Showing papers on "Breaking wave published in 1972"
TL;DR: In this paper, a nonlinear plane wave solution to this equation is found to correspond to the so-called Stokes wave, and the linear stability of this plane wave is essentially determined by the sign of the product of two coefficients in this equation, yielding Benjamin and Whitham's criterion.
Abstract: Slow modulation of gravity waves on water layer with uniform depth is investigated by using singular perturbation methods. It is found, to the lowest order of perturbation, that the complicated system of equations governing such modulation can be reduced to a simple nonlinear Schrodinger equation. A nonlinear plane wave solution to this equation is found to correspond to the so-called Stokes wave. The linear stability of this plane wave solution is essentially determined by the sign of the product of two coefficients in this equation, yielding Benjamin and Whitham's criterion. The same equation is found to give a weak cnoidal wave derived from the Korteweg-de Vries equation in the shallow-water limit.
510 citations
29 Jan 1972
TL;DR: In this article, an approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking, and experimental and theoretical results are compared and evaluated.
Abstract: A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.
477 citations
29 Jan 1972
TL;DR: In this article, a critical value for Yt> = H/h was used as a wave breaking criterion, where Hb and hb are respectively the wave breaker height and depth, and assuming conservation of the wave energy flux, one obtains 1/5 2 2/5 Hb = k g (TH) relating Hb to the wave period T and to the deep-water wave height H^.
Abstract: Using a critical value for Yt> = H./ h. as a wave breaking criterion, where Hb and hb are respectively the wave breaker height and depth, applying Airy wave theory, and assuming conservation of the wave energy flux, one obtains 1/5 2 2/5 Hb = k g (TH. ) relating Hb to the wave period T and to the deep-water wave height H^ . Three sets of laboratory data and one set of field data yield k = 0.39 for the dimensionless coefficient. The relationship, based on Airy wave theory and empirically fitted to the data, is much more successful in predicting wave breaker heights than is the commonly used equation of Munk, based on solitary wave theory. In addition, the relationship is applicable over the entire practical range of wave steepness values.
230 citations
TL;DR: In this paper, two prediction schemes for spectral changes in shoaling water are developed and compared with observed data, which are combined result of nondissipative forces (refraction, shoaling) and dissipative-generative forces.
Abstract: Significant changes occur in the sea-surface spectrum as it propagates from deep to shallow water. These changes are a combined result of nondissipative forces (refraction, shoaling) and dissipative-generative forces (bottom friction, wind generation, wave breaking). In this study two prediction schemes for these changes are developed. Numerical predictions of spectral changes in shoaling water are made and compared with observed data.
217 citations
TL;DR: In this article, a relationship between the breaker height-breaking depth ratio, the incident wave steepness and the beach slope is found, when combined with experimental observations of breaker travel, permits an estimate of the maximum breaking wave height a coastal structure might experience given a design wave period and design depth.
Abstract: Based on a re-evaluation of available experimental data on breaking waves, a relationship between the breaker height-breaking depth ratio, the incident wave steepness and the beach slope is found. This relationship, when combined with experimental observations of breaker travel, permits an estimate of the maximum breaking wave height a coastal structure might experience given a design wave period and design depth at the structure site. Breaker-type classification according to inshore and offshore parameters as presently defined cannot be reconciled to observations of the relationship between breaker-height index, wave steepness and beach slope. Revised criteria for breaker classification are presented.
180 citations
TL;DR: Atmospheric gravity waves similar to waves that occur on the surface of a body of water have been known since the nineteenth century, but their significance for the study of atmospheric dynamics has been realized only in the past ten years as mentioned in this paper.
Abstract: Atmospheric gravity waves similar to waves that occur on the surface of a body of water have been known since the nineteenth century, but their significance for the study of atmospheric dynamics has been realized only in the past ten years
144 citations
TL;DR: In this paper, the authors derived linearized equations for the mean flow and for the turbulent stresses over sinusoidal, travelling surface waves using assumptions similar to those used by Bradshaw, Ferriss & Atwell (1967) to compute boundary-layer development.
Abstract: Linearized equations for the mean flow and for the turbulent stresses over sinusoidal, travelling surface waves are derived using assumptions similar to those used by Bradshaw, Ferriss & Atwell (1967) to compute boundary-layer development. With the assumptions, the effects on the local turbulent stresses of advectal, vertical transport, generation and dissipation of turbulent energy can be assessed, and solutions of the equations are expected to resemble closely real flows with the same conditions. The calculated distributions of surface pressure indicate rates of wave growth (expressed as fractional energy gain during a radian advance of phase) of about 15(ρ a /ρ w ) (τ o / c 2 ), where τ o is the surface stress, c o the phase velocity and ρ a and ρ w the densities of air and water, unless the wind velocity at height λ/2π is less than the phase velocity. The rates are considerably less than those measured by Snyder & Cox (1966), by Barnett & Wilkerson (1967) and by Dobson (1971), and arguments are presented to show that the linear approximation fails for wave slopes of order 0.1.
