TY - JOUR

T1 - Focused wave evolution using linear and second order wavemaker theory

AU - Sriram, V.

AU - Schlurmann, T.

AU - Schimmels, S.

N1 - Cited By :39 Export Date: 1 February 2021 Funding details: Alexander von Humboldt-Stiftung Funding text 1: This research work is a part of ‘Violent wave–current interactions with offshore wind energy structure’ funded by Alexander Von Humboldt Foundation , Germany. Their support is acknowledged by the first author. Many fruitful discussions by the first author with Prof. K.F. Deamerich are greatly acknowledged, particularly the idea to represent the bound long waves in time domain for broad band spectra.

PY - 2015/10

Y1 - 2015/10

N2 - In this paper, the evolution of focused waves using different paddle displacements (piston type) under laboratory conditions is presented. It is well known that in intermediate water depths, linear paddle displacements will generate spurious, free, sub and super harmonics. Thus, a second order correction to suppress these spurious free sub and super harmonics was used to generate the focused waves. The focused waves were generated in the laboratory using a linear superimposition principle, in which the wave paddle displacement is derived based on the sum of a number of sinusoidal components at discrete frequencies, whose phases are accordingly set to focus at a particular location. For this method of generation, the second order wave maker theory proposed by Schäffer [24] can be easily adopted and was used in the present study. Two different centre frequencies (fc=0.68Hz and 1.08Hz) with three different bandwidth ratios (δf/fc=0.5, 0.75 and 1.0) were tested in a constant water depth, to consider both narrow and broadband spectra. These test cases correspond to wave focusing packets propagating in intermediate and deep water regions. Further, for each wave packet, two different amplitudes were considered in order to analyze non-breaking and breaking cases. Thus, by systematically generating the wave packets using the linear and second order paddle displacements, the analysis was carried out for the spectral and temporal evolution of selected long waves. The temporal evolution of the selected harmonics was analyzed using the Inverse Fast Fourier Transform (IFFT), to show the propagation of the spurious, free, long waves. Further, the variations in energy for the lower, higher and primary frequency ranges are reported for different wave paddle displacements. The analysis revealed that for the broadband spectrum the differences are more pronounced when using linear paddle displacements. We have also noticed a shift in focusing/breaking location and time (i.e. premature) due to the increase in crest height using linear displacements. The experiment data used in this paper has been provided as a supplementary, which can be used to validate the numerical models.

AB - In this paper, the evolution of focused waves using different paddle displacements (piston type) under laboratory conditions is presented. It is well known that in intermediate water depths, linear paddle displacements will generate spurious, free, sub and super harmonics. Thus, a second order correction to suppress these spurious free sub and super harmonics was used to generate the focused waves. The focused waves were generated in the laboratory using a linear superimposition principle, in which the wave paddle displacement is derived based on the sum of a number of sinusoidal components at discrete frequencies, whose phases are accordingly set to focus at a particular location. For this method of generation, the second order wave maker theory proposed by Schäffer [24] can be easily adopted and was used in the present study. Two different centre frequencies (fc=0.68Hz and 1.08Hz) with three different bandwidth ratios (δf/fc=0.5, 0.75 and 1.0) were tested in a constant water depth, to consider both narrow and broadband spectra. These test cases correspond to wave focusing packets propagating in intermediate and deep water regions. Further, for each wave packet, two different amplitudes were considered in order to analyze non-breaking and breaking cases. Thus, by systematically generating the wave packets using the linear and second order paddle displacements, the analysis was carried out for the spectral and temporal evolution of selected long waves. The temporal evolution of the selected harmonics was analyzed using the Inverse Fast Fourier Transform (IFFT), to show the propagation of the spurious, free, long waves. Further, the variations in energy for the lower, higher and primary frequency ranges are reported for different wave paddle displacements. The analysis revealed that for the broadband spectrum the differences are more pronounced when using linear paddle displacements. We have also noticed a shift in focusing/breaking location and time (i.e. premature) due to the increase in crest height using linear displacements. The experiment data used in this paper has been provided as a supplementary, which can be used to validate the numerical models.

KW - Focused waves

KW - Fully nonlinear potential flow theory

KW - Linear wavemaker theory

KW - Second order wavemaker theory

KW - Sub and super harmonics

KW - Fast Fourier transforms

KW - Wave packets

KW - Fully nonlinear potential flow

KW - Inverse fast Fourier transforms

KW - Laboratory conditions

KW - Second-order correction

KW - Sinusoidal components

KW - Super-harmonic

KW - Wavemaker theories

KW - Harmonic analysis

KW - Fourier transform

KW - harmonic analysis

KW - numerical model

KW - ocean wave

KW - wave modeling

UR - http://www.scopus.com/inward/record.url?scp=84945589577&partnerID=8YFLogxK

U2 - 10.1016/j.apor.2015.09.007

DO - 10.1016/j.apor.2015.09.007

M3 - Article

AN - SCOPUS:84945589577

VL - 53

SP - 279

EP - 296

JO - Applied Ocean Research

JF - Applied Ocean Research

SN - 0141-1187

ER -