Showing papers on "Breaking wave published in 1982"

Swash oscillations on a natural beach

Abstract: Run-up (swash) oscillations were measured on a gently sloping beach face for a variety of incident wave conditions. Run-up energy spectra at wind wave frequencies show an ƒ−3 dependence and energy levels that are independent of incident wave height. This suggests saturation. In contrast, run-up energy at surf beat periods increase approximately linearly with increasing incident wave energy. Thus, in the inner surf zone, where wave breaking limits the energy at wind wave frequencies, the principal manifestation of large incident wind waves is energetic surf beat.

Two-dimensional surf beat: Long wave generation by a time-varying breakpoint

Abstract: A two-dimensional parametrization of a surf zone with a time-dependent breakpoint due to groupiness in the incident wave field is developed. The breakpoint is defined in terms of a mean position X plus a modulation Δa. Free wave solutions are obtained on a plane beach at the group frequency and its harmonics. Shoreward of the breakpoint, standing waves are found, while seaward an outgoing progressive wave exists. The amplitude of the standing wave is relatively insensitive to the incident wave field. The amplitude of the outgoing wave depends on X, the group frequency σ, and the beach slope tan β. For certain values of X = (σ2X/g tan β) the amplitude of the outgoing wave goes to zero. It appears that any ‘resonant’ response of the standing wave shoreward of the breakpoint is suppressed by seaward radiation of energy by the outgoing wave.

Long Wave Generation by a Time-Varying Breakpoint

Abstract: A two-dimensional parametrization of a surf zone with a time-dependent breakpoint due to groupiness in the incident wave field is developed. The breakpoint is defined in terms of a mean position X plus a modulation Aa. Free wave solutions are obtained on a plane beach at the group frequency and its har- monics. Shoreward of the breakpoint, standing waves are found, while seaward an outgoing progressive wave exists. The amplitude of the standing wave is relatively insensitive to the incident wave field. The amplitude of the outgoing wave depends on X, the group frequency o, and the beach slope tan . For certain values of X -- (o2X?g tan ) the amplitude of the outgoing wave goes to zero. It appears that any 'resonant' response of the standing wave shoreward of the breakpoint is suppressed by seaward radiation of energy by the outgoing wave. As waves propagate onshore and through the surf zone, en- ergy is transferred away from the primary incident wave fre- quencies. Within the surf zone, a mean pressure gradient is es- tablished resulting in wave setup (Longuet-Higgins and Stewart, 1964) and obliquely incident waves drive longshore currents (Bowen, 1969; Longuet-Higgins, 1970a, b). The first reports of low frequency motions in the nearshore zone were made by Munk (1949) and Tucker (1950). Since then, rela- tively high levels of low frequency energy in the nearshore have been widely reported in the literature. The resonant excitation of free edge waves can account for a significant part of this low frequency energy (Huntley, 1976; Holman et al., 1978; Holman, 1979). Theoretically, obliquely incident wave groups may transfer energy to free waves satis- fying the edge wave dispersion relation (Gallagher, 1971; Bowen and Cruza, 1978), and this resonant process can result in large amplitude waves trapped to the shoreline. There is, however, evidence that other motion not associ- ated with free edge waves also contributes significantly to the low frequency energy (Tucker, 1950; Huntley et al., 1981). Tucker observed a correlation between a long wave and the envelope of the incoming swell, with a lag approximately equal to the time required for the swell to propagate into the surf zone and for the associated long wave to be reflected back as a free wave. Longuet-Higgins and Stewart (1964), using the concept of radiation stress, were able to show the existence of a long period forced wave associated with incident wave groups. This forced wave is 180 o out of phase with the in- cident wave group and travels at the group velocity. In view of Tucker's observations, Longuet-Higgins and Stewart suggest that this forced wave is released at the breakpoint and travels seaward as a free wave; but the mechanism by which this oc- curs is not discussed. Huntley et al. (1981) describe data from an extensive array of two component electromagnetic current meters that consistently show energy levels in the onshore- offshore component of flows to be substantially larger than predicted from measured longshore flows by using edge wave theory. Forced wave motion is a possible source of energy that, for near-normally incident waves, may be predominantly in the onshore-offshore direction. None of the published models of long wave forcing account

The interaction between waves and a turbulent current: waves propagating with the current

