Horizontal Water Particle Velocity Research Articles

Theoretical Model for Nonlinear Long Waves over a Thin Viscoelastic Muddy Seabed

We theoretically analyzed the interaction between surface water waves and a thin muddy seabed. Wave motion in the inviscid water layer was assumed to be irrotational and the soft mud was modeled as a linear viscoelastic fluid. Under the Boussinesq approximation for nonlinear long waves, we present a set of depth-integrated equations that can be solved for the depth-averaged horizontal water particle velocity and the free-surface displacement. The long wave model needs to be solved numerically in general. For the cases of linear progressive waves and solitary waves, further analytical solutions were obtained. The model-predicted wave amplitude attenuation rate was shown to reasonably agree with the field data. Our analysis suggests that the elasticity of mud can potentially enhance the wave damping efficiency of a muddy seabed. The present formulations generalize several existing linear and nonlinear models for the wave–mud problem reported in literature.

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.

On the influence of wave breaking on the height limits of two-dimensional wave groups propagating in uniform intermediate depth water

The empirical non-dimensionalisation of Nelson (1994) for determining wave height limits are critically reviewed using data assembled from recent studies of wave groups propagating in water of constant depth in the laboratory. The limiting wave height to water depth ratios of marginally breaking deep and intermediate water waves remain within 10% of Nelson's values. However, it is shown that the effect of wave grouping can produce waves in shallower water that are at least 30% greater in height than the limit proposed by Nelson (1994). The present study supports use of limits based on McCowan (1894) and Miche (1944) for coastal engineering design for marginal breaking waves and strongly-breaking deep water waves. Three-dimensional and more strongly breaking waves in shallower water may yield wave heights higher than those measured during this study.The present study provides more robust and universal characterisation of breaking in transitional water than previously determined by geometric wave observations. Using the same measurement techniques as those of Saket et al. (2017), we have investigated the breaking threshold proposed by Barthelemy et al. (2018) but for different classes of unforced unidirectional wave groups in intermediate water depths. The threshold parameter Bx =Us/C (where Us is the horizontal surface water particle velocity at the wave crest and C is the wave crest point speed) which distinguishes breaking from non-breaking waves was found to be 0.835 ± 0.005 with the experimental uncertainty of each data point of ±0.020. This threshold is applicable to water depth to wavelength ratios as low as 0.2 including the deep water conditions investigated by Saket et al. (2017). No dependence on peak spectral wavenumber was found.

Offshore monopile in the southern North Sea: Part I, calibrated input sea state

Safe, reliable access is an essential precondition for the successful maintenance of offshore wind farms. Access from vessels to wind turbines depends on the severity of the sea state in the vicinity of the turbine support structure. This paper presents a validation of a numerical boundary condition developed to reproduce the seasonal sea state at Teesside Offshore Wind Farm, off the coast of the UK. The boundary condition, called customSpectrum, was derived from wave energy spectra obtained by analysis of existing field measurements of wave free-surface displacement at the wind farm site and implemented in OpenFoam, the open-source computational fluid dynamics library. OpenFoam was then used to simulate typical spring, summer, autumn and winter sea states as uni-directional waves. Predicted surface elevations and significant wave heights were found to be in agreement with in situ buoy data, thus validating the OpenFoam model. Satisfactory agreement was achieved between analytical and numerically predicted spectral density functions for the horizontal and vertical water particle velocity components. It was found that the wave activity at Teesside is uni-modal in spring and autumn, and bi-modal in summer and winter. Extending the procedure to multi-directional waves in crossing seas is recommended.

