Evolution Of Surface Gravity Waves Research Articles

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

The Impacts of Gustiness on the Evolution of Surface Gravity Waves

AbstractSurface gravity waves are formed by kinetic energy transfer across the air‐sea interface. Significant improvements have been made in understanding the influence of wind on the energy input of waves. However, the impact of gustiness remains underexplored, and little is known about the mechanisms through which gusts alter the wavy surface. In this study, we utilize three‐months observational data collected during the 2010 Impact of Typhoons on the Ocean in the Pacific experiment to investigate the relationship between waves and gustiness. Results show that gustiness increases sea roughness and wave energy, leading to wave development beyond the theoretical peak of Pierson‐Moskowitz spectrum. We further find that the Hasselmann enhancement factor linearly increases with gustiness, indicating gustiness alters the wave development. We suggest that this occurs via two pathways, first, through direct coupling between swell and gustiness which increases wave‐wave interaction, and second through instantaneous reduction in wave age.

Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.

On ill-posedness of truncated series models for water waves

The evolution of surface gravity waves on a large body of water, such as an ocean, is reasonably well approximated by the Euler system for ideal, free-surface flow under the influence of gravity. The well-posedness theory for initial-value problems for these equations, which has a long and distinguished history, reveals that solutions exist, are unique, and depend continuously upon initial data in various function–space contexts. This theory is subtle, and the design of stable, accurate, numerical schemes is likewise challenging. Depending upon the wave regime in question, there are many different approximate models that can be formally derived from the Euler equations. As the Euler system is known to be well-posed, it seems appropriate that associated approximate models should also have this property. This study is directed to this issue. Evidence is presented calling into question the well-posedness of a well-known class of model equations which are widely used in simulations. A simplified version of these models is shown explicitly to be ill-posed and numerical simulations of quadratic- and cubic-order water-wave models, initiated with initial data predicted by the explicit analysis of the simplified model, lends credence to the general contention that these models are ill-posed.

Systematic study of rogue wave probability distributions in a fourth‐order nonlinear Schrödinger equation

Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of freak wave formation. The fourth‐order current‐modified nonlinear Schrödinger equation (CNLS4) is employed to describe the wave evolution. By solving CNLS4 numerically, we are able to obtain quantitative predictions for the wave height distribution as a function of key environmental conditions such as average steepness, angular spread, and frequency spread of the local sea state. Additionally, we explore the spatial dependence of the wave height distribution, associated with the buildup of nonlinear development.

Evolution of surface gravity waves over a submarine canyon

The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three‐dimensional coupled‐mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. However, a spectral refraction model predicts an even larger reduction by about a factor 10, because low‐frequency components cannot cross the canyon in the geometrical optics approximation. The coupled‐mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy ‘tunnels’ across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, confirming that evanescent modes and high‐order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles.

Extreme wave phenomena in down-stream running modulated waves

Modulational, Benjamin-Feir, instability is studied for the down-stream evolution of surface gravity waves. An explicit solution, the soliton on finite background, of the NLS equation in physical space is used to study various phenomena in detail. It is shown that for sufficiently long modulation lengths, at a unique position where the largest waves appear, phase singularities are present in the time signal. These singularities are related to wave dislocations and lead to a discrimination between successive ‘extreme’ waves and much smaller intermittent waves. Energy flow in opposite directions through successive dislocations at which waves merge and split, causes the large amplitude difference. The envelope of the time signal at that point is shown to have a simple phase plane representation, and will be described by a symmetry breaking unfolding of the steady state solutions of NLS. The results are used together with the maximal temporal amplitude MTA, to design a strategy for the generation of extreme (freak, rogue) waves in hydrodynamic laboratories.