Abstract: This paper describes an experimental programme carried out in a laboratory channel with rough and smooth beds, to investigate the interaction between gravity waves and a turbulent current. In particular, changes induced in the mean-velocity profiles, turbulent fluctuations, bed shear stresses and wave attenuation rates are considered for a range of wave heights, keeping the wave period constant. The smooth-boundary tests were carried out as a necessary preliminary to the more-realistic rough-boundary condition. A directionally sensitive laser anemometer was used to measure horizontal, vertical, and 45° velocity components in the oscillating fluid, and an on-line minicomputer was programmed to produce ensemble averages of velocities, Reynolds stresses and wave-elevation data. The cycle was sampled at 200 separate phase positions, with 180 observations at each position. Measurements were made at up to 30 points in the vertical. Preliminary tests were carried out on the unidirectional current and on the waves alone. These show that mean-velocity profiles and turbulence parameters of the current agree satisfactorily with previous experiments, and that the waves are approximated closely by Stokes’ second-order theory. For combined wave and current tests, mean-velocity profiles are generally found to differ from those suggested by a linear superposition of wave and current velocities, a change in boundary-layer thickness being indicated. However, shear stresses at the smooth boundary are found to be described by such a linear addition.

Energy saturation and phase speeds measured on a natural beach

Abstract: Field measurements of wave height and speed from 7-m depth shoreward are described. The experiment plan consisted of a shore-normal transect of closely spaced (compared to a dominant wave length) velocity, pressure, and elevation sensors on an almost plane profile having an inshore slope of 1:50. As the waves shoal and begin to break, the dominant dissipative mechanism is due to turbulence generated at the crest, and wave heights become increasingly depth controlled as they progress across the surf zone. Wave heights in the inner surf zone are strongly depth independent: the envelope of the wave heights is described by H/sub rms/ = 0.42 h. The depth dependence of the breaking wave height is shown to be related to the kinematic instability criterion. Celerity spectra were measured by using phase spectra calculated between pairs of adjacent sensors. Inshore of 4-m depth, the celerity was found distant over the energetic region of the spectrum. A 'mean' celerity was compared with linear theory and was within +20% and -10%, showing good agreement for such a nonlinear, dissipative region.

Instabilities of finite-amplitude water waves

Abstract: A numerical investigation of normal-mode perturbations of a finite-amplitude Stokes wave has revealed regions of instability lying near resonance curves given by the linear-dispersion relation. It is found that, for small amplitude, the dominant instability is two-dimensional (of Benjamin-Fier type) but, for larger amplitudes, the dominant instability becomes a three-dimensional perturbation. Results are compared with recent experimental observations of steep wave trains.

Experiments on nonlinear instabilities and evolution of steep gravity-wave trains

Abstract: A series of experiments on strong nonlinear instabilities of gravity-wave trains of large steepness 0·25 ≤ ak ≤ 0·34 in deep water in a long tow tank and a wide basin were performed. These experiments clarified several phenomena such as subharmonic instabilities, wave breaking, evolution of power spectra and directional energy spreading. It was found that an initial two-dimensional wavetrain of large steepness evolved into a series of three-dimensional spilling breakers, and was followed by a transition to a two-dimensional modulated wave train during which a series of oblique wave groups were radiated. The final stage of evolution was a series of modulated, two-dimensional wave groups with lower steepness and frequency. The three most frequent normal modes of two-dimensional subharmonic instabilities underlying the frequency downshifting, in the order of their relative occurrence, are found to be about 4/3, 5/4 and 3/2 in terms of the ratio of the fundamental to perturbed wave frequencies. The Bimescale for the phenomenon of the frequency downshifting is from 40 to 60 fundamental wave periods. Comparisons of the experimental results with existing theories showed that observed processes have several qualitative similarities with theoretical computations.

Field experiments on longshore sand transport in the surf zone

Abstract: Eight fluorescent sand tracer experiments were performed in energetic surf zones on natural beaches and on beaches near structures to measure the short-term longshore sand transport rate. Tracer of up to four distinct colors was injected on a line crossing the surf zone to investigate the on-offshore distributions of the longshore sand adveetion velocity and transport rate. The tracer advection velocity, v , and the depth of mixing into the bed, b, were determined from large numbers of cores taken in situ throughout the sampling area. The sand advection velocity and mixing depth were not constant across the surf zone, but usually exhibited a maximum either toward the shoreline or toward the breaker line, or in both regions. The local breaking wave height, H. , and horizontal current velocity in the surf zone (yielding an average longshore current velocity V) were also measured. The data were interpreted with simple dimensional arguments to give the following results: b = 0.027 H,, v = 0.011 V, and the volumetric transport rate Q = 0.024 H V. Agreement was also found between the measured total longshore sand transport rate and a predictive expression due to Bagnold involving the breaking wave power and average longshore current velocity. Although the results appear reasonable and consistent, a problem remains concerning the apparent decrease in tracer advection speed alongshore recorded in most experiments at the longer sampling times.