Wave-Induced Reynolds Stress in Three-Dimensional Nearshore Currents Model

ABSTRACT Chun, H. and Suh, K.-D., 2016. Wave-induced Reynolds stress in three-dimensional nearshore currents model. This paper presents the formulation of the wave-induced Reynolds stress (WIRS), i.e. the correlation of horizontal and vertical water particle velocities, based on the Airy's wave theory. Even though the correlation of the velocities is zero in a constant-depth water, it has a nonzero value if there are slopes on the bottom and mean water level. Comparison of the vertical gradient of the WIRS term with the horizontal gradient of wave-forcing terms shows that the two terms have the same order of magnitude, which in turn is comparable to that of the radiation stress in the surf zone. For the three-dimensional computation of nearshore currents, the WIRS term is incorporated into a three-dimensional ocean model in the σ coordinates. The numerical model is then applied to two laboratory experiments. To see the effect of the WIRS term on the mean flow, numerical simulations without this term are a...

Numerical Study on Geometrical Configurations of Perforated Cylindrical Structures under Regular Waves

AbstractOffshore tension leg platforms (TLPs) is often subjected to critical environmental loads that cause serious damage; Mars TLP in Gulf of Mexico, damaged by hurricane Katrina in the year 2005 is an example. Existence of external perforated cover reduces hydrodynamic forces on the existing members caused by direct wave impact. Although many studies confirm this fact but variations in the water particle kinematics along the water depth needs a detailed investigation to verify the phenomenon. Geometric configuration of the column member of the damaged MARS TLP is modeled on a 1:100 scale with an external perforated cover. Variations of water particle kinematics of the column member encompassed by perforated cover are presented through detailed computational fluid dynamics (CFD) analysis. Traces of the horizontal water particle velocity along the water depth are derived for a wide range of sea states for various chosen geometric configuration. Results of the numerical studies show that there is a signif...

Experimental Study on Sediment Transport Caused by Overtopping Waves across a Backshore

Laboratory experiments were performed on the sediment transport on backshore, which was caused by solitary waves as well as cyclic waves. Measurements were conducted for overtopped volume of water and sand, temporal variations of horizontal water particle velocities, surface elevations and suspended sediment concentration. Meyer-Peter-Muller's formula and Lane-Kalinske's formula were found to be consistent with the sand transport rate caused by long waves but inconsistent for solitary wave. Sediment suspension and convection on the foreshore due to breaking was found to be important to estimate the sand transport due to solitary wave. The saturation of suspended sand concentration was observed when the height of the incident solitary wave exceeded 7cm.

WAVECALC: an Excel-VBA spreadsheet to model the characteristics of fully developed waves and their influence on bottom sediments in different water depths

The generation and growth of waves in deep water is controlled by winds blowing over the sea surface. In fully developed sea states, where winds and waves are in equilibrium, wave parameters may be calculated directly from the wind velocity. We provide an Excel spreadsheet to compute the wave period, length, height and celerity, as well as horizontal and vertical particle velocities for any water depth, bottom slope, and distance below the reference water level. The wave profile and propagation can also be visualized for any water depth, modeling the sea surface change from sinusoidal to trochoidal and finally cnoidal profiles into shallow water. Bedload entrainment is estimated under both the wave crest and the trough, using the horizontal water particle velocity at the top of the boundary layer. The calculations are programmed in an Excel file called WAVECALC, which is available online to authorized users. Although many of the recently published formulas are based on theoretical arguments, the values agree well with several existing theories and limited field and laboratory observations. WAVECALC is a user-friendly program intended for sedimentologists, coastal engineers and oceanographers, as well as marine ecologists and biologists. It provides a rapid means to calculate many wave characteristics required in coastal and shallow marine studies, and can also serve as an educational tool.

Extreme value prediction of inundation drag force with and without current

This paper deals with drag forces due to irregular waves on a vertical slender structure in the splash zone, i.e. in the vicinity of still-water free surface, by considering the inundation effect due to instantaneous wave elevation. The force turns out to be a third-order quantity with respect to wave elevation. The focus of this paper is however limited to extreme value prediction of this force in stochastic waves. Based upon a transformation of random variables and use of the Rice formula, the mean up-crossing rate of inundation drag force is obtained in the frequency domain both by direct numerical integration and asymptotic evaluation for high levels using the Laplace method. The extreme value distribution of this force is then established by the Poisson probability law assuming independent up-crossing events. The proposed method agrees very well with time-domain simulations both for the mean up-crossing rate and the extreme value prediction. The effect of correlation between wave elevation and horizontal water particle velocity and the presence of current have been studied.