THE SHOALING WAVES EXPERIMENT

The Shoaling Waves Experiment (SHOWEX) was a 5-yr field-oriented departmental research initiative (DRI) by the Office of Naval Research to improve the scientific understanding of the properties and evolution of surface gravity waves in intermediateand shallow-water depths (typical of inner-continental shelves up to the edge of the surf zone). The focus for this research was driven by a range of U.S. Navy needs including improving wave forecasts, understanding the interactions between waves and acoustical and optical processes, air–sea interaction, remote sensing, forces on vessels and structures, and sediment transport issues. Two complementary field experiments, one off the North Carolina coast at Duck and the other in Lake George (Australia), were carried out to test critical hypotheses concerning processes such as nonlinear interactions, wind input, whitecapping and depth-induced breaking, interactions with complex shelf topography, and bottom boundary layer phenomena. In addition, theoretical and numerical studies were conducted to explore certain aspects of the mechanics of shoaling, wind-driven waves. This section is meant to provide an assessment and lasting documentation of the present knowledge and understanding of the dynamics of surface gravity waves in shoaling waters. The eight manuscripts in this section represent the first results from the SHOWEX program using new and/or innovative technical approaches and methodologies to examine wave dynamics in finite water depth. Two of the manuscripts (Donelan, Babanin, Young, Banner, and McCormick; and Young et al.) describe new insights in the source terms in finite water depth from the experiment in Lake George, Australia. The remaining six manuscripts employ remote sensing (Plant et al., Wyatt et al., Mahrt and D. Vickers, and Sun et al.) and modeling techniques (Ardhuin and Herbers) to observe the evolution of the directional wave spectrum in shoaling water and how it relates to the overlying wind conditions and changes in the bottom topography. In particular, one manuscript (Donelan, Dobson, Graber, Madsen, and McCormick) utilizes a SWATH ship to measure the momentum input by the wind into the waves. Such measurements have been elusive due to the diffuculty in carrying them out while following a wavy surface. These manuscripts will provide new data and a foundation to answer the scientific questions posed by the SHOWEX program.

Weak turbulent Kolmogorov spectrum for surface gravity waves.

We study the long-time evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in moderately small wave numbers. We numerically implemented the primitive Euler equations for the potential flow of an ideal fluid with free surface written in Hamiltonian canonical variables, using the expansion of the Hamiltonian in powers of nonlinearity of terms up to fourth order. We show that because of nonlinear interaction processes a stationary Fourier spectrum of a surface elevation close to <|eta(k)|(2)> approximately k(-7/2) is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.

Dynamic nuclear polarization of liquid 3 He

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Bleaney B. 1998Dynamic nuclear polarization of liquid 3HeProc. R. Soc. Lond. A.454899–902http://doi.org/10.1098/rspa.1998.0192SectionRestricted accessDynamic nuclear polarization of liquid 3He B. Bleaney B. Bleaney Oxford Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK Google Scholar Find this author on PubMed Search for more papers by this author B. Bleaney B. Bleaney Oxford Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 1998https://doi.org/10.1098/rspa.1998.0192AbstractMethods of producing dynamic nuclear polarization of liquid 3He by the ‘solid effect’ method have been proposed using ‘enhanced nuclear paramagnetic resonance’ in Van Vleck compounds with singlet ground states. A number of interesting alternatives are discussed: the use of antiferromagnetic resonance, and the application of acoustic magnetic resonance, since acoustic waves can be propagated into the liquid helium itself. Acoustic resonance can be induced using either electronic magnetic resonance or enhanced nuclear resonance.In each case an external magnetic field is needed, together with radiation at a frequency equal to the sum or difference of an electronic or enhanced nuclear frequency and the nuclear resonance frequency of 3He. The liquid is polarized in opposite directions according to whether the sum or difference of the two frequencies is used. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Ming-Wei Z, Guo-lin F and Xin-Quan G (2006) Sensitivity of intrinsic mode functions of Lorenz system to initial values based on EMD method, Chinese Physics, 10.1088/1009-1963/15/6/043, 15:6, (1384-1390), Online publication date: 1-Jun-2006. Peng B, Jin X, Min Y and Su X (2006) The Study on the sEMG Signal Characteristics of Muscular Fatigue Based on the Hilbert-Huang Transform Computational Science – ICCS 2006, 10.1007/11758501_23, (140-147), . Wang W (2005) Decomposition of Wave Groups with EMD Method The Hilbert-Huang Transform in Engineering, 10.1201/9781420027532.ch12, (267-280), Online publication date: 23-Jun-2005. Hsu C and Law Y (2004) Experiments on evolution of surface gravity waves from deep to shallow waters Environmental Hydraulics and Sustainable Water Management, Two Volume Set, 10.1201/b16814-170, (1023-1028), Online publication date: 15-Dec-2004. This Issue08 March 1998Volume 454Issue 1971 Article InformationDOI:https://doi.org/10.1098/rspa.1998.0192Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/1998Published in print08/03/1998 License: Citations and impact Keywordsnuclear magnetic resonanceliquid 3Hedynamic nuclear polarizationantiferromagnetic resonanceacoustic wavesVan Vleck paramagnetism

