A Phase-Amplitude Iteration Scheme for the Optimization of Deterministic Wave Sequences

Abstract

For the deterministic investigation of extreme events like capsizing, broaching or wave impacts, methods for the generation of deterministic wave sequences are required. These wave sequences can be derived from full scale measurements, numerical simulations or other sources. Most methods for the generation of deterministic wave sequences rely as a backbone on linear wave theory for the backwards transformation of the wave train from the target position in the wave basin to the position of the wave maker. This implies that nonlinear wave effects are not covered to full extend or they are completely neglected. This paper presents a method to improve the quality of the generated wave train via an experimental optimization. Based on a first wave sequence generated with linear wave theory and measured in the wave basin, the phases and amplitudes of the wave maker control signal are modified in frequency domain. The iteration scheme corrects both, shifts in time and in location, resulting in an improved deterministic wave train at the target location. The paper includes results of this method from three different basins with different types of wave generators, water depth and model scales. In addition, this method is applied to a numerical wave tank where the waves can be optimized before the actual basin testing.

Numerical modelling of interactions of waves and sheared currents with a surface piercing vertical cylinder

“…This inevitably results in a shift of the actual focus position due to non-linear wave-wave interactions (Rapp and Melville, 1990;Baldock et al, 1996;Johannessen and Swan, 2001). The iterative methods reconcile this issue by iteratively correcting either only the initial phases (Chaplin, 1996;Yao and Wu, 2005) or both the initial phases and the amplitudes (Schmittner et al, 2009;Fernandez et al, 2014;Buldakov et al, 2017) of different wave frequency components in a wave group. The iterative approach derived in Buldakov et al (2017) calculates the corrected input for the wavemaker considering only the linearized part of wave spectrum and therefore it differs from any previous methodology.…”

Application of Boundary Element Method for Determination of the Wavemaker Driving Signal

“…At the next step, a modification of an iterative scheme given in Ref. [12] is utilized for adjustment of the wavemaker motion aimed at improvement of agreement of the linear part of the surface elevation spectrum at x = 0 with the target one. For each free harmonic ω j , the wavemaker amplitudes S wm (ω j ) and phases ϕ wm (ω j ) at iteration l + 1 are adjusted by correcting their values at the previous iteration l by the difference between the target and the measured values of the amplitude and the phase in the complex surface elevation spectra:…”

“…The spatial version of the Zakharov equation was used as a theoretical model for computation of spectral changes during the wave train propagation along the experimental facility. Schmittner et al [12] utilized the phase-amplitude iteration scheme to experimentally synthesize extreme deterministic wave sequences. They indicate that this scheme is applicable even without a priorily knowing the transfer functions of the wave generator.…”

On the Generation of Tsunami in a Large Scale Wave Flume

“…The SCM was initially proposed by Daemrich et al, (1980Daemrich et al, ( , 1988 for regular and random wave generation, later used by Chaplin (1996) and Schmittner et al, (2009) for focused wave generation and recently extended for focused wave generation over variable water depth by the authors (Fernandez et al, 2014). The objective of this method is to generate a particular target wave profile at a certain position in a flume by an iterative (self-correcting) process.…”