Wave Kinematics Research Articles

Lagrangian kinematics of steep waves up to the inception of a spilling breaker

Horizontal Lagrangian velocities and accelerations at the surface of steep water-waves are studied by Particle Tracking Velocimetry for gradually increasing crest heights up to the inception of a spilling breaker. Localized steep waves are excited using wavemaker-generated Peregrine breather-type wave trains. Actual crest and phase velocities are estimated from video recorded sequences of the instantaneous wave shape as well as from surface elevation measurements by wave gauges. Effects of nonlinearity and spectral width on phase velocity, as well as the relation between phase velocity and crest propagation speed are discussed. The inception of a spilling breaker is associated with the horizontal velocity of water particles at the crest attaining that of the crest, thus confirming the kinematic criterion for inception of breaking.

Comparison of Extreme Offshore Structural Response from Two Alterna-tive Stretching Techniques

Linear random wave theory (LRWT) has successfully explained most properties of real sea waves with the ex-ception of some nonlinear effects for surface elevation and water particle kinematics. Due to its simplicity, it is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record; however, predicted water particle kinematics from LRWT suffer from unrealistically large high-frequency compo-nents in the vicinity of mean water level (MWL). To overcome this deficiency, a common industry practice for evaluation of wave kinematics in the free surface zone consists of using linear random wave theory in conjunction with empirical techniques (such as Wheeler and vertical stretching methods) to provide a more realistic representation of near-surface wave kinematics. It is well known that the predicted kinematics from these methods are different; however, no systematic study has been conducted to investigate the effect of this on the magnitude of extreme responses of an offshore structure. In this paper, probability distributions of extreme responses of an offshore structure from Wheeler and vertical stretching methods are compared. It is shown that the difference is significant; consequently, further research is required to deter-mine which method is more reliable.

A generalized approach to the mechanics of three-dimensional nonlinear ocean waves

The paper suggests a generalized approach to the analysis of second-order three-dimensional random wave fields that can represent either ocean waves in an undisturbed field or standing ocean waves. A nonlinear stochastic family is introduced that has a linear stationary Gaussian random contribution and a second-order correction exact in a Stokes expansion. This family can describe the nonlinear mechanics of a random wave field. Subsequently, in the considered random ocean field, the nonlinear mechanics of wave groups can be investigated conditional to the occurrence of a very high wave. The free-surface displacement and velocity potential may be obtained, as well as the nonlinear wave velocity and acceleration, for both the stochastic family and the very high wave groups. The results are of interest for the analysis of nonlinear wave kinematics when extreme surface wave events occur and thus for Morison′s wave forces on slender structures.

The role of the nonlinear wave kinematics on the global responses of an OWT in parked and operating conditions

High accuracy in the prediction of design loads for offshore wind turbines is a crucial prerequisite to achieve safe and economic designs. In this paper it is shown that numerical tools used to reproduce the wave-induced loads on offshore wind turbines are often based on overly simplistic mathematical models, which lead to important inaccuracies in the assessment of the system response. The study investigates the effects of nonlinear waves on the structural response of a bottom-supported offshore wind turbine. The main concern addresses the different behavior of the system when the turbine is in parked condition or when the turbine is in power production. In the parked configuration, the nonlinear wave kinematics used in the Morison equation causes dangerous effects in terms of internal stresses and resonant vibrations of the dynamical system. They are entirely missed when a linear wave kinematics is used. When the turbine is in power production the global damping increases dramatically due to the aeroelastic interaction of the rotor. Significant growth of the system response still occurs due to the nonlinear wave forcing; however, the resonant vibrations are completely damped out. A simple quantification of the equivalent linear damping ratio, modeling the first fore-aft mode of the tower as a 1-DOF linear damped mass–spring system, permits a rough estimation of the contribution to the global damping of the aeroelastic effects. During power production the system exhibits ten-time larger damping capabilities with respect to the parked condition.