A function to determine wavelength from deep into shallow water based on the length of the cnoidal wave at breaking—Reply to discussion by T.S. Hedges

The equations of Hedges [Hedges, T.S., 2009. Discussion of “A function to determine wavelength from deep into shallow water based on the length of the cnoidal wave at breaking” by J.P. Le Roux, Coastal Eng.], although yielding similar wavelengths, are not consistent with the fact that the horizontal water particle velocity in the wave crest should equal the wave celerity at breaking over a nearly horizontal bottom.

Experiment on Tsunami Flow in Wave Basin

In this study, it is discussed about the method to generate a strong flow by tsunami in a wave basin. The authors are tried to adopt the vertical jet system and measured horizontal water particle velocities. Before the experiments, numerical analysis has done, and the vertical distribution of horizontal water particle velocity is estimated to be almost the same. However, the horizontal water particle velocity in the vicinity of the bottom was a little small in the experiment. But it is negligible because the flow velocity is very large compared with the flow generated by regular waves. Moreover, by controlling the volume of the jet periodically, the oscillating flow can be generated. Therefore, it is concluded that the vertical jet system can apply to the large scale tsunami experiments.

An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves

This paper describes an experimental study of two-dimensional surface water waves propagating on a depth-varying current with a non-uniform vorticity distribution. The investigation is divided into two parts. The first concerns the ‘equilibrium’ conditions in which the oscillatory wave motion and the current co-exist. Measurements of the water-surface elevation, the water-particle kinematics, and the near-bed pressure fluctuations are compared to a number of wave and wave–current solutions including a nonlinear model capable of incorporating the vertical structure of the current profile. These comparisons confirm that the near-surface vorticity leads to an important modification of the dispersion equation, and thus affects the nature of the wave-induced orbital motion over the entire water depth. However, the inclusion of vorticity-dependent terms within the dispersion equation is not sufficient to define the combined wave–current flow. The present results suggest that vorticity may lead to a significant change in the water-surface profile. If a current is positively sheared, dU/dz > 0, with negative vorticity at the water surface, as would be the case in a wind-driven current, a wave propagating in the same direction as the current will experience increased crest–trough asymmetry due to the vorticity distribution. With higher and sharper wave crests there is a corresponding increase in both the maximum water-particle accelerations and the maximum horizontal water-particle velocities. These results are consistent with previous theoretical calculations involving uniform vorticity distributions (Simmen & Saffman 1985 and Teles da Silva & Peregrine 1988).The second part of the study addresses the ‘gradually varying’ problem in which there are changes in the current, the wavelength and the wave height due to the initial interaction between the wave and the current. These data show that there is a large and non-uniform change in the current profile that is dependent upon both the steepness of the waves and the vorticity distribution. Furthermore, comparisons between the measured wave height change and a number of solutions based on the conservation of wave action, confirm that the vorticity distribution plays a dominant role. In the absence of a conservation equation for wave action appropriate for nonlinear waves on a depth-varying current, an alternative approach based on the conservation of total energy flux, first proposed by Longuet-Higgins & Stewart (1960), is shown to be in good agreement with the measured data.

Breaking Wave Forces on Tripod Concrete Structure on Shoal

An experimental study has been carried out on the forces from breaking waves on a tripod structure located on a shoal. The main purpose was to investigate both horizontal and vertical forces as well as overturning moments due to waves acting on the tripod. In addition, horizontal water particle velocities and crest elevations directly over the shoal have been measured. Nondimensional relations between the maximum depth average particle velocities over the shoal, the wave height, wave period, water depth, and wave crest elevation have been obtained. Further nondimensional relations between the wave crest elevation, wave height, wave period, and water depth have also been obtained. Finally, a simple wave force calculation method was developed that may be used to obtain wave forces on similar structures on other shoals that do not deviate significantly from the conditions used during the present tests.

