Generation of Long Waves by Short Wave Groups

Dongeren, Ap van; Bakkenes, H.J.; Janssen, T. T.

doi:10.1142/9789812791306_0093

Cited by 7 publications

(12 citation statements)

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“…Thus, in the mild‐slope regime the breakpoint generation is ineffective whereas for those conditions the incident bound waves are enhanced strongly and may therefore be expected to dominate. These results lend support to and generalize the suggestion by List [1992] and the conclusion by van Dongeren et al [2002] that the fraction of the total nearshore lf energy due to incident bound waves, relative to contributions from breakpoint‐generated waves, increases with decreasing bed slope.…”

Section: Discussionsupporting

confidence: 86%

“…The dynamical significance of this phase lag is that it implies the possibility of a net energy transfer to the forced waves, as required for observed growth rates exceeding Green's law. This fact has been pointed out and exploited by van Dongeren [1997] and van Dongeren et al [2002]. Other than this, it does not seem to have received much attention.…”

Section: Energy Transfer To Shoaling Forced Wavesmentioning

confidence: 92%

“…With the energy flux F given by and the source term R given by , in which we substitute the values of and Δψ obtained from the observations, the time‐averaged lf energy balance () has for a sequence of distinct frequencies been integrated with respect to the cross‐shore distance, taking the most offshore observed value as boundary value. (A similar analysis was carried out by van Dongeren [1997], using a numerical model exclusively, and by van Dongeren et al [2002], with predicted values for and Δψ, the latter based on the theory by Janssen et al [2003].) The resulting values of have subsequently been converted into values of the surface elevation amplitude according to = h / c g .…”

Section: Energy Transfer To Lf Wavesmentioning

confidence: 96%

“…Analyses of the latter data by Janssen et al [2003] gave no indication of generation by a moving breakpoint. List [1992] and van Dongeren et al [2002] have indicated that the importance of breakpoint generation relative to (enhancement of) incident bound waves increases with increasing bed slope. We return to this question below.…”

Section: Introductionmentioning

confidence: 99%

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Shoaling of subharmonic gravity waves

et al. 2004

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[1] In this paper the energy budget of wave group-induced subharmonic gravity waves in the nearshore region is examined on the basis of the energy equation for long waves in conjunction with analyses of a high-resolution laboratory data set of one-dimensional random wave propagation over a barred beach. The emphasis is on the growth of forced subharmonics and the deshoaling of the reflected free waves in the shoaling zone. The incident lower-frequency subharmonics are nearly fully reflected at the shoreline, but the higher-frequency components appear to be subject to a significant dissipation in a narrow inshore zone including the swash zone. The previously reported phase lag of the incident forced waves behind the short-wave groups is confirmed, and its key role in the transfer of energy between the grouped short waves and the shoaling bound waves is highlighted. The cross-shore variation of the local mean rate of this energy transfer is determined. Using this as a source function in the wave energy balance allows a very accurate prediction of the enhancement of the forced waves in the shoaling zone, where dissipation is insignificant. The phase lag appears to increase with increasing frequency, which is reflected in a frequency-dependent growth rate, varying very nearly from the free-wave variation $ h À1/4 (Green's law) for the lower frequencies to the shallow-water equilibrium limit for forced subharmonics $h À5/2 for the higher frequencies. This observed frequency dependence is tentatively generalized to a dependence on a normalized bed slope, controlling whether a so-called mild-slope regime or a steep-slope regime prevails, in which enhanced incident forced waves dominate over breakpointgenerated waves or vice versa.

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Section: Discussionsupporting

confidence: 86%

Section: Energy Transfer To Shoaling Forced Wavesmentioning

confidence: 92%

Section: Energy Transfer To Lf Wavesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Shoaling of subharmonic gravity waves

et al. 2004

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“…For large values of β (

β_{b} > 0.45

) a “steep‐slope regime” is defined where the amplitude growth is weak and close to a free‐wave variation

\sim h^{- 1 / 4}

(Green's law). The parameter β has been also proposed to be inversely proportional to the ratio of the radiation stress to breakpoint long wave forcing [ Van Dongeren et al ., ]. Similarly, Baldock et al .…”

Section: Introductionmentioning

confidence: 99%

Transfer and dissipation of energy during wave group propagation on a gentle beach slope

Padilla

Alsina

2017

JGR Oceans

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The propagation of bichromatic wave groups over a constant 1:100 beach slope and the influence of the group modulation is presented. The modulation is controlled by varying the group frequency, fg, which is shown to remarkably affect the energy transfer to high and low frequency components. The growth of the high frequency (hf) wave skewness increases when fg decreases. This is explained by nonlinear coupling between the primary frequencies, which results in a larger growth of hf components as fg decreases, causing the hf waves to break earlier. Due to high spatial resolution, wave tracking has provided an accurate measurement of the varying breakpoint. These breaking locations are very well described ( R2>0.91) by the wave‐height to effective‐depth ratio (γ). However, for any given Iribarren number, this γ is shown to increase with fg. Therefore, a modified Iribarren number is proposed to include the grouping structure, leading to a considerable improvement in reproducing the measured γ‐values. Within the surf zone, the behavior of the Incident Long Wave also depends on the group modulation. For low fg conditions, the lf wave decays only slightly by transferring energy back to the hf wave components. However, for high fg wave conditions, strong dissipation of low frequency (lf) components occurs close to the shoreline associated with lf wave breaking. This mechanism is explained by the growth of the lf wave height, induced partly by the self‐self interaction of fg, and partly by the nonlinear coupling between the primary frequencies and fg.

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Can edge waves be generated by wind?

et al. 2022

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Edge waves, the infragravity waves trapped by near-shore topography, are important in morphodynamics and flooding on mildly sloping beaches. Edge waves are usually generated by swell via triad interactions. Here, we examine the possibility that edge waves might be also generated directly by wind. By processing data from the SandyDuck’97 near-shore experiment, we show that pronounced directional asymmetry of edge waves does occur in nature, apparently unrelated to the direction of swells and along-shore currents. These observations exhibit edge waves propagating in the downwind direction under moderate wind against the along-shore currents, while swell is incident nearly normally to the shoreline, which strongly suggests generation of edge waves by wind. We examine theoretically possible mechanisms of edge-wave excitation by wind. We show that the ‘maser’ mechanism suggested by Longuet-Higgins (Proc. R. Soc. Lond. A, vol. 311, issue 1506, 1969b, pp. 371–389) in the context of excitation of free water waves is effective under favourable conditions: nonlinearly interacting random short wind-forced waves create a viscous shear stress on the water surface with the variation of stress being phase linked to edge waves, which allows self-excitation of a coherent edge wave. The model we put forward is based upon the kinetic equation for short wind waves propagating on the inhomogeneous current due to an edge wave. The model needs a dedicated experiment for validation. Analysis of plausible alternative mechanisms of generation via Miles’ critical layer and via the viscous shear stresses induced by the edge wave in the air revealed no instability in the consideration confined to the main mode and constant slope bathymetry.

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Generation of Long Waves by Short Wave Groups

Cited by 7 publications

References 0 publications

Shoaling of subharmonic gravity waves

Shoaling of subharmonic gravity waves

Transfer and dissipation of energy during wave group propagation on a gentle beach slope

Can edge waves be generated by wind?

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