132 citations
01 Jan 1972
77 citations
29 Jan 1972
TL;DR: In this paper, energy losses in breaking irregular waves are estimated on the assumption that a wave, while breaking, loses only that portion of its height which would be in excess of the breaker height for the given wave period and the mean local depth.
Abstract: Energy losses in breaking irregular waves are estimated on the assumption that a wave, while breaking, loses only that portion of its height which would be in excess of the breaker height for the given wave period and the mean local depth. This leads to expressions for the magnitude of the radiation stresses as a function of the distance offshore. From this the variations in mean water level and the longshore current velocity are calculated with existing methods. Laboratory measurements of set-up in twodimensional irregular waves are described. The data appear to some extent to be internally inconsistent; this may be due to enclosed air bubbles.
TL;DR: In this article, the exact form of a nonlinear, stationary wave, travelling against a background of cold plasma, is investigated for stability, and the result is that it is marginally stable, and therefore can exist in practice.
Abstract: The exact form of a nonlinear, stationary wave, travelling against a background of cold plasma, is investigated for stability. The result is that it is marginally stable, and therefore can exist in practice. This is found without expanding in the wave amplitude. Another problem, that of a nonlinear wave at rest against a background of two counter-streaming cold electron beams, is also commented on.
TL;DR: In this article, a means of resolving incident and reflected wave heights for a partial standing wave through the use of two fixed wave sensors is demonstrated, in which the waves incident to the permeable rubblemound breakwater located in Monterey Harbor, CA, are spectrally resolved into incident, reflected and transmitted wave components.
Abstract: A means of resolving incident and reflected wave heights for a partial standing wave through the use of two fixed wave sensors is demonstrated. Field studies were conducted in which the waves incident to the permeable rubblemound breakwater located in Monterey Harbor, CA, are spectrally resolved into incident, reflected and transmitted wave components. Power-spectra and cross-spectra are calculated for various characteristic sea states. Amplitude and phase are determined for the spectral wave components compromising the partial standing wave phenomena and reflection and transmission coefficients determined. The reflection coefficients vary between 0.3 and 0.7 and the transmission coefficients between 0.1 and 0.2. The transmission and reflection coefficients are shown to be dependent on the frequency and amplitude of the incident waves and the tidal stage.
TL;DR: In this paper, a solution for the transient behavior of resonant growing standing waves by using a perturbation expansion was found for the same problem, which is similar to the one predicted by the expansion theory.
Abstract: A solution has been found for the transient behaviour of resonant growing standing waves by using a perturbation expansion. Comparison with laboratory experiments as well as a numerical nonlinear solution of the same problem leads to the conclusion that: (i) the transient behaviour and the nonlinear tendency of the standing waves are described well by the analytic expression; (ii) the numerical results describe the solution very well until the wave starts to break; (iii) from the laboratory experiments and the numerical results, the standing internal gravity waves break owing to local gravitational instability at a critical amplitude which is similar to the one predicted by the expansion theory; (iv) the critical amplitude seems to be the maximum amplitude that a wave can reach; (v) when the generation of turbulence is violent, the small eddies begin forcing a secondary flow characterized by layers of strong jets separated by patches of turbulence.
TL;DR: In this article, a dispersion relation is obtained for surface waves in two situations, one without a wave incident on the boundary, the other with such a wave, which includes all previous results as special cases.
Abstract: Vlasov's equation and the full set of Maxwell's equations are solved as an initial value problem in a semi-infinite plasma. On specifying boundary conditions, a dispersion relation is obtained for surface waves in two situations, one without a wave incident on the boundary, the other with such a wave. The former case includes all previous results as special cases. In the latter case, it is found that surface waves cannot be excited by a wave incident on the boundary.
Patent•
29 Nov 1972
TL;DR: In this article, a platform is supported beneath the surface of a body of water and may be remotely raised or lowered to a height causing waves passing thereover to break. Means are also provided to rotate the platform for further controlling the manner in which the waves break.
Abstract: A platform is supported beneath the surface of a body of water and may be remotely raised or lowered to a height causing waves passing thereover to break. Means are also provided to rotate the platform for further controlling the manner in which the waves break.
TL;DR: In this article, a simple numerical model is used to demonstrate that momentum exchange between wave and mean flow can substantially modify the process of "breaking" of internal gravity waves at great height.