TRANSFORMATION OF REGULAR WAVES.

Keywords MANCHESTER UNIVERSITY, OPEN UNIVERSITY WAVES, SHOALING, EXPERIMENTAL, DATA, PARALLEL, CURVES, SHALLOW, THEORY, DESIGN, HEIGHT, EVALUATION, PREDICTION, PARAMETERS, WATER, EQUATIONS, STREAMS, FUNCTIONS... Show All

ON THE RELATION BETWEEN CHANGES IN INTEGRAL QUANTITIES OF SHOALING WAVES AND BREAKING INCEPTION

This paper describes a mechanism of breaking waves over sloping bottoms in terms of changes in integral quantities of the waves. Systematic computations are made of wave profiles of shoaling waves up to the numerical unstable points by using the K-dV equation with variable coefficients and internal properties such as horizontal and vertical water particle velocities by a stream function method satisfying the conservation laws of mass and energy. Applicability of the numerical results is examined and a relation between numerical unstable points and actual breaker points is found. Characteristics of the integral quantities of shoaling waves are investigated in relation to the existence of the extremum of the energy of the shoaling waves and their breaking inception.

Field Observation of the Wave-Induced Water Particle Velocity in the Surf Zone

ABSTRACTField experiments were conducted in the surf zone of bar-type bottom profile. Surface elevation, wave angle and vertical distribution of horizontal water particle velocity were measured sim...

Laboratory Generated Waves and Wave Theories

Tests are carried out in a wave tank to record the waves, the water pressures, and the horizontal and vertical water particle velocities. The water depth is such that the waves generated during the test cover the deep, intermediate and shallow water ranges. In the intermediate and shallow water range the soliton effects are observed. In deep water, the Airy wave theory is found to describe the water particle kinematics adequately. Stokes' 3rd order wave theory is found to be valid for higher waves in intermediate water depths. Stream function theory is found to agree reasonably with the test data in general. Based on these comparisons, a region of validity of various wave theories is described and compared with other predicted regions in the literature.

Application of Morison's Equation to Fixed Offshore Platforms

Four methods for calculating wave forces acting on tubular members affixed offshore platforms are presented and compared under identical design conditions to demonstrate their significant differences. Many wave-crest locations and wave-approach directions are considered. Variation of base shears and overturning moments among these methods is found to exceed 21 percent. percent. Introduction Numerous technical papers, texts, and offshore design codes have used Morison's equation to determine hydrodynamic forces on small, tubular, structural elements. The Morison equation includes terms for both drag and inertial forces. The drag term includes a drag coefficient, CD, and water-particle velocity, while the inertia term includes an inertial coefficient, C1, and water-particle acceleration. This equation applies to small objects (compared with wave length) where wave kinematics do not change appreciably over a distance equal to the width of the structural element. Morison's equation was developed to determine the hydrodynamic force on a small cylindrical body that is at right angles to the water-particle velocity and acceleration vectors. However, when a cylinder is oriented randomly with respect to the mud line, there is considerable question about the application of Morison's equation. Borgman, Ippen, Bursnall et al., Chakrabarti et al., and Morgan et al. have shown how for a vertical cylinder Morison's equation may be applied to a cylindrical member oriented randomly with respect to the mud line. A review of the references reveals that there are many methods for calculating wave forces acting on tubular members of fixed offshore platforms. Four different methods are presented in this study, each within procedures generally used by the industry for computing procedures generally used by the industry for computing wave forces on a randomly oriented cylindrical member. Formulation of the methods considered is based on various interpretations of the application of Morison's equation. The wave-force calculation methods presented here are in the literature. This study compares these various methods with identical design conditions and demonstrates significant differences among the methods. The wave-force equation introduced by Morison et al. is -> -> -> -> F = 1/2 CDpdv x v x + 1/4 Clp d2 a x -> -> F p = ----,...................................(1) d -> -> where vx and ax are the horizontal water-particle velocity and acceleration vectors, respectively, acting on a vertical cylinder of a diameter, d, in water of mass density, p. Both water-particle kinematic vectors are normal to the cylinder and, consequently, the force vector, will be acting in a direction parallel to the mud line. Wave-induced motion, however, includes both horizontal and vertical kinematic components. Furthermore, except for conductors, offshore platforms rarely have cylindrical members that are perfectly vertical. In each wave-force calculation method presented, the total water-particle velocity vector is assumed to be -> -> -> v = v x + v y,...........................(2) and the total acceleration vector is -> -> -> a = a x + a y,...........................(3) P. 447