A fully-nonlinear computational method for wave propagation over topography

By assuming that the velocity potential is locally represented by a polynomial analytically satisfying Laplace's equation, a method is developed to compute the evolution of surface gravity waves over varying topography for one dimension in plan. This local polynomial approximation (LPA) method is fast and simple and has no essential approximations in its treatment of the free surface boundary conditions. Different degrees of approximating polynomial may be used, which makes the method highly flexible. Conservation of energy considerations and comparison with both analytic results and experimental data show that, with the right choice of parameters, almost any desired level of accuracy may be achieved.

Spectral evolution of shoaling and breaking waves on a barred beach

Field observations and numerical model predictions are used to investigate the effects of nonlinear interactions, reflection, and dissipation on the evolution of surface gravity waves propagating across a barred beach. Nonlinear interactions resulted in a doubling of the number of wave crests when moderately energetic (about 0.8‐m significant wave height), narrowband swell propagated without breaking across an 80‐m‐wide, nearly flat (2‐m depth) section of beach between a small offshore sand bar and a steep (slope = 0.1) beach face, where the waves finally broke. These nonlinear energy transfers are accurately predicted by a model based on the nondissipative, unidirectional (i.e., reflection is neglected) Boussinesq equations. For a lower‐energy (wave height about 0.4 m) bimodal wave field, high‐frequency seas dissipated in the surf zone, but lower‐frequency swell partially reflected from the steep beach face, resulting in significant cross‐shore modulation of swell energy. The combined effects of reflection from the beach face and dissipation across the sand bar and near the shoreline are described well by a bore propagation model based on the nondispersive nonlinear shallow water equations. Boussinesq model predictions on the flat section (where dissipation is weak) are improved by decomposing the wave field into seaward and shoreward propagating components. In more energetic (wave heights greater than 1 m) conditions, reflection is negligible, and the region of significant dissipation can extend well seaward of the sand bar. Differences between observed decreases in spectral levels and Boussinesq model predictions of nonlinear energy transfers are used to infer the spectrum of breaking wave induced dissipation between adjacent measurement locations. The inferred dissipation rates typically increase with increasing frequency and are comparable in magnitude to the nonlinear energy transfer rates.

Two-dimensional evolution of surface gravity waves on a fluid of arbitrary depth.

Nonlinear evolution equations (NEE's) are derived that describe weakly-two-dimensional motion of surface-gravity waves on a three-dimensional incompressible and inviscid fluid. When compared with the Kadomtsev-Petviashvili (KP) equation, the NEE's presented here have the following two advantages: (a) they are applicable to wave phenomena on a fluid of arbitrary depth; and (b) they can deal with head-on collisions of various wave structures. A discussion is then made of NEE's arising from the shallow- and deep-water limits. It is shown that the KP equation is a special case of our equations.

Nonlinear evolution of surface gravity waves over an uneven bottom

A unified theory is developed which describes nonlinear evolution of surface gravity waves propagating over an uneven bottom in the case of two-dimensional incompressible and inviscid fluid of arbitrary depth. Under the assumptions that the bottom of the fluid has a slowly varying profile and the wave steepness is small, a system of approximate nonlinear evolution equations (NEEs) for the surface elevation and the horizontal component of surface velocity is derived on the basis of a systematic perturbation method with respect to the steepness parameter. A single NEE for the surface elevation is also presented. These equations are expressed in terms of original coordinate variables and therefore they have a direct relevance to physical systems. Since the formalism does not rely on the often used assumptions of shallow water and long waves, the NEEs obtained are uniformly valid from shallow water to deep water and have wide applications in various wave phenomena of physical and engineering importance. The shallow- and deep-water limits of the equations are discussed and the results are compared with existing theories. It is found that our theory includes as specific cases almost all approximate theories known at present.