Showing papers on "Breaking wave published in 1985"
TL;DR: In this paper, the nature of the equilibrium range is reexamined, using the dynamical insights into wave-wave interactions, energy input from the wind and wave-breaking that have been developed since 1960.
Abstract: Recent measurements of wave spectra and observations by remote sensing of the sea surface indicate that the author's (1958) conception of an upper-limit asymptote to the spectrum, independent of wind stress, is no longer tenable. The nature of the equilibrium range is reexamined, using the dynamical insights into wave–wave interactions, energy input from the wind and wave-breaking that have been developed since 1960. With the assumption that all three of these processes are important in the equilibrium range, the wavenumber spectrum is found to be of the form , where p ∼ ½ and the frequency spectrum is proportional to u*gσ−4. These forms have been found by Kitaigorodskii (1983) on a quite different dynamical basis; the latter is consistent with the form found empirically by Toba (1973) and later workers. Various derived spectra, such as those of the sea-surface slope and of an instantaneous line traverse of the surface, are also given, as well as directional frequency spectra and frequency spectra of slope.The theory also provides expressions for the spectral rates of action, energy and momentum loss from the equilibrium range by wave-breaking and for the spectrally integrated rates across the whole range. These indicate that, as a wave field develops with increasing fetch or duration, the momentum flux to the underlying water by wave-breaking increases asymptotically to a large fraction of the total wind stress and that the energy flux to turbulence in the water, occurring over a wide range of scales, increases logarithmically as the extent of the equilibrium range increases. Interrelationships are pointed out among different sets of measurements such as the various spectral levels, the directional distributions, the total mean-square slope and the ratio of downwind to crosswind mean-square slopes.Finally, some statistical characteristics of the breaking events are deduced, including the expected length of breaking fronts (per unit surface area) with speeds of advance between c and c+dc and the number of such breaking events passing a given point per unit time. These then lead to simple expressions for the density of whitecapping, those breaking events that produce bubbles and trails of foam, the total number of whitecaps passing a given point per unit time and, more tenuously, the whitecap coverage.
858 citations
TL;DR: In this paper, the influence of breaking gravity waves on the dynamics and chemical composition of the 60- to 110-km region has been investigated with a two-dimensional dynamical/chemical model that includes a parameterization of gravity wave drag and diffusion.
Abstract: The influence of breaking gravity waves on the dynamics and chemical composition of the 60- to 110-km region has been investigated with a two-dimensional dynamical/chemical model that includes a parameterization of gravity wave drag and diffusion. The momentum deposited by breaking waves at mesospheric altitudes reverses the zonal winds, drives a strong mean meridional circulation, and produces a very cold summer and warm winter mesopause, in general agreement with observations. The seasonal variations of the computed eddy diffusion coefficient are consistent with the behavior of mesospheric turbulence inferred from MST radar echoes. In particular, it is found that eddy diffusion is strong in summer and winter but much weaker at the equinoxes and that this seasonal behavior has important consequences for the distribution of chemical species. Comparison between computed atomic oxygen and ozone, and the abundances of these constituents inferred from the 557.7-nm and 1.27-μm airglow emissions, reveals excellent agreement. The consistency between model results and these diverse types of observations lends strong support to the hypothesis that gravity waves play a very important role in determining the zonally averaged structure of the mesosphere and lower thermosphere.
805 citations
TL;DR: In this article, the average rate of energy dissipation in random waves breaking in shallow water, published previously by Battjes and Janssen (1978), has been applied to an extensive set of data for the purposes of calibration and verification.
Abstract: A model describing the average rate of energy dissipation in random waves breaking in shallow water, published previously by Battjes and Janssen (1978), has been applied to an extensive set of data for the purposes of calibration and verification. Both laboratory and field data were used, obtained on beaches with a more or less plane slope as well as on barred beaches, and for a wide range of wave conditions. Optimal values have been estimated for an adjustable breaking wave height-coefficient in the model; these appear to vary slightly but systematicaly with the incident wave steepness, in a range that is physically realistic. A parameterization of this dependence allows the use of the model for prediction. Applied to the present data set, the correlation coefficient between measured and predicted rms wave heights is 0.98, with an rms normalized error of 6% and a bias that does not differ significantly from zero.
