Abstract
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.
Highlights
September 2010, three applied mathematicians at the University of Twente made requests to create a soliton in a make-shift wave tank for a new “research plaza” opening festivity
(1 − cos(ωt)), with 9.3348 s−1
We have reported in detail on the creation of the bore–soliton–splash, summarised modelling of this hydrodynamic splash, and showed how it inspired a novel wave-energy device
Summary
September 2010, three applied mathematicians at the University of Twente made requests to create a soliton in a make-shift wave tank for a new “research plaza” opening festivity. Solitons or solitary waves can be generated at the beginning of a rectangular channel with vertical walls: using either a piston moving bespokely, a block lowered at a finite yet fast speed into the water or by a quick sluice-gate removal between a higher rest-water level (h1) lock section and a lower rest-water level (h0) main section. We have used the latter for solitary-wave generation with an extra channel feature, sketched in Fig. 1 with dimensions in Table 1: a V-shaped channel end with vertical walls
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