Importance of second-order wave generation for focused wave group run-up and overtopping

Orszaghova, Jana; Taylor, Paul H.; Borthwick, Alistair G.L.; Raby, Alison

doi:10.1016/j.coastaleng.2014.08.007

Cited by 61 publications

(35 citation statements)

References 49 publications

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“…In terms of frequency spectrum, this band and the following bands of higher frequencies (1 Hz and 1.25 Hz) are less intense than the main band (0.28 Hz). Higher frequency waves travel slower than lower frequency waves and reach the shore after the solitary wave [19]. Therefore, high frequency waves do not have a significant impact on the spatial evolution of the main solitary wave.…”

Section: Characteristic Frequencymentioning

confidence: 99%

Physical Modelling of Extreme Waves: Gaussian Wave Groups and Solitary Waves in the Nearshore Zone

Abroug¹,

Abcha²,

Jarno³

et al. 2019

AAFM

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Laboratory-scale waves of two distinct types were generated in a twodimensional wave flume to model the spatial evolution of the frequency spectrum in the nearshore zone. The two generated types are Gaussian wave groups of different spectra widths and solitary waves. In the experiment, the time series of free surface elevation along the flume are obtained along a distance of 10m using wave gauges. For each Gaussian wave train, four regions were defined, namely peak, transfer, high frequency and low frequency region referred to as E1, E2, E3 and E4. The repartition was based on the maximum frequency spectrum situated in E1 at X=4m. Focusing is a complex process; this is mainly due to nonlinear energy transfer between different frequency ranges. It was concluded that the energy keeps stable in E1 and spreads toward E3 before breaking. The frequency spectrum in E2 has a decreasing trend during the wave train propagation and this is more appreciable for stronger wave breaking. After the breaking, the frequency spectrum in E2 stops decreasing. It was found also that frequency spectrum increases during the focusing process in E4. Concerning solitary waves, it was found that the frequency spectrum of the main solitary wave decreases as the wave approaches the breaking zone. Key words: Gaussian wave train/ frequency spectrum/ solitary wave/ peak frequency region/ Transfer region.Nomenclature E1, E2, E3 and E4: peak region, transfer region, high frequency region and low frequency region (Gaussian waves).Es: mains solitary wave frequency region situated between 0.7fp and 1.5fp, where fp being the peak frequency. X [m]: Distance along the flume. A' [m]: Solitary wave amplitude at the toe of the slope. A0 [m]: Solitary wave amplitude at X=4m from the wave maker. Ab [m]: local breaking height. As [m]: Solitary wave amplitude. C [m.s -1 ]: Solitary wave celerity. fc [Hz]: Center frequency.Physical modelling of extreme waves 3 fp [Hz]: Peak frequency. fs [Hz]: Characteristic frequency; Eq. 3. g [m.s -2 ]: Gravitational acceleration. h [m]: Water depth. hb [m]: local breaking depth. k [rad.m -1 ]: Wave number. S0: Global wave steepness (at X=4m from the wave maker). S(f): Frequency spectrum. Xb [m]: Breaking position. η (x, t) [m]: Free surface elevation. Δf [Hz]: Frequency stepping. φ [rad]: Phase at focusing.

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Section: Characteristic Frequencymentioning

confidence: 99%

Physical Modelling of Extreme Waves: Gaussian Wave Groups and Solitary Waves in the Nearshore Zone

Abroug¹,

Abcha²,

Jarno³

et al. 2019

AAFM

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“…Although it can be ignored in sufficiently deep water [15], the set-down of the wave-averaged free surface becomes important when the water depth is finite. Ignoring set-down or incorrectly reproducing it in numerical or laboratory experiments has been shown to lead to incorrect predictions of run-up on beaches [16]. Generation of wavepackets using linearly controlled wave paddles leads to spurious 'error waves' on the scale of the group, which travel ahead of the wavepacket as free waves, typically at the shallow-water phase velocity in laboratory flumes [17] (see also the discussion in [16,18]).…”

Section: Introductionmentioning

confidence: 99%

“…Ignoring set-down or incorrectly reproducing it in numerical or laboratory experiments has been shown to lead to incorrect predictions of run-up on beaches [16]. Generation of wavepackets using linearly controlled wave paddles leads to spurious 'error waves' on the scale of the group, which travel ahead of the wavepacket as free waves, typically at the shallow-water phase velocity in laboratory flumes [17] (see also the discussion in [16,18]). Second-order wave generation, where the sub-harmonic frequencies represent the correct generation of the mean flow and the set-down of the wave-averaged free surface, has been proposed to remedy this [19,20].…”

Section: Introductionmentioning

confidence: 99%

Laboratory study of the wave-induced mean flow and set-down in unidirectional surface gravity wave packets on finite water depth

et al. 2019

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The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modelling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wavepackets that is valid for all water depths, both relative to the length of the wave and the length of the wavepacket. To validate this solution, we carry out Particle Tracking Velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wavepackets, finding good agreement. The extraction technique is able to deal with small background motion and sub-harmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wavepacket scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

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“…The window reconstruction method was therefore successfully applied for a linear reconstruction of components for random waves which is the predominant method used in both CFD and physical modelling studies. There is an ongoing discussion in the research and engineering community for the use of 2 nd order nonlinear correction for wave generation (Orszaghova et al 2014), which would require the generation of wave components outside of the primary frequency band (see Tucker 1995, Schaffer 1996and Dalzell 1999. The number of operations for performing the calculation of these components would be O(N 2 ) rather than O(N), thus severely aggravating computational cost.…”

Section: Demonstration and Benchmarking Of The Windowed Reconstructiomentioning

confidence: 99%

Fast random wave generation in numerical tanks

Dimakopoulos

Lataillade

Kees

2019

Proceedings of the Institution of Civil Engineers - Engineering

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Generating and absorbing random waves in numerical models is a challenging problem, in particular when meaningful wave statistics should be generated to meet design sea state requirements. The methodology presented herein allows for the generation of random wave fields (free surface elevation and velocities) to be reconstructed in time and in space by using window processing from a reference time series. It is demonstrated that the methodology is efficient in reproducing long non-repeating wave sequences by using only O(101)-O(102) wave components, rather than O(103)-O(104) required by a direct reconstruction from a single spectrum. This reduces the computational times required for the development of wave-train time series elements by 40 times. Errors in instantaneous surface elevation and particle velocity between windowed and non-windowed reconstruction techniques were less than 0.4% and 0.2% respectively in the cases considered. The technique was combined with the relaxation zone method typically used in numerical wave tanks for generating waves. The simulations were performed using Proteus, a rapidly developing CFD-FEM toolkit for modelling fluid structure interaction cases. The use of windowed reconstruction reduced the overall computational time associated with the simulation of waves in a numerical wave tank by ~40% and ~70% for serial and parallel execution. Results of the study show windowed reconstruction to be suitable for the representation of long-duration wave trains. Wave height and peak period are conserved within 2% and 1% respectively.

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Importance of second-order wave generation for focused wave group run-up and overtopping

Cited by 61 publications

References 49 publications

Physical Modelling of Extreme Waves: Gaussian Wave Groups and Solitary Waves in the Nearshore Zone

Physical Modelling of Extreme Waves: Gaussian Wave Groups and Solitary Waves in the Nearshore Zone

Laboratory study of the wave-induced mean flow and set-down in unidirectional surface gravity wave packets on finite water depth

Fast random wave generation in numerical tanks

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