Nonlinear long-wave deformation and runup in a basin of varying depth

Nonlinear transformation and runup of long waves of finite amplitude in a basin of variable depth is analyzed in the framework of 1-D nonlinear shallow-water theory. The basin depth is slowly varied far offshore and joins a plane beach near the shore. A small-amplitude linear sinusoidal incident wave is assumed. The wave dynamics far offshore can be described with the use of asymptotic methods based on two parameters: bottom slope and wave amplitude. An analytical solution allows the calculation of increasing wave height, steepness and spectral amplitudes during wave propagation from the initial wave characteristics and bottom profile. Three special types of bottom profile (beach of constant slope, and convex and concave beach profiles) are considered in detail within this approach. The wave runup on a plane beach is described in the framework of the Carrier-Greenspan approach with initial data, which come from wave deformation in a basin of slowly varying depth. The dependence of the maximum runup height and the condition of a wave breaking are analyzed in relation to wave parameters in deep water

Freak waves in 2005

International audienceInformation about freak wave events in the ocean reported by mass media and derived from personal observations in 2005 is collected and analysed. Nine cases are selected as true freak wave events from a total number of 27 mentioned. Besides rogue waves in the open sea, the problem of freak wave events on the shore is emphasized. These accidents are related to unexpected wave impact upon the coast and shore constructions or to sudden intensive flooding of the coast. Of the nine events considered reliable here, three events correspond to open-sea cases, while the six others occurred nearshore

Long wave propagation, shoaling and run-up in nearshore areas

This paper discusses the possibility to study propagation, shoaling and run-up of these waves over a slope in a 300-meter long large wave flume (GWK), Hannover. For this purpose long bell-shaped solitary waves (elongated solitons) of different amplitude and the same period of 30 s are generated. Experimental data of long wave propagation in the flume are compared with numerical simulations performed within the fully nonlinear potential flow theory and KdV equations. Shoaling and run-up of waves on different mild slopes is studied hypothetically using nonlinear shallow water theory. Conclusions about the feasibility of using large scale experimental facility (GWK) to study tsunami wave propagation and run-up are made.Alexander von Humboldt foundationRFBR/14-02-00983RFBR/14-05-0009

Alfv\'en Reflection and Reverberation in the Solar Atmosphere

Magneto-atmospheres with Alfv\'en speed [a] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A common example involves uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfv\'en speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where a(x) is analytic and unbounded present no internal reflection of harmonic Alfv\'en waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as O(t-1) or O(t-1 ln t), depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfv\'en waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.Comment: Accepted by Solar Physic

Rogue waters

In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for sailing and sea use. A number of huge wave accidents resulted in damages, ship losses and people injuries and deaths are known. Now marine researchers do believe that these waves belong to a specific kind of sea waves, not taken into account by conventional models for sea wind waves. This paper addresses to the nature of the rogue wave problem from the general viewpoint based on the wave process ideas. We start introducing some primitive elements of sea wave physics with the purpose to pave the way for the further discussion. We discuss linear physical mechanisms which are responsible for high wave formation, at first. Then, we proceed with description of different sea conditions, starting from the open deep sea, and approaching the sea cost. Nonlinear effects which are able to cause rogue waves are emphasised. In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear opticsComment: will be published in Contemporary Physic

Steepness and spectrum of nonlinear deformed wave in shallow water

Process of the nonlinear deformation of the surface wave in shallow water is studied. Main attention is paid to the relation between the Fourier-spectrum and wave steepness. It is shown that the spectral harmonics of the initially sine wave can be expressed through the wave steepness, and this is important for applications.Comment: 10 pages in Russian with English abstrac

Influence of the nonlinearity on statistical characteristics of long wave runup

Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values) is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Brσ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Brσ and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Brσ causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast

New developments in tsunami science: From hazard to risk

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