380 citations
TL;DR: In this paper, an analytical solution for wave height transformation due to shoaling and breaking on a flat shelf, a plane slope, and an equilibrium beach profile is derived and then compared to laboratory data with favorable results.
Abstract: An intuitive expression for the spatial change in energy flux associated with waves breaking in the surf zone is developed. Using shallow water linear wave theory, analytical solutions for wave height transformation due to shoaling and breaking on a flat shelf, a plane slope, and an “equilibrium” beach profile are derived and then compared to laboratory data with favorable results. The effect of beach slope on wave decay is included explicitly, while wave steepness effects are included implicitly by specification of the incipient conditions. Set-down/set-up in the mean water level, bottom friction losses, and bottom profiles of arbitrary shape are introduced, and solutions are obtained numerically. The model is calibrated and verified using laboratory data with very good results for the wave decay but not so favorable results for set-up. A test run on a prototype scale profile containing two bar and trough systems demonstrates the model's ability to describe the shoaling, breaking, and wave re-forming process commonly observed in nature. Bottom friction is found to play a negligible role in wave decay in the surf zone when compared to shoaling and breaking.
359 citations
TL;DR: In this paper, the behavior of steady, periodic, deep-water gravity waves on a linear shear current is investigated and a weakly nonlinear approximation for the small amplitude waves is constructed via a variational principle.
Abstract: The behavior of steady, periodic, deep-water gravity waves on a linear shear current is investigated. A weakly nonlinear approximation for the small amplitude waves is constructed via a variational principle. A local analysis of those large amplitude waves with sharp crests, called extreme waves, is also provided. To construct solutions for all waveheights (especially the limiting ones) a convenient mathematical formulation which involves only the wave profile and some constants of the motion is derived and then solved by numerical means. It is found that for some shear currents the highest waves are not necessarily the extreme waves. Furthermore a certain non-uniqueness in the sense of a fold is shown to exist and a new type of limiting wave is discovered.
131 citations
TL;DR: In this paper, the authors considered the implications of a nonuniform turbulent diffusion due to the IOM saturation of a gravity wave via convective instabilities and found that both wave and turbulence fluxes of heat can be reduced dramatically, depending on the amplitude of the wave motion and the extent to which the turbulent diffusion is localized.
Abstract: We consider the implications of a nonuniform turbulent diffusion due to the IOM saturation of a gravity wave via convective instabilities It is found that both wave and turbulence fluxes of heat can be reduced dramatically, depending on the amplitude of the wave motion and the extent to which the turbulent diffusion is localized These results suggest that previous studies that assumed a uniform turbulent diffusion may have overestimated the beat and constituent fluxes due to gravity wave saturation
128 citations
TL;DR: In this article, a telemetry system is used to continuously record wave forces at an exposed site; the interpretation of one such record is presented as a case study of the nature of wave forces.
Abstract: Breaking waves impose large forces on intertidal organisms, and these forces are important in structuring wave-swept communities. Here a telemetry system is used to continuously record wave forces at an exposed site; the interpretation of one such record is presented as a case study of the nature of wave forces. For waves with a breaking height of 2-4 m, water velocities of at least 8 m s-l and accelerations of at least 400 m s-~ are present near the substratum. The forces imposed on organisms by these flows depend on the size and shape of the organism. For a limpet (CoZZzkeZIa pelta) an average force is about 0.6 N, a maximum about 3 N. The magnitude and direction of wave forces are unpredictable in both time and space over periods of seconds to hours, although predictability is possible over longer periods. A quantitative exposure index, based on an organism’s ability to withstand wave forces, shows that various organisms exposed to the same flow are at widely varying risks. No impact forces were observed during this study.
124 citations
TL;DR: In this article, the numerical method of Longuet-Higgins & Cokelet (1976) was extended to account for a horizontal bottom contour, and used to investigate breaking waves in water of finite depth.