Improved methods for determining the kinematics of coronal mass ejections and coronal waves

The study of solar eruptive events and associated phenomena is of great importance in the context of solar and heliophysics. Coronal mass ejections (CMEs) and coronal waves are energetic manifestations of the restructuring of the solar magnetic field and mass motion of the plasma. Characterising this motion is vital for deriving the dynamics of these events and thus understanding the physics driving their initiation and propagation. The development and use of appropriate methods for measuring event kinematics is therefore imperative. Traditional approaches to the study of CME and coronal wave kinematics do not return wholly accurate nor robust estimates of the true event kinematics and associated uncertainties. We highlight the drawbacks of these approaches, and demonstrate improved methods for accurate and reliable determination of the kinematics. The Savitzky-Golay filter is demonstrated as a more appropriate fitting technique for CME and coronal wave studies, and a residual resampling bootstrap technique is demonstrated as a statistically rigorous method for the determination of kinematic error estimates and goodness-of-fit tests. It is shown that the scatter on distance-time measurements of small sample size can significantly limit the ability to derive accurate and reliable kinematics. This may be overcome by (i) increasing measurement precision and sampling cadence, and (ii) applying robust methods for deriving the kinematics and reliably determining their associated uncertainties. If a priori knowledge exists and a pre-determined model form for the kinematics is available (or indeed any justified fitting-form to be tested against the data), then its precision can be examined using a bootstrapping technique to determine the confidence interval associated with the model/fitting parameters.

Band‐limited ray tracing

ABSTRACTWe develop a new ray‐tracing method, namely, band‐limited ray tracing, which aims to overcome some of the limitations of standard high‐frequency ray tracing in complex velocity models that contain complex interfaces. Band‐limited ray tracing is based on the Kirchhoff integral representation of the transmitted wavefield. In our discussion we consider the Kirchhoff integral for the acoustic wave equation, however, our method can be extended to the Kirchhoff integral for the elastic wave equation. When compared to finite‐difference wave propagation, the new method captures the wave kinematics more accurately than conventional ray tracing while staying within the ray‐tracing framework, without requiring processing or alteration to the original model. We present the theory of band‐limited ray tracing and demonstrate its capability. We compare the Kirchhoff migration examples obtained using conventional ray‐tracing and band‐limited ray‐tracing methods. Our synthetic example demonstrates that band‐limited ray tracing provides better results than conventional ray tracing, especially in estimating wavefronts. In the case of the real data example, the results are comparable to each other while presenting different focusing characteristics. The different focusing characteristics indicate the necessity of performing a full model building workflow for an extended evaluation on real data application.

Rogue waves, rogue events and extreme wave kinematics in spatio-temporal fields of simulated sea states

Abstract. An approach to the extensive study of rogue wave occurrence in numerical simulations is presented. As a result of numerical simulations of the unidirectional wave evolution, spatio-temporal fields of wave data of the size 20 min × 10 km are obtained with high resolution in time and space and are used for statistical analysis with the focus on extreme waves. Having the exhaustive information on the wave evolution enables us to capture the detailed picture of individual rogue waves; to detect intermittent rogue wave events, which last for a significantly longer time, and hence, to depict the portrait of a rogue wave. Due to the benefit of having full-wave data, the question of relation between extreme wave kinematics and extremely high waves is discussed in the statistical sense.

Assessment of GeoEye-1 stereo-pair-generated DEM in flood mapping of an ungauged basin

A very high resolution (VHR) digital elevation model (DEM) is produced from a GeoEye-1 0.5-m-resolution satellite stereo pair and is used for floodplain management and mapping applications such as watershed delineation and river cross-section extraction. For this purpose, a 2 m × 2 m resolution terrain surface is produced from the stereo pair by using the Leica Photogrammetry Suite (LPS) enhanced Automatic Terrain Extraction (eATE) algorithm. DEM accuracy is assessed by comparison with measured individual ground control points (GCPs), stream cross-sections and other landscape features. Results show that the produced DEM is in good agreement with ground truth and superior to products of lower resolution, such as 90 m NASA Shuttle Radar Topography Mission (SRTM) and 1:5,000 topographical maps. One- and two-dimensional hydraulic models are used to simulate rainfall–runoff characteristics and flood wave kinematics of the flash flood event of 17 October 2006 that occurred in the ungauged basin of Almirida, using the 2 m VHR-DEM as an input. Results show that the hydraulic simulation based on the generated VHR-DEM, calibrated and validated via field data, produces an accurate extent and water level of the flooded area. Remote sensing stereo reconstruction is a promising alternative to traditional survey methods in flood mapping applications.