Abstract: A simple numerical model is used to demonstrate that momentum exchange between wave and mean flow can substantially modify the process of “breaking” of internal gravity waves at great height. The momentum exchange results in appreciable transfer of energy from wave to mean flow.
TL;DR: In this article, the deformation of long waves in a stratified fluid is investigated as influenced by the curvature of the vertical profile of density, by the terms neglected in the Boussinesq approximation and by the vertical shear.
Abstract: An investigation is made of the deformation of long waves in a stratified fluid as influenced by the curvature of the vertical profile of density, by the terms neglected in the Boussinesq approximation and by the vertical shear. In the continuous case these are taken to be small effects and the results for waves with an even number of nodal surfaces are as follows: (1) If the density profile is concave upward, a wave of elevation tends to break in the direction of the propagation, i.e. the forward part of the wave steepens; if the profile is convex upward, it tends to break backward. (2) The terms neglected in the Boussinesq approximation cause a wave of elevation to tend to break backward. (3) If the wave is propagating toward negative x and the fluid speed along the x -axis increases with height, the wave of elevation tends to break forward. To the first order there is no tendency for breaking if the waves have an odd number of nodal surfaces. An analysis is also made of a two-fluid system. The same tendencies exist in (1) above provided the concave-upward profile corresponds to a shallower lower fluid. In (2) and (3) above the tendencies for breaking in the continuous system and in the two-fluid system are opposite. DOI: 10.1111/j.2153-3490.1972.tb01536.x
TL;DR: In this article, the decay of surface capillary-gravity waves passing through a zone of turbulent water suggests a dissipative decay mechanism that is proportional to the square of the wave amplitude.
Abstract: The decay of surface capillary-gravity waves passing through a zone of turbulent water suggests a dissipative decay mechanism that is proportional to the square of the wave amplitude.
01 Jan 1972
TL;DR: In this article, a survey of methods to design wave run-up and overtopping for dikes and other sloping structures for regular and irregular breaking waves is presented. But this survey is limited to the case of dikes.
Abstract: Overview of methods to design wave run-up and overtopping for dikes and other sloping structures for regular and irregular breaking waves. Summary of experimental data and suggestions for design formulae
TL;DR: A sequence of double-peaked open-ocean wave spectra was observed simultaneously with eddy correlation estimates of momentum flux and atmospheric stability over a 15-hour interval at Argus Island tower (near Bermuda) on March 22 and 23, 1967 as discussed by the authors.
Abstract: A sequence of double-peaked open-ocean wave spectra was observed simultaneously with eddy correlation estimates of momentum flux and atmospheric stability over a 15-hour interval at Argus Island tower (near Bermuda) on March 22 and 23, 1967. The wave spectra were associated with a generating sea and advecting swell in the fetch of the warm sector of an advancing cyclone. The equilibrium range constant for these wave spectra was estimated at (7.8 ± 1.6) × 10−3. The Miles-Phillips exponential growth parameter was in reasonably good agreement with other field investigations, and observations support predicted amplification factors given by Phillips (1966) over the range 20 ≤ C/U* ≤ 32 where C is wave phase speed and U* is the friction velocity. Two observations of both linear and exponential growth parameters associated with spectral frequencies of 0.13 and 0.14 Hz were available to compare predicted and observed wave growth, with good results after correction for residual wave background. Observed temporal overshoot-undershoot of a particular wave component is interpreted in terms of an energy balance between wind input, wave-wave interactions, and wave breaking as a wave component evolves to its equilibrium condition. An example of spectral growth associated with advecting lower-frequency swell illustrates wave-induced fluctuations associated with momentum transfer from the sea to the atmosphere. Peaks in the horizontal and vertical wind-velocity spectra and the cospectra and quadrature spectra associated with wave spectral peaks are clearly evident when ocean swell propagates through the observation area.
TL;DR: In this article, the behavior of a gravity wave moving over a horizontal bed into a region where the flow is sheared in a vertical direction is analyzed, assuming that the fluid is inviscid and that the hydrostatic pressure law holds.
Abstract: : An analysis is given of the behavior of a gravity wave moving over a horizontal bed into a region where the flow is sheared in a vertical direction. No restriction is placed on the amplitude of the wave. The only assumptions made are that the fluid is inviscid and that the hydrostatic pressure law holds. The results can be used to analyze the behavior of tsunamis and weather fronts. It is shown that even with an arbitrary ambient shear, the variation in height of the free surface in a long progressing wave can be similar to that in a simple wave except that the local wave speed depends on the shear profile. The interaction of such a wave with a uniform shear is described in detail. (Author)
TL;DR: In this article, the amplitude of the wave-induced temperature fluctuation is proportional to the wave amplitude and to the square root of wave period, where the wave period is sufficiently small (≲3 sec).