Abstract: The numerical method of Longuet-Higgins & Cokelet (1976), for waves on deep water, is extended to account for a horizontal bottom contour, and used to investigate breaking waves in water of finite depth. It is demonstrated that a variety of overturning motions may be generated, ranging from the projection of a small-scale jet at the wave crest (of the type that might initiate a spilling breaker) to large-scale plunging breakers involving a significant portion of the wave. Although there seems to be a continuous transition between these wave types, a remarkable similarity is noticed in the overturning regions of many of the waves.Three high-resolution computations are also discussed. The results are presented in the form of interrelated space-, velocity- and acceleration-plane plots which enable the time evolution of individual fluid particles to be followed. These computations should be found useful for the testing of analytical theories, and may also be applied, for example, to studies of slamming forces on shipping and coastal structures.
118 citations
TL;DR: In this article, a general definition of wave breaking is discussed, in order to deal with some points on which misunderstanding appears to have arisen, and a strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.
Abstract: A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into ‘breaking’ and ‘not breaking’ is a generic classification based on dynamical considerations, and not a statement about any unique ‘signature’ or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the ‘nonacceleration’ theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not ‘break’ in the sense envisaged.
110 citations
TL;DR: In this article, a description of major features and patterns of motion in water waves just after breaking is presented, and new observations utilized to develop a new qualitative picture of the breaking process.
Abstract: A description of major features and patterns of motion in water waves just after breaking is presented. Previous literature is synthesized and new observations utilized to develop a new qualitative picture of the breaking process. Both classic spilling and plunging‐type breakers are found to have similar initial breaking motions, but at vastly different scales. Two primary vortex motions are identified. A plunger vortex is initially created by the overturning jet, which in turn causes a splash‐up of trough fluid and subsequent formation of a surface vortex similar to the roller in a hydraulic jump. Introduced for the first time is the hypothesis that the plunger vortex translates laterally to push up a new surface wave with vastly different wave kinematics that continues propagating into the inner surf zone. Of primary interest is the outer or transition region where momentum is being exchanged between mean, periodic and random flow processes along with some energy loss. Evidence is presented from the lit...
97 citations
TL;DR: In this paper, the authors used two days of field data from a low slope beach with moderate wave heights (H∼70cm), some low order, normalized moments are compared to results from simple monochromatic and linear random wave models.
Abstract: Recent models for nearshore sediment transport suggest the importance of various moments of the fluid velocity field in determining transport rates. Using two days of field data from a low slope beach with moderate wave heights (H∼70cm), some low order, normalized moments are compared to results from simple monochromatic and linear random wave models. Not surprisingly, the random wave model is substantially more accurate than the monochromatic model. However, wave breaking and other nonlinearities introduce effects not explained by either formalism. The observed cross‐shore velocity variance is decomposed into wind wave and surf beat components. The surf beat contribution is maximum at the shoreline, while the wind wave component is maximum offshore. The total variance is nearly constant across the surf zone. This observation contradicts assumptions that are fundamental to many models of surf zone dynamics and sediment transport. Analysis of a wider range of wave conditions is needed to assess the general...
TL;DR: In this paper, the authors present the first well-controlled laboratory measurements of the momentum flux lost by wave breaking, and support the conclusion that wave breaking plays an important role in momentum transfer across the air-sea interface.
Abstract: Wave breaking is believed to be important in air–sea interaction. Laboratory measurements1 suggest that the momentum flux from the atmosphere to the ocean may be significantly enhanced by breaking and recent field measurements2–4 have demonstrated the important role of breaking in bubble generation and gas transfer. It has long been speculated that the loss of momentum flux from the wave field due to breaking could act as a source of momentum for current generation5 and Mitsuyasu6 has drawn attention to the large discrepancy between the momentum flux from the wind and that carried by the waves, suggesting that the loss may be due to wave breaking. Here we present what we believe are the first well-controlled laboratory measurements of the momentum flux lost by wave breaking. These measurements are consistent with Mitsuyasu's hypothesis and recent measurements of wave growth, and support the conclusion that wave breaking plays an important role in momentum transfer across the air–sea interface.