Diffraction imaging of sub‐vertical fractures and karst with full‐resolution 3D Ground‐Penetrating Radar

ABSTRACTVertical fractures with openings of less than one centimetre and irregular karst cause abundant diffractions in Ground‐Penetrating Radar (GPR) records. GPR data acquired with half‐wavelength trace spacing are uninterpretable as they are dominated by spatially undersampled scattered energy. To evaluate the potential of high‐density 3D GPR diffraction imaging a 200 MHz survey with less than a quarter wavelength grid spacing (0.05 m × 0.1 m) was acquired at a fractured and karstified limestone quarry near the village of Cassis in Southern France. After 3D migration processing, diffraction apices line up in sub‐vertical fracture planes and cluster in locations of karstic dissolution features. The majority of karst is developed at intersections of two or more fractures and is limited in depth by a stratigraphic boundary. Such high‐resolution 3D GPR imaging offers an unprecedented internal view of a complex fractured carbonate reservoir model analogue. As seismic and GPR wave kinematics are similar, improvements in the imaging of steep fractures and irregular voids at the resolution limit can also be expected from high‐density seismic diffraction imaging.

Interpreting Solar EUV Wave Observations from Different Viewing Angles Using an MHD Model

We study the effect of projection and line-of-sight integration on the interpretation of the morphology and kinematics of EUV waves. We have performed a three-dimensional magnetohydrodynamic simulation of a coronal mass ejection (CME) erupting in an environment that mimics the low solar corona and calculated the resulting emission measure of the event from five different viewing angles. Our study provides more quantitative information about the impact of the viewing angle and projection effect on the properties of EUV waves than previous studies on the subject. Analyzing the emission measure of the lower corona reveals wave-like increases that move away from the eruption site, which we interpret as EUV waves. Behind the EUV wave front we can recognize coronal dimming regions. A comparison of the emission measure and calculated density supports the view that EUV waves are true waves. Our results show that the origin of the observed EUV wave is height-dependent, which means that the measured speed and the morphology depend on the viewing direction. Consequently, care should be taken when EUV observations are used to infer the true propagation speeds of EUV wave fronts.

Nonlinear response of fixed jacket offshore platform under structural and wave loads

The structural design requirements of an offshore platform subjected to wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good estimation of wave loadings are essential. A nonlinear response analysis of a fixed offshore platform under structural and wave loading is presented, the structure is discretized using the finite element method, wave plus current kinematics (velocity and acceleration fields) are generated using 5th order Stokes wave theory, the wave force acting on the member is calculated using Morison's equation. Hydrodynamic loading on horizontal and vertical tubular members and the dynamic response of fixed offshore structure together with the distribution of displacement, axial force and bending moment along the leg are investigated for regular and extreme conditions, where the structure should keep production capability in conditions of the 1-yr return period wave and must be able to survive the 100-yr return period storm conditions. The result of the study shows that the nonlinear response investigation is quite crucial for safe design and operation of offshore platform.

Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth

AbstractOceanic pressure measurements, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 s, which is believed to be excited by ocean surface gravity waves. Most of this noise is explained by a nonlinear wave–wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical work on seismic noise focused on surface (Rayleigh) waves, and did not consider finite-depth effects on the generating wave kinematics. These finite-depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that were limited to vertical propagation only. Finally, the noise generation theory is also extended beyond the domain of Rayleigh waves, giving the first quantitative expression for sources of seismic body waves. In the limit of slow phase speeds in the ocean wave forcing, the known and well-verified gravity wave result is obtained, which was previously derived for an incompressible ocean. The noise source of acoustic, acoustic-gravity and seismic modes are given by a mode-specific amplification of the same wave-induced pressure field near zero wavenumber.