Study on Water Particle Velocities of Shoaling and Breaking Waves

Abstract: In this paper, the wave shoaling problem is analyzed by the energy flux method in which the fifth-order Stokes and the third-order cnoidal wave theories are used appropriately according to the appl...

Shock pressure of breaking waves on vertical walls

Abstract: Breaking wave impact on vertical walls is studied experimentally with beaches having four different slopes. It is found that a breaking wave having its front face parallel to the wall at the instant of impact produces the greatest shock pressures. Deepwater wave steepness and the bench slope are the two parameters governing the magnitude and location of the maximum dimensionless impact pressure from breaking waves. The greatest pressures are produced with a beach sloping at about one in ten. The length of virtual mass which participates in the impact process, is not constant but varies vertically.

Parametric solutions for breaking waves

Abstract: Time-dependent flows such as occur in breaking surface waves are often most con- veniently described in parametric form, with the coordinate z and velocity potential χ each expressed in terms of a third complex variable ω and the time t.In this paper we discuss some interesting flows given in terms of elementary functions of ω and t. Included are the Stokes 120° corner flow, the 45° rotor or rotating wedge, and a decelerated upwelling flow, with an exactly plane surface.Lastly it is shown that a class of cubic flows, which are related to the plane upwelling flow just mentioned, has a free surface that corresponds with remarkable accuracy to the forward face of an overturning, or plunging, breaker.

Finite-amplitude interfacial waves in the presence of a current

Abstract: Solutions for interfacial waves of permanent form in the presence of a current wcre obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simple analytical solutions to second order in wave height. Numerical methods were usctl to obtain solutions for larger wave amplitudes, details are reported for a number of selected cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existence of steady solutions are examined.

Normal-Mode Global Rossby Waves: Theory and Observations

Abstract: This study addresses first the question of what normal-mode global Rossby waves might exist in the Earth's atmosphere. Then it identifies fourteen of these theoretically predicted waves in the NMC global tropospheric analyses. Normal modes of linearized global primitive shallow water equations were found given a basic state of latitudinally dependent steady zonal flow. The solutions are free Rossby and gravity waves. Many of the waves' north-south structures are similar to Hough functions, which are the solutions of the simpler problem of free waves in an atmosphere at rest. By projecting 1200 consecutive days of twice-daily NMC global tropospheric analyses of velocity and geopotential onto idealized three-dimensional, normal-mode Rossby wave structures, time series of wave amplitudes and phases were formed. Spectral analyses of these time series for zonal wavenumbers 1–4 revealed statistically significant peaks at eight out of 25 theoretical Rossby wave frequencies. Six additional woes may exist...

The transient critical‐level interaction in a Boussinesq fluid

Abstract: A numerical model was used to examine the consequences of transience and nonlinearity in the critical-level interaction of an internal gravity wave. Wave packets in a shear flow were observed to evolve as predicted by the linear, initial-value results of Booker and Bretherton (1967) until convectively unstable layers evolved. Once formed, such layers were found to break down via a convective instability, presumably resulting in the turbulent dissipation of the incident wave packet. Several simulations were used to illustrate the transient stabilization of, and the Eulerian mean flow accelerations induced by, critical-level interactions. Other simulations were performed to examine the evolution of a wave packet in a time-dependent shear flow. The latter suggest that critical-level absorption and wave action dissipation can be either greatly accelerated or effectively eliminated depending upon the tendency of the mean velocity shear. The implications of these findings for internal gravity wave propagation in the atmosphere and the oceans are discussed.

On the nonlinear reflection of a gravity wave at a critical level. Part 2

Abstract: In part 1 of this work (Brown & Stewartson 1980b) we examined the nonlinear interaction of a forced internal gravity wave in a stratified fluid with its critical level. Although the Richardson number J was taken to be large, the method described there was, in principle, applicable to all Richardson numbers and as such we did not take advantage of the asymptotic properties of the solution of the linearized equations. Here in part 2 we re-develop the linearized solution for a general basic shear and temperature profile when J [Gt ] 1 as the large-time limit of an initial-value problem for a wave incident from above the shear layer. On this time scale it is known that the reflection and transmission coefficients are 0(e−νπ), ν = (J −¼)½. It is shown that, when J [Gt ] 1, the solution in the neighbourhood of the critical layer consists only of algebraically decaying elements with a direction of propagation parallel to the layer (critical-level noise) below a certain level, but of critical-level noise and a wavelike term, corresponding to the imposed incident wave, above this level. On a longer time scale, specifically , where e is the amplitude of the forced wave, the nonlinear terms are no longer negligible; the development of the reflection and transmission coefficients on this time scale is the subject of part 3 (Brown & Stewartson 1982).