TL;DR: In this paper, maps of Ertel's potential vorticity, Q, are computed on an isentropic surface in the middle of the stratosphere using data from stratospheric sounding units on board NOAA satellites.
Abstract: Maps of Ertel's potential vorticity, Q, are computed on an isentropic surface in the middle of the stratosphere. They are derived using data from stratospheric sounding units on board NOAA satellites. the reliability of the maps is demonstrated mainly by conservation of Q that is shown in successive analyses, and by the close agreement obtained using independent data from two satellites.
The maps are used to follow the movement of material during the course of strong disturbances which occurred in December 1981. They clearly show the breaking of planetary waves in the stratosphere, an inherently nonlinear process. the effect of wave breaking on the structure of the westerly vortex is considered. Any mixing of Q on isentropic surfaces during wave breaking is shown to be far from complete in the examples studied.
The behaviour of diagnostics based on zonal averaging, such as the Eliassen-Palm flux, is accounted for by local changes in the distribution of Q. the implications of our findings for the study of stratospheric dynamics are discussed.
TL;DR: In this article, a new method for the calculation of gravity waves on deep water is proposed based on some recently discovered quadratic identities between the Fourier coefficients an in Stokes's expansion.
Abstract: A new method is proposed for the calculation of gravity waves on deep water. This is based on some recently discovered quadratic identities between the Fourier coefficients an in Stokes's expansion. The identities are shown to be derivable from a cubic potential function, which in turn is related to the Lagrangian of the motion. A criterion for the bifurcation of uniform waves into a series of steady waves of non-uniform amplitude is expressed by the vanishing of a particular determinant with elements which are linear combinations of the coefficients an. The critical value of the wave steepness for the symmetric bifurcations discovered by Chen & Saffman (1980) are verified. It is shown that a truncated scheme consisting of only the coefficients a0, a1 and a2 already exhibits Class 2 bifurcation, and similarly for Class 3. Asymmetric bifurcations are also discussed. A recent suggestion by Tanaka (1983) that gravity waves exhibit a Class 1 bifurcation at the point of maximum energy is shown to be incorrect.
TL;DR: In this article, the microwave reflectivity properties of small-scale breaking water waves are investigated and it is concluded that microwave reflectivities are consistent with Bragg scattering from these disturbances.
Abstract: The aim of this paper is to elucidate the microwave reflectivity properties of small-scale breaking water waves, which are a widespread feature of the wind-driven air-sea interface. By using a laboratory wave flume in which a small-scale breaking wave was held stationary against an opposing current, a detailed investigation of the microwave reflectivity at X-band revealed significantly enhanced levels of local backscattered power from the crest regions of small-scale breaking waves. A surprising level of organization is discovered in the hydrodynamic disturbances generated in such breaking zones. Their wavenumber-frequency spectral properties are reported in detail, from which it is concluded that the microwave reflectivity is consistent with Bragg scattering from these disturbances. The application of these findings to active microwave remote sensing of the oceans is discussed.
TL;DR: In this paper, an inviscid two-dimensional model consisting of piecewise uniform-vorticity layers is proposed to study the wave propagation in a shear flow, where the leading edge of the front evolves into a robust structure whose propagation speed can be explained by simple shock-joining theory.
Abstract: Vorticity fronts can form in a shear flow as the result of fast patches of fluid catching up with slower ones. This process and its consequences are studied in an inviscid two-dimensional model consisting of piecewise uniform-vorticity layers. Calculations using the method of contour dynamics for ‘intrusive’ initial states indicate that the leading edge of the front evolves into a robust structure whose propagation speed can be accounted for by a simple shock-joining theory. Behind the leading edge several different effects can occur depending upon the relative amplitude of the intrusion. These effects include lee-wave generation with possible wave breaking and folding of the front. A critical value of the frontal slope, above which wave breaking occurs, is suggested.
TL;DR: The relativistic electron fluid equations describing driven electron oscillations with phase velocities near the speed of light in a cold, collisionless plasma are reduced to a single, approximate ordinary differential equation of a parametrically excited nonlinear oscillator and amplitude-phase equations describing the asymptotic solutions are given.