The effect of an emergent vegetation (i.e. Phragmistes Australis) on wave attenuation and wave kinematics

ABSTRACT Akgul, M.A., Yilmazer, D., Oguz, E., Kabdasli, M.S., Yagci, O., 2013. The effect of an emergent vegetation (i.e. Phragmistes Australis) on wave attenuation and wave kinematics Coastal vegetation acts as a natural barrier at many coastal zones, protecting the landside against wave effects and coastal erosion. It is known that coastal vegetation affects wave properties, and studies regarding this topic have been made in a wide variety, mostly focusing on wave attenuation. In this study, laboratory experiments have been conducted in a wave basin to inspect the effect of an emergent vegetation on wave attenuation, wave transformation and wave kinematics. A blank area is present along the reed field, which enables energy transformation during wave propagation. Three different regular waves have been sent to a natural reed field, and wave heights and kinematics have been measured around the structure. The results indicate that crest-parallel energy transmission takes place as the waves propagate along ...

Nonlinear Finite Element Analysis of Spar Platform

In recent decades, oil and gas exploration technology has moved towards the offshore deep-water deposits. Conventional fixed jacket type platforms and bottom supported compliant platforms are found to be inefficient for exploring these resources. Floating Spar platform is suitable alternative in deep water regions. The present study performs coupled analysis of integrated Spar platform with full hull cylinder. This mathematical model incorporates almost all the major nonlinearities. Time domain analysis is done adopting an automatic Newmark- I² time integration technique. Airy's wave theory is used for calculating for wave kinematics. Wave induced spar hull motion in surge, heave and pitch directions along with maximum tension in mooring line has been assessed for extreme wave height condition in 1018 m water depth.

Karhunen–Loeve representation of stochastic ocean waves

A new stochastic representation of a seastate is developed based on the Karhunen–Loeve spectral decomposition of stochastic signals and the use of Slepian prolate spheroidal wave functions with a tunable bandwidth parameter. The new representation allows the description of stochastic ocean waves in terms of a few independent sources of uncertainty when the traditional representation of a seastate in terms of Fourier series requires an order of magnitude more independent components. The new representation leads to parsimonious stochastic models of the ambient wave kinematics and of the nonlinear loads and responses of ships and offshore platforms. The use of the new representation is discussed for the derivation of critical wave episodes, the derivation of up-crossing rates of nonlinear loads and responses and the joint stochastic representation of correlated wave and wind profiles for use in the design of fixed or floating offshore wind turbines. The forecasting is also discussed of wave elevation records and vessel responses for use in energy yield enhancement of compliant floating wind turbines.

The Temporal Autocorrelation Structure of Sea Surface Winds

Abstract The temporal autocorrelation structures of sea surface vector winds and wind speeds are considered. Analyses of scatterometer and reanalysis wind data demonstrate that the autocorrelation functions (acf) of surface zonal wind, meridional wind, and wind speed generally drop off more rapidly in the midlatitudes than in the low latitudes. Furthermore, the meridional wind component and wind speed generally decorrelate more rapidly than the zonal wind component. The anisotropy in vector wind decorrelation scales is demonstrated to be most pronounced in the storm tracks and near the equator, and to be a feature of winds throughout the depth of the troposphere. The extratropical anisotropy is interpreted in terms of an idealized kinematic eddy model as resulting from differences in the structure of wind anomalies in the directions along and across eddy paths. The tropical anisotropy is interpreted in terms of the kinematics of large-scale equatorial waves and small-scale convection. Modeling the vector wind fluctuations as Gaussian, an explicit expression for the wind speed acf is obtained. This model predicts that the wind speed acf should decay more rapidly than that of at least one component of the vector winds. Furthermore, the model predicts a strong dependence of the wind speed acf on the ratios of the means of vector wind components to their standard deviations. These model results are shown to be broadly consistent with the relationship between the acf of vector wind components and wind speed, despite the presence of non-Gaussian structure in the observed surface vector winds.

