We derive relations between the pressure, density, magnetic field strength, velocity, and other quantities across shocks for the case of longitudinal tube waves. Due to the extreme coupling of the Rankine-Hugoniot relations for this type of waves, these relationships cannot be given separately as function of a given shock strength Ms, contrary to the case of acoustic waves. In case of weak shoc...

Finite-thickness slabs of hyperbolic media with tilted optical axes exhibit asymmetry properties for waves propagating upward and downward with respect to slab interfaces. Under certain conditions, asymmetric hyperbolic media acquire extreme permittivity parameters and the difference between upward and downward propagating waves becomes very large. Furthermore, both waves can be perfectly match...

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during ex...

Extreme waves significantly affect the coastal structures, activities, and population. Therefore, investigation of extreme wave impact on regions is essential. In this study, a mathematical...

We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance...

This paper concerns the description and the predictability of a freak event when at a certain position information in the form of a time signal is given. The prediction will use the phase information for an estimate of the position and time of the occurrence of a large wave, and to predict the measure of phase coherence at the estimated focussing position. The coherence and the spectrum will de...

In the present paper we propose a method for studying extreme-wave appearance based on the HigherOrder Spectral (HOS) technique proposed by West et al. (1987) and Dommermuth and Yue (1987). The enhanced HOS model we use is presented and validated on test cases. Investigations of freak-wave events appearing within longtime evolutions of 2-D and 3-D wavefields in open seas are then realized, and ...

Extreme all-direction wave conditions and joint probabilities of high waves and high water levels are derived at selected locations in the southern Arabian Gulf. The wave conditions are obtained using the spectral wave model SWAN with wind and offshore wave information procured from ocean weather, supplemented with local water level records. Wave transformations from offshore to nearshore and w...