From bore-soliton-splash to a new wave-to-wire wave-energy model

We explore extreme nonlinear water-wave amplification in a contraction or, analogously, wave amplification in crossing seas. The latter case can lead to extreme or rogue-wave formation at sea. First, amplification of a solitary-water-wave compound running into a contraction is disseminated experimentally in a wave tank. Maximum amplification in our bore–soliton–splash observed is circa tenfold. Subsequently, we summarise some nonlinear and numerical modelling approaches, validated for amplifying, contracting waves. These amplification phenomena observed have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-activated buoy motion and magnetically induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Most importantly, we develop a novel wave-to-wire mathematical model of the combined wave hydrodynamics, wave-activated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is in a subtle way solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LED loads, are added a posteriori. New is also the intricate and compatible finite-element space–time discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised wave-energy model are encouraging and involve a first study of the resonant behaviour and parameter dependence of the device

Rogue waves in 2006–2010

The evidence of rogue wave existence all over the world during last five years (2006–2010) has been collected based mainly on mass media sources. Only events associated with damage and human loss are included. The waves occurred not only in deep and shallow zones of the World Ocean, but also at the coast, where they were manifested as either sudden flooding of the coast or high splashes over steep banks or sea walls. From the total number of 131 reported events, 78 were identified as evidence of rogue waves (which are expected to be at least twice larger than the significant wave height). The background significant wave height was estimated from the satellite wave data. The rogue waves at the coast, where the significant wave height is unknown or meaningless, were selected based on their unexpectedness and hazardous character. The statistics built on the selected 78 events suggests that extreme waves cause more damage in shallow waters and at the coast than in the deep sea and can be used for hazard assessment of the rogue wave phenomenon

Tsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth

Tsunami wave generation by submarine landslides of a variable volume in a basin of variable depth is studied within the shallow-water theory. The problem of landslide induced tsunami wave generation and propagation is studied analytically for two specific convex bottom profiles (<i>h</i> ~ <i>x</i><sup>4/3</sup> and <i>h</i> ~ <i>x</i><sup>4</sup>). In these cases the basic equations can be reduced to the constant-coefficient wave equation with the forcing determined by the landslide motion. For certain conditions on the landslide characteristics (speed and volume per unit cross-section) the wave field can be described explicitly. It is represented by one forced wave propagating with the speed of the landslide and following its offshore direction, and two free waves propagating in opposite directions with the wave celerity. For the case of a near-resonant motion of the landslide along the power bottom profile <i>h</i> ~ <i>x</i><sup>γ</sup> the dynamics of the waves propagating offshore is studied using the asymptotic approach. If the landslide is moving in the fully resonant regime the explicit formula for the amplitude of the wave can be derived. It is demonstrated that generally tsunami wave amplitude varies non-monotonically with distance

Laboratory Modeling of Resonance Phenomena in the Long Wave Dynamics

International audienceTwo sets of experiments in a wave flume to demonstrate resonance phenomena in laboratory conditions have been performed. The first set was performed to investigate nonlinear wave run-up on the beach. It is revealed that under certain wave excitation frequencies, a significant increase in run-up amplification is observed Ezersky et al. (Nonlin Processes Geophys 20:35, 2013, [1]). It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. The second set of experiments was performed to model an excitation of localized mode (edge waves) by breaking waves propagating towards shoreline. It is shown that the excitation of edge waves is due to parametric instability similar to pendulum with vibrating point of suspension. The domain of instability in the plane of parameters (amplitude—frequency) of surface wave is found. It was found that for amplitude of surface wave slightly exceeding the threshold, the amplitude of edge wave grows exponentially with time, whereas for the large amplitude, the wave breaking appears and excitation of edge wave does not occur. It was shown that parametric excitation of edge wave can increase significantly (up to two times) the maximal run-up height

Rogue waves and solitons on a cnoidal background

Solutions of the nonlinear Schr¨odinger equation, appearing as rogue waves on a spatially-periodic background envelope, are obtained using the Darboux transformation scheme. Several particular examples are illustrated numerically. These include soliton and breather solutions on a periodic background as well as higher-order structures. The results enrich our knowledge of possible analytic solutions that describe the appearance of rogue waves in a variety of situations.The authors acknowledge the support of the Australian Research Council (Discovery Project number DP110102068). N.A. and A.A. acknowledge support from the Volkswagen Stiftung