Abstract

Over the last few decades, solitary waves have been commonly used as the model tsunami waves, but their wavelength-to-depth ratios are much smaller than that of tsunamis in reality. On the other hand, generating waves that are longer than solitary waves in laboratory is in fact a very challenging task. In this study, a new kind of wave maker is designed and investigated, which has a moving bottom at the toe of the beach as the wave generating mechanism with adjustable slope. By changing some characteristic parameters, different waves are generated and investigated theoretically and experimentally.

Introduction

Since the early 1970s, solitary wave has been the most commonly used tsunami wave model in theoretical and experimental studies of tsunamis (e.g., Synolakis, 1987; Liu et al., 1995; Li and Raichlen, 2002; Craig, 2006). It has been usually believed solitary wave can capture many main features of how tsunami waves behave in coastal region. Typical solitary wave expression as a solution to the KdV equation (e.g., Madsen and SchΓ€ffer, 2010) reads

π›ˆ(π‘₯, 𝒕) = 𝑨ₛ sech2'(𝐾:β‚›(π‘₯ - 𝒄 𝒕)), 𝑲ₛ = 1/𝒉 √ 3𝑨ₛ / 4𝒉 (1)

where π›ˆ 𝑨ₛ c and h denote free surface elevation, wave height, phase velocity and static water depth, respectively. Notice that wavenumber Ks is tied to amplitude-to-depth ratio 𝑨ₛ/h which is usually regarded as nonlinearity.

However, based on the definition of the wavenumber 𝐾ₛ, Madsen et al. (2008) questioned the link between solitary wave and geophysical tsunamis, and clarified their views that solitary wave is not appropriate to model important characteristics of tsunamis. First of all, because of the linear dispersion occurs in deep water, they suggested linear KdV equation to be used for wave generation. Secondly, along with tsunami waves approaching the beach, frequency dispersion will decrease while the nonlinearity will increase significantly, leading to skewness of waves, which is already beyond the KdV scale. Moreover, during wave breaking, some very short KdV waves in the front of the tsunami wave will break too early which can mislead people to make wrong investigation of the corresponding run-up. Therefore, Madsen et al. (2008) illustrated that the tie between the wavenumber 𝐾ₛ and the nonlinearity 𝑨ₛ/𝒉 in Eq. (1) is no longer realistic for geophysical tsunamis. In fact, full scale tsunami measurements confirmed the inadequacy of using solitary wave paradigm as well. In Fig. 1 the records of the 2011 Japan Tohoku tsunami clearly show that solitary wave is not long enough when compared to the observed leading tsunami wave with the same amplitude.

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