Abstract: This brief report predicts the variation of surface temperature induced by a plane progressive irrotational linear water wave when a thermal boundary layer exists. The following conclusions are drawn. (1) When the wave period is sufficiently small (≲3 sec), the amplitude of the wave-induced temperature fluctuation is proportional to the wave amplitude and to the square root of the wave period. This result is in perfect agreement with experiments that, however, are by no means definitive. (2) Surface temperature maximums lead wave crests by one-eighth of a period when the average surface temperature is less than the bulk water temperature; surface temperature minimums lead wave crests by one-eighth of a period when the average surface temperature exceeds that of the water below.
29 Jan 1972
TL;DR: In this paper, a number of wave types were examined, including periodic waves, solitary waves, and standing waves, over both constant depth and uniform slopes, and the conclusion was drawn that surface tension should be taken into account in development of a satisfactory theory of breakers.
Abstract: Breaking criteria in the vicinity of the crest, such as limit crest angle and limit form, and larger dimensions such as limit height (H/L) and breaker height (Hb/db)» are found experimentally to be significantly affected by change in surface tension. A number of wave types were examined, including periodic waves, solitary waves, and standing waves, over both constant depth and uniform slopes. Variations in natural waters in some cases were found to be of equivalent magnitude to those induced for the experiments. The conclusion is drawn that surface tension should be taken into account in development of a satisfactory theory of breakers. It is also an important factor in experimental studies, particularly engineering model studies involving breaking waves.
TL;DR: In this paper, the behavior of finite amplitude long gravity waves in a water layer with an irregular bottom surface is investigated by means of a nonlinear perturbation method under the assumption that the irregularities are of small size, a simple set of nonlinear equations is presented.
Abstract: Behavior of finite amplitude long gravity waves in a water layer with an irregular bottom surface is investigated by means of a nonlinear perturbation method. Under the assumption that the irregularities are of small size, a simple set of nonlinear equations is presented. There arise two effects in the propagation characteristic of shallow water waves, change in phase velocity and damping of amplitude. For the one-dimensional and unidirectional motion of shallow water waves the set of equations is reduced to a simpler one, the generalized Korteweg-de Vries equation. The decay rate of a solitary wave is also obtained.
TL;DR: In this paper, the dispersion function of wave motion is characterized by an external driving force, which is closely related to the energetic properties of the wave motion, and then also to the averaged Lagrangian density.
Abstract: By inclusion of an. external driving force, wave motion of any kind can be characterized by a dispersion function. This function is closely related to the energetic properties of wave motion, and then also to the averaged Lagrangian density. Linear and nonlinear wave interaction can be analysed by inclusion of internal driving forces. Normalization procedures for the amplitudes can be avoided and time and space perturbations studied simultaneously. This analysis is further connected to slowly varying amplitudes and quasi-monochromatic waves. This paper presents the above-mentioned method and applies it to linear two-wave coupling, and non-linear three-wave coupling between positive and negative energy waves, and finally to amplitude modulation. The general equations obtained by this procedure are useful for general discussions. The simplicity of the method may prove useful in different applications.
01 Jan 1972
TL;DR: In this paper, the authors present methods to design wave run-up and overtopping for dikes and other sloping structures for regular and irregular breaking waves, and present experimental data and suggestions for design formulae.
Abstract: Overview of methods to design wave run-up and overtopping for dikes and other sloping structures for regular and irregular breaking waves. Summary of experimental data and suggestions for design formulae. English translation of: Golfoploop en golfoverslag - http://resolver.tudelft.nl/uuid:522060cb-8202-4276-bc48-ace65e137f40
TL;DR: In this article, a thin barrier of finite length in water of finite depth and infinite extent is considered, and an incident gravity wave, attacking the obstacle from infinity, is diffracted and scattered by the thin barrier.
Abstract: A thin barrier of finite length in water of finite depth and infinite extent is considered. An incident gravity wave, attacking the obstacle from infinity, is diffracted and scattered by the thin b...
TL;DR: In this paper, the life-time of ion waves in unstable and turbulent plasmas is investigated experimentally using a boxcar integrator, showing that in unstable states, life time is almost constant and independent of the boundary conditions and the electron drift velocity.
Abstract: The life-time of ion waves in unstable and turbulent plasmas is investigated experimentally. The life-time, a measure of the auto-correlation time of ion waves, is studied by a Boxcar Integrator. In unstable states, life-time strongly depends on the boundary condition of the plasma. In turbulent states, however, life-time is almost constant and independent of the boundary conditions and the electron drift velocity, whereas the turbulence energy increases with the drift velocity. Such a constancy may be expected from the Wiener-Khintchine theorem in noise theory. Several types of interaction between ion waves like oscillatory energy exchange or mode locking are also examined.