Individual Wave Analysis of Irregular Wave Deformation in the Nearshore Zone

Abstract: In a field observation, water surface fluctuations were measured at many points on line from the shoreline to just outside the surf zone. The data were analyzed by an individual wave method, where the concept of primary individual wave is introduced in order to investigate irregular wave deformation. Primary individual waves are defined by applying the zero-down crossing method with a suitable band width at the zero level to the high-pass filtered water surface fluctuation. It is shown that a wave thus defined behaves like a regular wave with a fixed period in the nearshore zone. A deterministic model based on wave height change of monochromatic waves on non-uniform beaches is then introduced. The model is found to describe the observed deformation process expressed by the primary individual waves.

An extended Miles' theory for wave generation by wind

Abstract: Miles' inviscid theory of surface wave generation by wind is (a) modified by replacing the logarithmic shear velocity profile with one which applies right down to the wave surface and which exhibits an explicit dependence on the roughness of the surface, and (b) extended to include the effects of the interaction of wave with air flow turbulence by considering the wave-modified mean flow as the mean of the actual turbulent air flow over water waves and using this in a mixing-length model. The surface pressure is shown to depend significantly on the flow conditions being aerodynamically smooth or rough. Its component in phase with the surface elevation is practically unaffected by the wave-turbulence interaction. However, such interaction tends to increase the rate of energy input s from wind to waves travelling in the same direction, e.g., the increase is 2gk 2 for aerodynamically rough flow, where gk is the Von Karman constant. It also provides damping of waves in an adverse wind which can be about 10% of the growth rate in a favourable wind.

Spectrum of Shallow Water Waves

Abstract: A complete and coherent formulation for defining different spectral shallow water wave bands is stated. It takes into account the attenuation and dispersion characteristics of the waves and the predominant physical mechanisms. It is shown that the relevant parameter which accounts for the importance of attenuation and dispersion effects is the phase difference between the velocity-wave and the depth-wave. Practical criteria for defining the limits of the spectral bands are introduced for any required accuracy. The results presented can be used to obtain a rough and quick determination of the main characteristics of a flood wave from its dimensionless wave number and the Froude number of the mean-flow.

Wave-produced bubbles observed by side-scan sonar

Abstract: When a wave breaks in deep water, forming a whitecap, many small bubbles are generated and carried below the surface by turbulence. The breaking wave forms a strong acoustic target when viewed from below by an inverted side-scan sonar. The bubbles remaining in the water after the breaking wave has passed out of the sonar beam are also good acoustic scatterers and their drift towards or away from the sonar provides a means of remotely measuring that component of the near-surface current without interference of the flow and without exposing instruments to the hazard of violent near-surface conditions. This current changes rapidly as the wind changes. The sonar display shows regions of convergence or divergence of bubble clouds, perhaps associated with Langmuir circulations, and may, in calm weather, respond to the presence of surface slicks.

Measurements of Sea-State Variations Across Oceanic Fronts Using Laser Profilometry

Abstract: As part of the Grand Banks Experiment in May 1979, airborne laser profilometer measurements of the ocean wave field were made across a large cold-water extrusion situated over the Newfoundland Ridge The feature is actually an extension of the Labrador Current which is bordered on the west side by the Gulf Stream and on the east side by the North Atlantic Current Star-shaped flight patterns were flown over the fronts on each side of the cold-water feature A graphic technique was applied to the apparent wavenumber spectra in order to determine the changes in wave energy, wavelength and direction of propagation of the dominant wind-wave and swell components as they move across the fronts At the western front, the sea state increased abruptly and the results indicate that wave-current interactions were the most important mechanism for wave modification although boundary-layer effects were present and increased wave breaking was observed At the eastern front, changes in the swell are compared to