KINEMATICS OF BREAKING WAVES

The sight and sound of breaking waves and surf is so familiar and enjoyable that we tend to forget how little we really understand about them. Why is it, that compared to other branches of wave studies our knowledge of breaking waves is so empirical and inexact? The reason must lie partly in the difficulty of finding a precise mathematical description of a fluid flow that is in general nonlinear and time-dependent. The fluid accelerations can no longer be assumed t o be small compared t o gravity, as in Stokes's theory for periodic waves and the theory of cnoidal waves in shallow water, nor is the particle velocity any longer small compared to the phase velocity. The aim of this paper is to bring together s ome recent contributions to the calculation both of steep symmetric waves and of time-dependent surface waves. These have a bearing on the behaviour of whitecaps in deep water and of surf in the breaker zone . Since spilling breakers in gently shoaling water closely resemble solitary waves, we begin with the description of solitary waves of limiting amplitude, then discuss steep waves of arbitrary height. The observed intermittency of whitecaps is discussed in terms of the energy maximum, as a function of wave steepness, In Sections 6 and 7 a simpler description of steady symmetric waves is proposed, using an asymptotic expression for the flow near the wave crest. Finally we describe a new numerical technique (MEL, or mixed Eulerian-Lagrangian) with which it has been found possible to follow the development of periodic waves past the point when overturning takes place. Measurement of waves, and vertical and horizontal water particle velocities were made of spilling, plunging and surging breakers at sandy beaches in the vicinity of Monterey, California. The measured breaking waves, derived characteristically from swell-type waves, can be described as highly nonlinear. Spectra and cross spectra were calculated between waves and velocities. Secondary waves were noted visually and by the strong harmonics in the spectra. The strength of the harmonics is related to the beach steepness, wave height and period. The phase difference between waves and horizontal velocities indicates the unstable crest of the wave leads the velocities on the average by 5-20 degrees. Phase measurements between wave gauges in a line perpendicular to the shore show breaking waves to be frequency nondispersive indicating phase-coupling of the various wave components. The coherence squared values between the sea surface elevation and the horizontal water particle velocity were high in all runs, ranging above 0.8 at the peak of the spectra. The high coherence suggests that most of the motion in the body of breaking waves is wave-induced and not turbulent.

Relationship Between Vertical Distribution of Water Particle Velocity and Type of Breakers on Beaches

ABSTRACTIn order to clarify the water particle velocity field of breaking waves on beaches, experiments were carried out for three kinds of beach slopes (1/10, 1/20 and 1/30). Neutrally buoyant particles were used as tracers to measure the velocities with a 16 mm high speed cinecamera. Since photographs of the wave profile near breaking were also taken in the same films, the change of the wave profile near breaking was also examined. It was found that vertical distributions of horizontal water particle velocities at the crest and trough phases of breaking waves on beaches cannot be explained by the finite amplitude wave theories for uniform depth. Then, they were discussed in comparison with the breaker types. As a result, it was shown that the dimensionless vertical distribution of horizontal water particle velocity at the crest phase of breaking waves is determined by the combination of the beach slope and the deep-water wave steepness.