Runup of Tsunami Waves in U-Shaped Bays

The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of 1D shallow water theory with the use of an assumption of the uniform current on the cross-section. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied within rigorous solutions of the shallow water theory. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection. The tsunami runup in such bays is significantly larger than for a plane beach.     

Fission of a weakly nonlinear interfacial solitary wave at a step

The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.     

Steepness and spectrum of a nonlinearly deformed wave on shallow waters

The process of nonlinear deformation of a surface wave on shallow waters is investigated. The main attention is given to the relationship between the wave Fourier spectrum and the steepness of wave front slope. It is shown that an unambiguous relationship couples these quantities in the case of an initially sinusoidal wave, which allows estimation of the spectral composition of the wave field from the observed wave steepness.     

The 1996 Sulawesi Tsunami

On 1 January, 1996 at 16:05 p.m. local time, an earthquake of magnitude M = 7.8 struck the central part of Sulawesi Island (Indonesia). It was accompanied by tsunami waves 2–4 m high. Nine people were killed and 63 were injured. A tsunami survey was conducted by Indonesian and Russian specialists. The measured tsunami runup heights and eyewitness accounts are reported and discussed. Historical data on the Sulawesi Island tsunamis are analysed and tsunami risk prediction in the central part of Sulawesi Island carried out for the first time.     

Generation of long waves by random sources

A statistical approach is applied to solving the problem of long wave generation due to the ocean bottom shift. Various models of random sources are studied. The dependence of the amplitudinal characteristics of long waves on the time scale of random processes is considered. Results of the solution of the dynamic and random source problems are compared.Translated by V. Puchkin.     

The effect of the Airy phase during the propagation of edge waves

Peculiarities of the edge wave evolution a great distance away from the source are considered. It is shown that waveguide dispersion may result in discrimination of the region in a wave train corresponding to the Airy phase. The effect of the discrimination of the Airy wave in the remote zone for the model of a step-like shelf is compared with real edge waves (using the marigrams of tsunami observed in the Sea of Japan in 1983).Translated by Mikhail M. Trufanov.     

Amplitude variations of edge waves on a shelf slowly varying in the alongshore direction

Within the framework of the linear shallow-water theory, the dynamics of edge waves over a shelf characterized by a cylindrical bottom relief is investigated under the assumption that shelf parameters vary slowly in the alongshore direction. An asymptotic theory and an energy approach are used to calculate the amplitude of the edge wave. In the analytic form, the results are obtained for shelves of three different profiles with parameters varying along the shore: an infinite linear profile, a concave exponential profile, and a stepwise profile.     

Propagation of long waves in straits

The non-linear effects induced when a long wave propagates in a strait of arbitrary cross-section are investigated. Comparative analysis of the wave parameters for straits with different geometries is carried out. The relationships between the wave amplitudinal characteristics, the non-linearity scales, and the parameters of the strait's cross-section are considered.Translated by Mikhail M. Trufanov.     

Run-up of solitary waves on slopes with different profiles

The problem of sea-wave run-up on a beach is discussed within the framework of exact solutions of a nonlinear theory of shallow water. Previously, the run-up of solitary waves with different forms (Gaussian and Lorentzian pulses, a soliton, special-form pulses) has already been considered in the literature within the framework of the same theory. Depending on the form of the incident wave, different formulas were obtained for the height of wave run-up on a beach. A new point of this study is the proof of the universality of the formula for the maximum height of run-up of a solitary wave on a beach for the corresponding physical choice of the determining parameters of the incident wave, so that the effect of difference in form is eliminated. As a result, an analytical formula suitable for applications, in particular, in problems related to tsunamis, has been proposed for the height of run-up of a solitary wave on a beach.