Rapid spectral evolution of steep surface wave groups with directional spreading

Barratt, Dylan; Bingham, Harry B.; Taylor, Paul H.; Bremer, Ton S. van den; Adcock, Thomas A. A.

doi:10.1017/jfm.2020.835

Cited by 9 publications

(16 citation statements)

References 86 publications

(192 reference statements)

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“…This observation is consistent with Trulsen & Dysthe (1997) and the rapid energy transfer reported in Barratt et al. (2021). Barratt et al.…”

Section: Resultssupporting

confidence: 93%

“…For the relevant cases computed in this section, we used and m which is typical of the North Sea (Barratt et al. 2021). Using the spectra described by (6.1 a , b ), linear elevation at is given as input by with for unidirectional waves, where denotes the dimensionless steepness of a wave group at linear focus; and denote the evenly spaced discrete wavenumbers and the total number chosen for numerical implementations, respectively; the subscript ‘’ denotes the position or time for the wave group at linear focus; denotes the wave phase at linear focus; for multidirectional waves, with where and denote the evenly spaced discrete wave directions in the range of and the total number chosen for numerical implementations, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…Barratt et al. (2021) focus on a numerical study of the propagation of a steep wave group based on direct numerical solutions of fully nonlinear potential flow equations. Barratt et al.…”

Section: Resultsmentioning

confidence: 99%

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Three-dimensional surface gravity waves of a broad bandwidth on deep water

2021

J. Fluid Mech.

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A new nonlinear Schrödinger equation (NLSE) is presented for ocean surface waves. Earlier derivations of NLSEs that describe the evolution of deep-water waves have been limited to a narrow bandwidth, for which the bound waves at second order in wave steepness are described in leading-order approximations. This work generalizes these earlier works to allow for deep-water waves of a broad bandwidth with large directional spreading. The new NLSE permits simple numerical implementations and can be extended in a straightforward manner in order to account for waves on water of finite depth. For the description of second-order waves, this paper proposes a semianalytical approach that can provide accurate and computationally efficient predictions. With a leading-order approximation to the new NLSE, the instability region and energy growth rate of Stokes waves are investigated. Compared with the exact results based on McLean (J. Fluid Mech., vol. 511, 1982, p. 135), predictions by the new NLSE show better agreement than by Trulsen et al. (Phys. Fluids, vol. 12, 2000, pp. 2432–2437). With numerical implementations of the new NLSE, the effects of wave directionality are investigated by examining the evolution of a directionally spread focused wave group. A downward shift of the spectral peak is observed, owing to the asymmetry in the change rate of energy in a more complex manner than that for uniform Stokes waves. Rapid oblique energy transfers near the group at linear focus are observed, likely arising from the instability of uniform Stokes waves appearing in a narrow spectrum subject to oblique sideband disturbances.

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“…This observation is consistent with Trulsen & Dysthe (1997) and the rapid energy transfer reported in Barratt et al. (2021). Barratt et al.…”

Section: Resultssupporting

confidence: 93%

Section: Resultsmentioning

confidence: 99%

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Three-dimensional surface gravity waves of a broad bandwidth on deep water

2021

J. Fluid Mech.

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“…Only the parameters of the MNLS carrier wave and the dimensionless depth (k pd ) of the domain are varied. Barratt et al (2021) showed that the absence of the spectral tail can result in augmented wave-wave interactions. Thus, the spectra used in this study represent a conservative test of the MNLS equation, since more realistic spectra are likely to result in weaker wave-wave interactions than those observed in this investigation.…”

Section: Initial Conditionsmentioning

confidence: 99%

“…For the MNLS simulations, removal of the bound harmonics is not necessary and ϕ 0 is set to zero, causing linear focus to occur at (x = 0, y = 0, t/T 0 = 0). For the OceanWave3D simulations, each simulation is repeated with ϕ 0 values of 0 • , 90 • , 180 • and 270 • to remove the bound harmonics with four-phase separation, as used by Barratt et al (2021). The angular frequency of each component (ω i ) is calculated from the arbitrary-depth linear dispersion relationship, ω i = √ gk i tanh (k i d), allowing the initial conditions to be calculated at t/T 0 = −15.…”

Section: Initial Conditionsmentioning

confidence: 99%

MNLS simulations of surface wave groups with directional spreading in deep and finite depth waters

Barratt

Bremer

Adcock

2021

J. Ocean Eng. Mar. Energy

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We simulate focusing surface gravity wave groups with directional spreading using the modified nonlinear Schrödinger (MNLS) equation and compare the results with a fully-nonlinear potential flow code, OceanWave3D. We alter the direction and characteristic wavenumber of the MNLS carrier wave, to assess the impact on the simulation results. Both a truncated (fifth-order) and exact version of the linear dispersion operator are used for the MNLS equation. The wave groups are based on the theory of quasi-determinism and a narrow-banded Gaussian spectrum. We find that the truncated and exact dispersion operators both perform well if: (1) the direction of the carrier wave aligns with the direction of wave group propagation; (2) the characteristic wavenumber of the carrier wave coincides with the initial spectral peak. However, the MNLS simulations based on the exact linear dispersion operator perform significantly better if the direction of the carrier wave does not align with the wave group direction or if the characteristic wavenumber does not coincide with the initial spectral peak. We also perform finite-depth simulations with the MNLS equation for dimensionless depths ($$k_{\text {p}}d$$ k p d ) between 1.36 and 5.59, incorporating depth into the boundary conditions as well as the dispersion operator, and compare the results with those of fully-nonlinear potential flow code to assess the finite-depth limitations of the MNLS.

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