Abstract: We analytically study the generation of longitudinal plasma waves in an underdense plasma by two electromagnetic waves with frequency difference approximately equal to the plasma frequency, as envisioned in the plasma beat-wave accelerator concept of Tajima and Dawson (Phys. Rev. Lett. 43, 267 (1979)). The relativistic electron fluid equations describing driven electron oscillations with phase velocities near the speed of light in a cold, collisionless plasma are reduced to a single, approximate ordinary differential equation of a parametrically excited nonlinear oscillator. We give amplitude-phase equations describing the asymptotic solutions to this equation valid for plasma-wave amplitudes below wave breaking. We numerically compare the behavior of the asymptotic equations with that of the original equation and with particle-simulation results.
TL;DR: In this article, the physical characteristics of inhomogeneous wave fields, derived in terms of those for homogeneous fields, are utilized to specify the characteristics and a set of reference curves for general P and S wave fields in arbitrary viscoelastic solids as a function of wave inhomogeneity.
Abstract: The physical characteristics for general plane-wave radiation fields in an arbitrary linear viscoelastic solid are derived. Expressions for the characteristics of inhomogeneous wave fields, derived in terms of those for homogeneous fields, are utilized to specify the characteristics and a set of reference curves for general P and S wave fields in arbitrary viscoelastic solids as a function of wave inhomogeneity and intrinsic material absorption. The expressions show that an increase in inhomogeneity of the wave fields causes the velocity to decrease, the fractional-energy loss ( Q −1 ) to increase, the deviation of maximum energy flow with respect to phase propagation to increase, and the elliptical particle motions for P and type-I S waves to approach circularity. Q −1 for inhomogeneous type-I S waves is shown to be greater than that for type-II S waves, with the deviation first increasing then decreasing with inhomogeneity. The mean energy densities (kinetic, potential, and total), the mean rate of energy dissipation, the mean energy flux, and Q −1 for inhomogeneous waves are shown to be greater than corresponding characteristics for homogeneous waves, with the deviations increasing as the inhomogeneity is increased for waves of fixed maximum displacement amplitude. For inhomogeneous wave fields in low-loss solids, only the tilt of the particle motion ellipse for P and type-I S waves is independent to first order of the degree of inhomogeneity. Quantitative estimates for the characteristics of inhomogeneous plane body waves in layered low-loss solids are derived and guidelines established for estimating the effect of inhomogeneity on seismic body waves and a Rayleigh-type surface wave in low-loss media.
TL;DR: In this paper, it was shown that the momentum transferred from wind to water surface goes largely into water waves when the steepness of the waves is large, and only a small amount is advected by the wind waves.
Abstract: Momentum balance in the air-sea boundary process is discussed on the basis of a recent study (Mitsuyasu and Honda, 1982). It is shown that the momentum transferred from wind to water surface goes largely into water waves when the steepness of the waves is large. For wind-generated waves, however, much of the momentum transferred from wind to waves is lost by wave breaking, and only a small amount is advected by the wind waves.
TL;DR: In this paper, a collaboration between the Laboratoire de Geochimie Isotopique (Centre d'Etudes Nucleaires, Saclay), the Institut de Mecanique Statistique de la Turbulence (IMST, Marseille), and the Institute fur Umweltphysik (Heidelberg), for the first time gas exchange experiments have been carried out in the large IMST wind-wave facility.
Abstract: In a collaboration between the Laboratoire de Geochimie Isotopique (Centre d'Etudes Nucleaires, Saclay), the Institut de Mecanique Statistique de la Turbulence (IMST, Marseille), and the Institut fur Umweltphysik (Heidelberg), for the first time gas exchange experiments have been carried out in the large IMST wind-wave facility. The experiments included simultaneous measurements of Rn and He gas exchange rates, wave slope measurements at four fetches, and bubble measurements. Compared with transfer velocities measured previously in smaller tunnels, our results are considerably lower. This effect can be explained qualitatively by differences in the wave field, which must be taken into account as an important parameter for gas exchange. Wave breaking, starting at 12 m/s wind, was not intense. Consequently, only low bubble densities are obtained, not significantly enhancing gas exchange.
