Observation and analysis of solitary internal waves in the coastal zone of the Sea of Okhotsk

Experimental data on the measurement of solitary internal waves in the coastal zone of the Sea of Okhotsk are reported. The non-linear and dispersion coefficients of the Korteweg-de Vries (KdV) equation are determined for weakly non-linear disturbances of the first mode. The shapes and parameters of solitary waves are compared with the corresponding parameters of solitons. It is shown that at least ten observed solitary waves are similar to the KdV solitons. Histograms of the distribution of the amplitudes, duration, and spatial dimensions are plotted for a large number of solitary waves.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.     

Dynamics of a Wave Packet on the Surface of an Inhomogeneously Vortical Fluid (Lagrangian Description)

A nonlinear Schrödinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously vortical infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is shown that the modulational instability criteria for the weakly vortical waves and potential Stokes waves on deep water coincide. The effect of vorticity manifests itself in a shift of the wavenumber of high-frequency filling. A special case of Gerstner waves with a zero coefficient at the nonlinear term in the NSE is noted.     

The Moneron Tsunami of September 5, 1971, and Its Manifestation on the Sakhalin Island Coast: Numerical Simulation Results

Observation data on the September 5, 1971, earthquake that occurred near the Moneron Island (Sakhalin) have been analyzed and a numerical simulation of the tsunami induced by this earthquake is conducted. The tsunami source identified in this study indicates that the observational data are in good agreement with the results of calculations performed on the basis of shallow-water equations.     

Asteroid impact in the Black Sea. Death by drowning or asphyxiation?

Normally the consequences of an impact of an asteroid in a water body are discussed in terms of the beach run up of impact-generated waves. If even a small asteroid would hit the Black Sea, however, the potential emissions of toxic and flammable gases could be more disastrous to the region (comprised of Romania, Ukraine, Russia, Georgia, Turkey and Bulgaria) than the tsunami caused by the impact.     

Transformation of internal waves over an uneven bottom: Analytical results

The transformation of internal waves over the oceanic shelf of variable depth is studied analytically within a linear theory of a two-layer flow. It is shown that, at a specific character of depth variation, the internal wave propagates without reflection from the slope even if it is sufficiently steep. The properties of such progressive waves are studied—their form and the current structure in the upper and lower layers. The transformation of the wave propagating from the open ocean, where the depth is assumed to be constant, is considered. It is shown that the wave is transformed at the shelf edge and does not change its form in the course of time during its further propagation over the shelf. The height and form of the internal wave are calculated at the interface of the transition of the two-layer flow into the one-layer flow. Applications of the developed analytical theory to the estimation of internal wave transformation over a real shelf are discussed.     

Nonlinear effects at the initial stage of tsunami-wave development

An analytical solution to shallow-water nonlinear equations determining the height of tsunami waves leaving the source is obtained. The initial water-level displacement in the source and the distribution of particle velocities are set. The numerical solution showed that analytical estimates fit well with source characteristics varying in a broad range, even if the waves produced by the source collapse.     

Resonance three-wave interactions of stokes edge waves

Nonlinear three-wave interactions of Stokes edge waves propagating both in one direction and in opposite directions along a uniformly sloping shelf are considered. In the cases when only the lowest four modes participate in interaction, the synchronism conditions are determined and interaction coefficients are calculated. It is shown that the interaction coefficients of unidirectional edge-wave modes can vanish for certain triads. The spatiotemporal dynamics of a triad of edge waves is investigated. In addition, expressions are given for the resonance interaction coefficients of edge waves over the bottom of an arbitrary profile.