Run-up characterstics of symmetrical solitary tsunami waves of unknown shapes

The problem of tsunami wave run-up on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the run-up characteristics for various shapes of the incoming symmetrical solitary tsunami waves. It will be demonstrated that the extreme (maximal) wave characteristics on a beach (run-up and draw-down heights, run-up and draw-down velocities and breaking parameter) are weakly dependent on the shape of incident wave if the definition of the significant wave length determined on the 2/3 level of the maximum height is used. The universal analytical expressions for the extreme wave characteristics are derived for the run-up of the solitary pulses. They can be directly applicable for tsunami warning because in many case the shape of the incident tsunami wave is unknown.Comment: Submitted to PAGEOP

Preface Sea hazards

This Special Issue (SI) collects papers that were presented in different symposia related with sea hazards at the European Geosciences Union (EGU) General Assembly that was held in Vienna from 3-8 April 2011. Tsunamis are the most known and most disastrous sea hazards and can occur in all world oceans as well as in closed or almost closed seas like the Mediterranean. Interest in tsunamis has substantially increased in the last few years, especially after the case of the 2004 Indian Ocean tsunami that devastated the coasts of several near-field and far-field countries and that claimed a death toll of about 220 thousands human lives mostly in Indonesia, India, Sri Lanka and Thailand. Since then and even more after the big Japan tsunami of 11 March 2011, the issues of what we can learn from past experiences and of how coastal communities can be protected from the attack of catastrophic tsunamis have become of paramount importance. This SI collects a number of papers on the Tohoku tsunami that address different aspects of this event and papers on how to improve the response promptness and accuracy of the Tsunami Early Warning Systems. The SI addresses further the topic of rogue waves providing new contributions to the experimental and theoretical work that has been done in the last years. The third main topic of the SI regards sea level rise, storm surges and coastal floods that are subjects of particular interest to researchers, planners, and disaster control managers, since this type of natural hazard can represent an enormous threat to human life and economic assets

Long Wave Dynamics along a Convex Bottom

Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the uniqueness of this wave class is established through construction of a 1:1 transformation of the general 1D wave equation to the analogous wave equation with constant coefficients. The general solution of the Cauchy problem consists of two travelling waves propagating in opposite directions. It is found that generally a zone of a weak current is formed between these two waves. Waves are reflected from the coastline so that their profile is inverted with respect to the calm water surface. Long wave runup on a beach with this profile is studied for sine pulse, KdV soliton and N-wave. Shown is that in certain cases the runup height along the convex profile is considerably larger than for beaches with a linear slope. The analysis of wave reflection from the bottom containing a shallow coastal area of constant depth and a section with the convex profile shows that a transmitted wave always has a sign-variable shape.Comment: Submitted to Journal of Fluid Mechanic

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

New developments in tsunami science: From hazard to risk

Peer Reviewe

Non-dispersive traveling waves in inclined shallow water channels

Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic crosssection. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied