Interaction of capillary waves with longer waves. Part 1. General theory and specific applications to waves in one dimension

Watson, Kenneth; Buchsbaum, Steven B.

doi:10.1017/s0022112096007653

Cited by 14 publications

(15 citation statements)

References 22 publications

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“…If 1/W < ∆ k non-resonant interactions could lead thus to a net energy transfer. This hypothesis is similar to the results of Kenneth Watson (Watson & Buchsbaum 1996) describing a wave-field as interacting spatial modes. One-dimensional non-resonant threewave interactions reproduce qualitatively parasitic capillary wave generation, with a typical mismatch of 400 s −1 from the temporal resonant conditions |ω 1 ± ω 2 − ω 3 | = 0.…”

Section: Wave Correlations In Time Fourier Spacesupporting

confidence: 89%

“…Beyond this theory, in order to describe statistically spectra of gravitycapillary wave field, few authors consider the dynamics of wave action spectrum modeled with a kinetic equation including Three-Wave interactions numerically (Dulov & Kosnik 2009;Kosnik et al 2010) and analytically (Stiassnie 1996). Finally to study statistically gravity-capillary waves at higher nonlinearity an interesting approach in Fourier space consists in enabling a given mismatch to resonant conditions in wave interactions (Watson & McBride 1993;Watson & Buchsbaum 1996;Watson 1999). Parasitic waves can be numerically reproduced by considering non-resonant unidirectional Three-Wave interactions (Watson & Buchsbaum 1996;Watson 1999).…”

Section: Introductionmentioning

confidence: 99%

“…Finally to study statistically gravity-capillary waves at higher nonlinearity an interesting approach in Fourier space consists in enabling a given mismatch to resonant conditions in wave interactions (Watson & McBride 1993;Watson & Buchsbaum 1996;Watson 1999). Parasitic waves can be numerically reproduced by considering non-resonant unidirectional Three-Wave interactions (Watson & Buchsbaum 1996;Watson 1999). Therefore, at sufficiently high steepness, energy transfer to the small scales could occur through non-resonant Three-Wave interactions under the form of parasitic capillary wave generation.…”

Section: Introductionmentioning

confidence: 99%

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Turbulence of capillary waves forced by steep gravity waves

2018

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We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free-surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2 − 0.3), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from large scale to small scale. Analysis of temporal fluctuations of spatial spectrum demonstrates that the capillary powerlaw spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of wave spectrum are found to be in agreement with those of the weakly nonlinear Wave Turbulence Theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with Wave Turbulence Theory. These results suggest that theoretical developments beyond the classic Wave Turbulence Theory are necessary to describe the dynamics and statistics of capillary waves in natural environment. In particular, in presence of broad scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions could be reconsidered. † An example of the free-surface reconstruction is depicted in Fig. 2 (a) for the highest forcing amplitude σ h = 3.6 mm at t = 1.51 s. In this example, a large gravity wave

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Section: Wave Correlations In Time Fourier Spacesupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Turbulence of capillary waves forced by steep gravity waves

2018

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“…Remarkably there is little in the literature to indicate that the incorporation of such terms has been considered in a systematic fashion. Indeed examples of including dissipation within deterministic models are usually ad hoc, see e.g., Smith [1998] and Watson and Buchsbaum [1996]. The term ad hoc does not need to be taken in a perjorative sense: the terms used in these works were in accord with the stated aims of their investigations.…”

Section: Introductionmentioning

confidence: 99%

Deterministic modelling of driving and dissipation for ocean surface gravity waves

Willemsen¹

2001

J. Geophys. Res.

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Abstract. Consider two questions. What qualitative features should a spectrum of wind driven wave amplitudes possess in deep water? Then, is it possible to compute such a spectrum ab initio? In answer to the first question, at the least the spectrum should exhibit a spectral peak determined by the acting wind; an asymptotic power law tail; and an angular dependence between the dominant wind and wave directions. The principal result of this paper is that a model to calculate a wind-driven sea spectrum that satisfies the first two requirements starting from a broad suite of initial conditions has been constructed and exercised. To this end, wind driving mechanisms and models for dissipation caused by wave breaking are investigated. This study does not include detailed hydrodynamic calculations, but rather an evaluation of physically plausible model interaction terms. These are appended to Hamilton's equations for a wave field in deep water. This methodology leads to deterministic ordinary differential equations for the evolution of the wave field in which three and four wave nonlinear interactions are incorporated. The deterministic form of the equations is preserved through the introduction of nonstochastic driving and dissipation terms. The time evolution results presented fulfill the qualitative expectations desired for the spectrum. The calculations also yield much more information. Full phase information is retained. The relative magnitudes of the nonlinear interaction terms may be assessed as functions of time. The same applies for the magnitudes of the driving and dissipating terms. This information will be used to improve the model to where it is ready to confront experimental data.

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“…The coefficients and h are given, for example, in ref (1). The quantity T 4 in (2) is similar to (3), but contains sums of products of three a's.…”

Section: Form Approved Omb No 0704-0188mentioning

confidence: 99%

Excitation, Generation and Propagation of Short Capillary Waves Interacting with Longer Waves

Watson¹

1997

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LONG-TERM GOALThe first goal of this effort is to achieve a better understanding of the role of capillary waves in ocean surface phenomena. A second goal is to investigate the propagation of ocean waves into shallow water, as on beaches and reefs, and the generation of capillary waves from these. OBJECTIVESObjectives of this research are to demonstrate a physical model and a practical computational model for investigating capillary wave interactions with longer waves and to apply this to applications, such as generation and spectra in both wavenumber and frequency.Further objectives are to model nonlinear waves in shallow water, including the generation of capillary waves by these. (1) to waves in one dimension (when I refer to waves in "one dimension" I mean one surface dimenstion; when I refer to waves in two dimensions, I mean waves in two surface dimensions). Applications to waves in two dimensions have been made during the current year. APPROACH Capillary wave interactions with longer waves: The model developed is described in ref(1). Applications were made in refThe model used begins with a conventional formulation of irrotational surface wave hydrodynamics. The displacement of the water surface is Fourier expanded in a rectangular box of sides L x and L y :Use Word 6.0c or later to view Macintosh picture.(1)

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Interaction of capillary waves with longer waves. Part 1. General theory and specific applications to waves in one dimension

Cited by 14 publications

References 22 publications

Turbulence of capillary waves forced by steep gravity waves

Turbulence of capillary waves forced by steep gravity waves

Deterministic modelling of driving and dissipation for ocean surface gravity waves

Excitation, Generation and Propagation of Short Capillary Waves Interacting with Longer Waves

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