المؤلفون: Lin, Guobin¹ (AUTHOR) lgb401@shu.edu.cn

المصدر: Symmetry (20738994). May2024, Vol. 16 Issue 5, p618. 32p.

مصطلحات موضوعية: *GRAVITY waves, *WATER depth, *SURFACE waves (Fluids), *HAMILTON'S equations, *RESONANCE

مستخلص: Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions, the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant second-, third-, fourth-, and fifth-order nonlinear terms though a suitable canonical transformation. The four kernels of the equation and the 18 coefficients of the transformation are expressed in explicit form in terms of the expansion coefficients of the gravity wave Hamiltonian in integral-power series in normal variables. The possibilities of the existence of integrals of motion for the wave momentum and the wave action are discussed, particularly the special integrals for the latter. For ocean surface capillary–gravity waves on a fluid with a finite depth, the sixth-order expansion coefficients of the Hamiltonian in integral-power series in normal variables are concretely provided, thus naturally including the classical fifth-order kinetic energy expansion coefficients given by Krasitskii. [ABSTRACT FROM AUTHOR]

المؤلفون: Feddersen, F.¹ (AUTHOR) ffeddersen@ucsd.edu, Amador, Andre¹ (AUTHOR), Pick, Kanoa¹ (AUTHOR), Vizuet, A. (AUTHOR), Quinn, Kaden¹ (AUTHOR), Wolfinger, Eric² (AUTHOR), MacMahan, J. H.³ (AUTHOR), Fincham, Adam⁴ (AUTHOR)

المصدر: Coastal Engineering Journal. Mar2024, Vol. 66 Issue 1, p44-57. 14p.

مصطلحات موضوعية: *GRAVITY waves, *TURBULENCE, *WATER waves, *WATER depth, *KINEMATICS, *LAGRANGE equations, *MOTION

مستخلص: Waves and wave breaking are important to many deep and shallow water processes. We describe the wavedrifter, an in situ water-following inertial measurement unit (IMU)-based drifter that measures wave steepening and overturning kinematics, and the subsequent transition to turbulence. The wavedrifter has 5 cm diameter, 77 g mass, and 0.84 saltwater specific gravity. GPS provides time synchronization. MATLAB's Attitude, Heading, Reference System (AHRS) library provides wavedrifter orientation. Laboratory experiments quantify the wavedrifter vertical oscillation mode, water following properties, and ability to reproduce wave spectra for small, $f = 1.5$ f = 1.5 Hz waves. The wavedrifter observed wave overturning and the transition to turbulence at the Surf Ranch wave basin. Synchronized video observations provide context. The upper-back of the overturn had large ($ \approx 4g$ ≈ 4 g) accelerations and $14g$ 14 g acceleration magnitude occurs with the impact of the overturning jet. Trajectories reveal the Lagrangian structure of the overturn and subsurface vortex. Although it has limitations, the wavedrifter is a powerful in situ tool to probe wave processes. [ABSTRACT FROM AUTHOR]

المؤلفون: Riquier, Alan, Dormy, Emmanuel

المصدر: Journal of Fluid Mechanics; 4/10/2024, Vol. 984, p1-13, 13p

مصطلحات موضوعية: WATER waves, BOUNDARY layer (Aerodynamics), VISCOSITY, VORTEX motion, GRAVITY waves

مستخلص: We introduce a numerical strategy to study the evolution of two-dimensional water waves in the presence of a plunging jet. The free-surface Navier–Stokes solution is obtained with a finite, but small, viscosity. We observe the formation of a surface boundary layer where the vorticity is localised. We highlight convergence to the inviscid solution. The effects of dissipation on the development of a singularity at the tip of the wave is also investigated by characterising the vorticity boundary layer appearing near the interface. [ABSTRACT FROM AUTHOR]

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المؤلفون: Bennetts, Luke G., Williams, Timothy D., Porter, Richard

المصدر: Journal of Fluid Mechanics; 4/10/2024, Vol. 984, p1-27, 27p

مصطلحات موضوعية: OCEAN waves, ICE shelves, VERTICAL motion, VARIATIONAL principles, LINEAR equations, GRAVITY waves

مستخلص: A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean draught. The variational principle is used to form a thin-plate approximation for the ice shelf, which includes water–ice coupling at the shelf front and extensional waves in the shelf, in contrast to the benchmark thin-plate approximation for ocean wave interactions with an ice shelf. The thin-plate approximation is combined with a single-mode approximation in the water, where the vertical motion is constrained to the eigenfunction that supports propagating waves. The new terms in the approximation are shown to have a major impact on predictions of ice shelf strains for wave periods in the swell regime. [ABSTRACT FROM AUTHOR]

: Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: Hansen, Christine Lynggård, Bredmose, Henrik, Vincent, Maude, Steffensen, Stefan Emil, Pegalajar-Jurado, Antonio, Jensen, Bjarne, Dixen, Martin

المصدر: Journal of Fluid Mechanics; 3/10/2024, Vol. 982, p1-34, 34p

مصطلحات موضوعية: OCEAN waves, RESONANT vibration, WAVE forces, NONLINEAR waves, GRAVITY waves, POWER spectra

مستخلص: The dynamics and nonlinear wave forcing of a flexible floating structure are investigated experimentally and numerically. The floater was designed to match sub-harmonic rigid-body natural frequencies of typical floating wind turbine substructures, with the addition of a flexible bending mode. Experiments were carried out for three sea states with phase-shifted input signals to allow harmonic separation of the measured response. We find for the weakest sea states that sub-harmonic rigid-body motion is driven by even-harmonic difference frequency forcing, and by linear forcing for the strongest sea state. The flexible mode was tested in a soft, linearly forced layout, and a stiff layout, forced by second-, third- and fourth-harmonic frequency content, for increasing severity of the sea state. Further insight is gained by analysis of the amplitude scaling of the resonant response. A new simplified approach is proposed and compared with the recent method of Orszaghova et al. (J. Fluid Mech., vol. 929, 2021, A32). We find that resonant surge and pitch motions are dominated by even-harmonic potential-flow forcing and that odd-harmonic response is mainly potential-flow driven in surge and mainly drag driven in pitch. The measured responses are reproduced numerically with second-order forcing and quadratic drag loads, using a recent and computationally efficient calculation method, extended here for the heave, pitch and flexible motions. We are able to reproduce the response statistics and power spectra for the measurements, including the subharmonic pitch and heave modes and the flexible mode. Deeper analysis reveals that inaccuracies in the even-harmonic forcing content can be compensated by the odd-harmonic loads. [ABSTRACT FROM AUTHOR]

: Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: Onorato, Miguel, Janssen, Peter A. E. M.

المصدر: Journal of Fluid Mechanics; 2/10/2024, Vol. 980, p1-14, 14p

مصطلحات موضوعية: GRAVITY waves, WATER depth, WATER waves, EVOLUTION equations, PLANE wavefronts, WAVE analysis, SHALLOW-water equations

مستخلص: The Zakharov equation describes the evolution of weakly nonlinear surface gravity waves for arbitrary spectral shape. For deep-water waves, results from the Zakharov equation are well established. However, for two-dimensional propagation, in intermediate and shallow water, there are problems related to the treatment of apparent singularities in the contribution of the wave-induced set-up to the evolution of the surface gravity waves. More specifically, the kernel in the integral term is characterized by a regular and an apparent singular contribution. Here, we show that the Davey-Stewartson equation can be directly derived from the Zakharov equation, also in the shallow water limit. This result provides guidance on how to treat the singular contribution to the evolution of the action variable. A relevant result that is obtained is that the growth rate obtained from the stability analysis of a plane wave in shallow water does not depend on the singular part of the kernel of the Zakharov equation. [ABSTRACT FROM AUTHOR]

: Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: Simonis, Ashleigh, Hrabski, Alexander, Yulin Pan

المصدر: Journal of Fluid Mechanics; 1/25/2024, Vol. 979, p1-16, 16p

مصطلحات موضوعية: NONLINEAR waves, GRAVITY waves, DISPERSION relations, LINEAR orderings, WAVE equation, TURBULENCE, ELASTIC waves

مستخلص: As presented in Annenkov & Shrira (Phys. Rev. Lett., vol. 102, 2009, 024502), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ‘fast’ dynamic time scale of O(ε⁻²), with ε a measure of wave steepness. This observation poses a challenge to wave turbulence theory that predicts an evolution with a kinetic time scale of O(ε⁻⁴). We revisit this unresolved problem by studying the same situation in the context of a one-dimensional Majda–McLaughlin–Tabak equation with gravity wave dispersion relation. Our results show that the kinetic and dynamic time scales can both be realised, with the former and latter occurring for weaker and stronger forcing perturbations, respectively. The transition between the two regimes corresponds to a critical forcing perturbation, with which the spectral evolution time scale drops to the same order as the linear wave period (of some representative mode). Such fast spectral evolution is mainly induced by a far-from-stationary state after a sufficiently strong forcing perturbation is applied. We further develop a set-based interaction analysis to show that the inertial-range modal evolution in the studied cases is dominated by their (mostly non-local) interactions with the low-wavenumber ‘condensate’ induced by the forcing perturbation. The results obtained in this work should be considered to provide significant insight into the original gravity wave problem. [ABSTRACT FROM AUTHOR]

: Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: Gramstad, Odin, Lian, Gunnar

المصدر: Journal of Fluid Mechanics; 1/25/2024, Vol. 979, p1-24, 24p

مصطلحات موضوعية: KURTOSIS, OCEAN waves, NUMERICAL calculations, GRAVITY waves

مستخلص: An efficient numerical method for calculation of the sea surface skewness and kurtosis for arbitrary wave spectra, taking up to third-order nonlinear effects into account, is developed. The skewness and kurtosis are calculated for a large number of sea states, covering a wide range of sea-state parameters in terms of wave steepness, water depth, directional spreading and frequency bandwidth. The results are used to propose new accurate expressions for skewness and kurtosis, valid over a wide range of sea states. Existing expressions for skewness and kurtosis reported in the literature are reviewed, and their accuracy is evaluated. Comparison to model-test results and phase-resolved numerical simulation are presented. It is suggested that the new improved parametrizations for skewness and kurtosis, which include dependence on wave steepness, water depth, spectral bandwidth and directional spreading, represent a convenient way to include these covariates into higher-order distributions for crest heights, wave heights and surface elevation. [ABSTRACT FROM AUTHOR]

: Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: Haiqi Fang, Lian Tang, Pengzhi Lin

المصدر: Journal of Fluid Mechanics; 1/25/2024, Vol. 979, p1-34, 34p

مصطلحات موضوعية: NONLINEAR waves, SAND bars, SURFACE scattering, GRAVITY waves, ANALYTICAL solutions, WAVENUMBER

مستخلص: Based on the multiple-scale expansion technique, a new set of extended nonlinear Schrödinger (ENLS) equations up to the third order is derived to account for the additional high-order bottom and dispersion effects as well as the nonlinear wave interaction on wave transformation over periodic sandbars of sinusoidal geometry. By employing the small-amplitude wave assumption, a closed-form analytical solution for Bragg scattering is obtained from the linearised ENLS equations, which demonstrates that a downshift of wave frequency of the maximum reflection is mainly due to the inclusion of the high-order bottom effect. The factors that affect the downshift of the resonant frequency are identified and a theoretical expression in parabolic form is derived to quantify the downshift magnitude. The fully ENLS equations are further analysed to reveal the additional wave nonlinear effects on Bragg scattering characteristics. Under the condition of infinitesimal sandbar amplitude, the ENLS equations render a theoretical expression of the critical value of kh when the nonlinear wave self-modulation effect and the nonlinear wave cross-modulation effect are equal, whereas the former effect is responsible for wavenumber upshifting and the latter downshifting. When kh is larger than the critical value, the increase of wave nonlinearity will enhance the downshift magnitude of the Bragg resonance, and vice versa. For finite amplitude of the bottom sandbar, the ENLS equations are solved numerically to examine the influence of both wave nonlinearity and sandbar amplitude on the characteristics of Bragg resonance. The results reveal that as the increase of sandbar amplitude, the critical kh increases monotonically. [ABSTRACT FROM AUTHOR]

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المؤلفون: Bonneton, Philippe

المصدر: Journal of Fluid Mechanics; 12/25/2023, Vol. 977, pA48-1-A48-25, 35p

مصطلحات موضوعية: ENERGY dissipation, GRAVITY waves, STRESS waves, SURFACE waves (Seismic waves), WATER depth, HAMBURGERS

مستخلص: The spectral behaviour of random sawtooth waves propagating in the inner surf zone is investigated in this study. We show that the elevation energy spectrum exhibits a universal shape with an ω^-2 tendency in the inertial subrange and an exponential decay in the diffusive subrange (ω being the angular frequency). A theoretical spectrum is derived based on the similarities between sawtooth waves in the inner surf zone and Burgers wave solutions. Very good agreement is shown between this theoretical spectrum and laboratory experiments covering a large range of incident random wave conditions. Additionally, an equation describing the universal shape of the dissipation spectrum is derived. It highlights that the dissipation spectrum is nearly constant in the inertial subrange, consistent with prior laboratory observations. The findings presented in this study can be useful to improve broken wave dissipation parametrizations in stochastic spectral wave models. [ABSTRACT FROM AUTHOR]

: Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)