TL;DR: In this paper, the vertical wave number spectra of gravity waves can be divided into subranges of weak and strong wave interactions and that observed −2.5 to −3 power law spectra may fall within the strong interaction subrange.
Abstract: It is pointed out that vertical wave number spectra of gravity waves can be divided into subranges of weak and strong wave interactions and that observed −2.5 to −3 power law spectra may fall within the strong interaction subrange. An elementary criterion is derived to help distinguish between weak and strong waves. It is then shown that the strong wave subrange is predicted by a well-known theory of Lumley. The relation of theory and observation to breaking gravity waves, turbulence dissipation, and length scales is discussed. The validity of Lumley's theory is summarized, and unresolved questions for future investigations of atmospheric wave spectra are raised.
TL;DR: In this paper, the causes of breaking for deep-water waves are now a little better understood, with the exception of the classical turbulent bore or hydraulic jump, their present models are still some way from giving a quantitative appreciation of important effects such as energy dissipation and momentum transfer.
Abstract: Most practical predictions of water-wave propagation use linear approximations based on the concepts of ‘geometric’ rays and group velocity. Although this is successful, or adequate, in many instances, there are phenomena that can only be fully understood in terms of nonlinear effects. The recent boom in soliton-related studies has shed much light on the nonlinear aspects of wave propagation in shallow water. However, for waves on deeper water some of the nonlinear effects are only now being appreciated. A few, such as the focusing pattern of steady wave fields have direct parallels in shallow water; while others, such as deep-water soliton solutions, have their own rich structure. In deep or shallow water, wavebreaking is the most eye-catching development of a wave field. With the exception of the classical turbulent bore or hydraulic jump, our present models are still some way from giving a quantitative appreciation of important effects such as energy dissipation and momentum transfer, but causes of breaking for deep-water waves are now a little better understood.
TL;DR: In this article, a hierarchy of moment equations is obtained by taking statistical ensemble averages to the interaction equations, the closure condition of which can be effected by making a random phase approximation, and the obtained kinetic equation is Boltzmann-like and describes the time evolution of wave action.
Abstract: Previous work has shown that a primary gravity wave of sufficient amplitude will always decay through resonant wave-wave interactions with two secondary gravity waves. The interaction among the resonant trio can be reasonably rapid and may be an important process responsible for energy exchange among gravity waves of different wavelengths in the atmosphere. By taking statistical ensemble averages to the interaction equations we obtain an hierarchy of moment equations, the closure condition of which can be effected by making a random phase approximation. The obtained kinetic equation is Boltzmann-like and describes the time evolution of wave action. The nonlinear kinetic equation is impossible to solve in general except numerically, but the equation is drastically simplified in three limiting cases identified as elastic scattering, parametric subharmonic instability, and induced diffusion processes. Through elastic scattering, an upgoing wave is scattered into a downgoing wave by interacting resonantly with a vertical shear. This process is thus responsible for making the atmospheric spectrum vertically symmetric if it is not so initially. The parametric subharmonic instability process is responsible for transferring energetic large-scale waves to small-scale waves at one-half the frequency. The induced diffusion process is responsible for time evolution of small-scale waves by a three-wave process involving two nearly identical waves of small scales interacting resonantly with a large-scale vertical shear. The rapidity with which these three processes take place in the atmosphere and their implication in the atmospheric spectrum are investigated and discussed.
TL;DR: Simultaneous measurements of the water surface elevation and Eulerian water particle velocities inside the breaker zone were performed at various locations in a wave flume for spilling and plunging.
Abstract: Simultaneous measurements of the water surface elevation and Eulerian water particle velocities inside the breaker zone were performed at various locations in a wave flume for spilling and plunging...
TL;DR: In this paper, the effects of wave-wave interactions and convective adjustment on the propagation of gravity waves in the middle atmosphere were examined, and it was found that wave interactions, while reducing primary wave amplitudes somewhat, are unable to prevent the formation of convectively unstable layers.