Forces induced by breakers on piles

Abstract: This paper consists of three parts. The first part presents a method for analyzing the forces exerted by breaking waves on a cirular pile. The force consists of two components, a slowly varying force and a much larger but very short duration quasi-impact force (probably of the order of 1/100 of a second). The second part is concerned with breaker characteristics, with emphasis being given to the few field data that have been measured. The third part consists of a presentation of some available data on surf zone bottom profile variations with time. Information on all three of these parts is needed for the proper design of a pile supported structure in the surf zone. If the bottom along the site of a proposed pier is sand, an estimate of the variability with time of the profile must be made. The effect of bottom depth and configuration on the height of waves moving shoreward, and the effect of this, in turn, on the wave loading is important in the calculations of wave-induced moments about the bottom. The ability of the structure to withstand these horizontal loads depends in part upon the depth of penetration of the piles. If the bottom varies with time, then calculations of wave characteristics and wave-induced loads on the piles should be made for appropriate bottom configurations.

A Note on the Limits of Rossby Wave Amplitudes

Abstract: Quasi-geostrophic dynamics, as usually formulated, centers on the conservation of pseudopotential vorticity (PV) on isobaric surfaces. The present study has the objective to investigate some simple constraints which conservation of PV imposes on internal Rossby waves. Attention is given to some of the limitations that conservation of potential vorticity imposes on the dynamics of the stratosphere. Another possible constraint imposed by hydrodynamic stability is also discussed. The quantitative limitations these constraints put on the amplitudes of internal Rossby waves are assessed and compared with observations of the lower stratosphere.

Irregular wave refraction due to current

Abstract: The phenomenon of wave refraction due to current is an important factor in the longshore current generation and the wave transformation in the vicinities of narrow strait and river mouth. The existing numerical models of wave refraction due to current are all for regular waves. A numerical model is proposed for the computation of the change of the directional spectral density of irregular waves due to current-depth refraction. The wave action equation is applied as the basic equation, in which the wave direction is introduced as the fourth independent variable. Several sample computations show that this model can explain the change of the directional spectra due to current. It is found that the significant wave height changes more rapidly than that of the corresponding regular waves having the same wave height, period and direction as those of the irregular waves. The change of a mean wave direction of the irregular waves is different from that of the corresponding regular waves.

Acoustic wave scattering from a fluid/solid periodic rough surface

Abstract: A rigorous theory based on the extended boundary condition method is proposed to solve the problem of elastic wave scattering from a periodic fluid/solid interface. The diffraction efficiencies of the reflected compressional wave in the fluid and the transmitted shear and compressional waves are calculated. The energy conservation criterion is used to check the accuracy of the numerical results. The effect of loss (viscoelasticity) in the solid is also included. The wave diffraction from a water and acrylic rough surface is measured. Good agreement between the theory and the experiment is obtained.

Sediment suspension due to breaking waves.

Abstract: In order to investigate on-offshore sediment transport mechanism and two-dimensional beach transformation, sediment movement under the agitation of wave breaking was considered. Sediment movement i...

A Simple Model for Nonlinear Critical Layers in an Unstable Baroclinic Wave

Abstract: Weakly nonlinear theory is developed for finite-amplitude dynamics of a slightly dissipative baroclinic wave at the point of minimum critical shear in the β-plane two-layer model. At this parameter setting the nonlinear theory provides a simple manifestation of critical layer dynamics since the Doppler-shifted frequency vanishes in one of the two layers. Calculations show that when the dissipation is proportional to the potential vorticity and is weak, the new equilibrium steady state has uniform potential vorticity in the critical layer although this is not required for wave stabilization. The spatial harmonics of the fundamental play an important role in both the transient and final state. For a weakly dissipative flow, the potential vorticity due to the harmonics is conserved along streamlines of the fundamental wave. An analytical theory is given for the equilibrated wave amplitude based on the assumption of uniform potential vorticity in the critical layer, and this prediction agrees well wi...

Turbulence generated by wave breaking on beach

Abstract: Horizontal and vertical velocities are measured with a hot-film anemometer (HFA) and a two-component laser-doppler velocimeter(LDV) in surf zones on uniform slopes of about 1/30 in two wave tanks. The turbulence generated by wave breaking is detected from the records. Following three aspects of the turbulence are discussed : (1) the distribution of the turbulence intensity in the surf zone, (2) the variation of the vertical distribution of the turbulence during one wave period and (3) the variation of the Reynolds stress during one wave period. It is found that the pattern of the distribution of the turbulence in the surf zone depends on the breaker type. A model is proposed, by extending the turbulent wake theory, to explain the variation of the vertical distribution of the turbulence during one wave period.