account for the shape of the tsunamis.Plain Language Summary The shape of a wave generated by an avalanche or landslide greatly influences its size and speed as it propagates away from the source region, which are critical parameters needed to estimate the impacts of these waves on coastal communities. In this study, laboratory data are produced from waves generated by the impact of water-impact slides into a reservoir that propagate and evolve along a wave flume. Water surface observations are made using wave probes, and the water depths and source volumes of water are varied in the experiments. The wave shape is quantified by calculating the "asymmetry," and the experimental results indicate that waves with positive or near-zero asymmetry in the near field have small changes in the maximum wave amplitude along the flume. However, waves with negative asymmetry in the near field change rapidly in shape and amplitude due to breaking until a stable state with symmetrical shape is reached. A novel framework is developed to mathematically describe asymmetrical waves, and this new method can be used to create time series needed to account for the shape of the tsunamis.

Impact of Fluidized Granular Flows into Water: Implications for Tsunamis Generated by Pyroclastic Flows

“…It is important to recall that the H o independency of wave features is observed in the near‐field region, at least up to x / l 1 ∼2 from the shoreline. At sufficiently long times and far enough from the shoreline, it is expected that the H o dependency of the wave will be recovered, as already shown in the case of water flows entering water (Bullard, Mulligan, Carreira, & Take, 2019; Bullard, Mulligan, & Take, 2019). However, the distance required is probably too large with respect to the dimensions of our experimental setup to observe this near‐ to far‐field transition, in the range of parameters considered here.…”

Non-Hydrostatic Modeling of Waves Generated by Landslides with Different Mobility

“…Tests with different mobility were selected as end-member examples in the present study. However, a considerable number of experiments have been conducted by [13], and some of these tests are described by [14]. Material is released from a source volume box at the top of the slope, accelerates down the landslide slope, impacts the water with thickness s and velocity v s where it generates waves, propagates along the flume and runs up the slope at the end of the flume.…”

“…The mean water depth h was very similar for both tests, differing by 0.01 m. The landslide and near field wave properties were observed using a system of high-speed cameras, and these slides generate very different waves, as illustrated by the images of the near-field waves in Figure 2. The observational methods and accuracy of data obtained in the experiments are described in detail by [13,14]. The water surface was also measured using nine capacitive probes (P1-P9) along the flume that sample at 100 Hz, and the maximum wave amplitudes were 0.09 m and 0.29 m at P1 for the low LM and high LM tests, respectively.…”

Simulations of Landslide Wave Generation and Propagation Using the Particle Finite Element Method

“…The next stage is to determine the landslide properties at impact with water using a landslide dynamic model and use these to estimate the maximum wave amplitude (Figure 1b) via a semi‐empirical relationship (e.g., Heller & Hager, 2010) or a momentum transfer equation (e.g., Mulligan & Take, 2017). The wave amplitude can then be used to estimate the time series for input to a wave propagation model (Figure 1c) after considering the wave shape that could, for example, be represented by the solitary wave equation modified to account for asymmetry depending on the impact properties (Bullard, Mulligan, & Take, 2019). The wave shape is critical, at it is also indicative of the breaking or non‐breaking behavior of the near‐field wave that can drastically influence the evolution of wave amplitude as it propagates to the far field.…”

“…Recently, additional experimental data sets have become available to permit increasingly quantitative validation of numerical model outcomes for landslide‐generated waves. In particular, large‐scale flume experiments conducted by Bullard, Mulligan, Carreira, and Take (2019) and Bullard, Mulligan, & Take (2019) using water as the slide material have created a data set of the behavior of highly mobile slides prior to impact with the reservoir, during impact, and as the resulting wave propagates to the far field. The use of water as the sliding material removes uncertainty associated with the rheological behavior of the slide, permitting the validation exercise to focus solely on the ability of the numerical model to quantitatively reproduce key aspects of the behavior in the near and far fields particularly relevant to hazard mitigation (e.g., wave shape, amplitude, breaking behavior, wave celerity, and fluid velocity).…”