Abstract: In this study we examine some of the effects of wave-wave interactions and convective adjustment on the propagation of gravity waves in the middle atmosphere. For both a nearly monochromatic wave and a super-position of waves, nonlinear wave-wave interactions, while reducing primary wave amplitudes somewhat, are found to be unable to prevent the formation of convectively unstable layers. In contrast, convective adjustment of the wave field causes significant amplitude reductions, resulting in amplitudes for a spectrum of wave motions that achieve only a fraction of their monochromatic saturation values. Neither process is found to cause a major disruption of the primary wave field. Both wave-wave interactions and convective adjustment are found to excite harmonies of the primary wave motions. Excitation by convective adjustment appears to dominate for a monochromatic wave, whereas both processes become important for a spectrum of wave motions. In each case, the characteristics of the excited wave...
TL;DR: In this article, a wave propagation model for wave breaking in the mesosphere has been proposed based on wave action density and Ray Tracing (RT) is used to follow the gravity wave packets through varying wind conditions.
Abstract: Lindzen (1981, 1984) has considered the effects of monochromatic, steady gravity waves propagating into the upper atmosphere. These waves reach such large amplitudes in the mesosphere that they become convectively unstable. The wave is effectively dissipated by the convection, and the pseudomomentum carried by the wave is transferred to the basic flow. The net effect is to accelerate the background flow to the phase speed of the breaking gravity wave. Schoeberl et al. (1983) have discussed modifications to Lindzen's parameterization. The present paper has the objective to develop a type of parameterization scheme for wave breaking that, in principle, can handle lateral wave propagation. Ray tracing is used to follow the gravity wave packets through varying wind conditions. The theory considered uses both the propagation properties of the wave packet and the concept of the conservation of wave action density to determine the local amplitude and position of the wave packet.
TL;DR: In this paper, the temporal evolution of large amplitude quasi-geostrophic disturbances in a piecewise uniform potential vorticity flow is elucidated by numerical solutions of the contour dynamica equations.
Abstract: The temporal evolution of large amplitude quasi-geostrophic disturbances in a piecewise uniform potential vorticity flow is elucidated by numerical solutions of the “contour dynamica” equations. Lateral wavebreaking occurs when the initial disturbance amplitude exceeds a certain value, and at later times tongues of the 1ower vorticity fluid are engulfed or entrained into the higher vorticity shear flow. The effect appears to be important for the evolution of “shingles” observed between the coastal water and the cyclonic side of the Gulf Stream. The effect may also be in important phase in initiating the mixing process at the perimeter of an eddy embedded in another water mass.
TL;DR: In this paper, a barotropic Rossby wave incident to a region of increasing mean flow velocity opposing the wave group velocity undergoes a reversal of direction at a stopping point where the mean flow and local wave group velocities are equal and opposite.
Abstract: A barotropic Rossby wave incident to a region of increasing mean flow velocity opposing the wave group velocity undergoes a reversal of direction at a stopping point where the mean flow velocity and local wave group velocities are equal and opposite. Incident wave amplitude increases approaching this stopping point, which may be referred to as a group velocity critical layer, but eventually suffers a decrease along its trajectory so that the reflected wave amplitude and energy tend to zero on approach to a phase velocity critical layer located where the opposing flow vanishes. Some applications of this process to observations of synoptic scale Rossby waves are suggested and an example of the interaction of an incident wave with a barotropic model of the Hadley circulation is presented to illustrate these ideas.
01 Jan 1985
TL;DR: In this article, the authors show evidence of strong coupling between two different types of instabilities for finite-amplitude surface gravity waves in deep water and show that the three-dimensional, crescent-shaped breaking waves of wave trains and wave packets with the initial wave steepness (aoko) as low as 0.12.
Abstract: Experimental results are presented that show evidence of strong coupling between two different types of instabilities for finite-amplitude surface gravity waves in deep water. A consequence of this coupling is the three-dimensional, crescent-shaped breaking waves of wave trains and wave packets with the initial wave steepness (aoko) as low as 0.12. A second consequence is to provide a new mechanism or observed energy dissipation and directional energy spreading during evolution of waves when about 0.14 ≤ aoko ≤ 0.18, corresponding to the most commonly observed wave steepness during the rapid growth stages of wind-generated ocean waves.