Particle trajectories beneath wave-current interaction in a two-dimensional field

Abstract. Within the Lagrangian reference framework we present a third-order trajectory solution for water particles in a two-dimensional wave-current interaction flow. The explicit parametric solution highlights the trajectory of a water particle and the wave kinematics above the mean water level and within a vertical water column, which were calculated previously by an approximation method using an Eulerian approach. Mass transport associated with a particle displacement can now be obtained directly in Lagrangian form without using the transformation from Eulerian to Lagrangian coordinates. In particular, the Lagrangian wave frequency and the Lagrangian mean level of particle motion can also be obtained, which are different from those in an Eulerian description. A series of laboratory experiments are performed to measure the trajectories of particles. By comparing the present asymptotic solution with laboratory experiments data, it is found that theoretical results show excellent agreement with experimental data. Moreover, the influence of a following current is found to increase the relative horizontal distance traveled by a water particle, while the converse is true in the case of an opposing current.

A study of flow structure of bichromatic waves through PIV analysis

An experimental study was carried out in order to understand the kinematics of bichromatic waves. Bichromatic waves are generated in a two-dimensional wave tank, and measured by panorama PIV technique, which allows the flow fields to be captured with respect to a spatial coordinate system. We compared wave profiles and velocities of wave particles obtained by experiment with theoretical results using Stokes 1st and 2nd order waves. The velocity distribution at wave crest and trough of the highest and lowest point of a bichromatic wave are investigated in this study.

Kinematics and amplitude evolution of global coronal extreme ultraviolet waves

With the observations of the Solar-Terrestrial Relations Observatory (STEREO) and the Solar Dynamics Observatory (SDO), we analyze in detail the kinematics of global coronal waves together with their intensity amplitudes (so-called “perturbation profiles"). We use a semi-automatic method to investigate the perturbation profiles of coronal waves. The location and amplitude of the coronal waves are calculated over a 30° sector on the sphere, where the wave signal is strongest. The position with the strongest perturbation at each time is considered as the location of the wave front. In all four events, the wave velocities vary with time for most of their lifetime, up to 15 min, while in the event observed by the Atmospheric Imaging Assembly there is an additional early phase with a much higher velocity. The velocity varies greatly between different waves from 216 to 440 km s−1. The velocity of the two waves initially increases, subsequently decreases, and then increases again. Two other waves show a deceleration followed by an acceleration. Three categories of amplitude evolution of global coronal waves are found for the four events. The first is that the amplitude only shows a decrease. The second is that the amplitude initially increases and then decreases, and the third is that the amplitude shows an orderly increase, a decrease, an increase again and then a decrease. All the extreme ultraviolet waves show a decrease in amplitude while propagating farther away, probably because the driver of the global coronal wave (coronal mass ejection) is moving farther away from the solar surface.

The New Year Wave in a seakeeping basin: Generation, propagation, kinematics and dynamics

In the past years the existence of freak waves has been affirmed by observations, registrations, and severe accidents. One of the famous real-world registrations is the so-called “New Year Wave” recorded in the North Sea at the Draupner jacket platform on January 1, 1995. Since there is only a single point registration available, it is not possible to draw conclusions on the spatial development in front of and behind the point of registration, which is indispensable for a complete understanding of this phenomenon. This paper presents the temporal and spatial development of the “New Year Wave” generated in a seakeeping basin. This extreme sea state is measured at different locations in the tank, in a range from 2163 m (full scale) ahead of to 1470 m behind the target position—520 registrations altogether. The focus lies on the detailed description of a possible evolution of the “New Year Wave” over a large area. The group velocity, wave propagation and energy flux of this wave group as well as the wave kinematics and dynamics are analysed. As a case study a Ro/Ro vessel has been investigated in the “New Year Wave”, with special emphasis on the vertical bending moment.