Showing papers on "Breaking wave published in 1993"

Wave-breaking-free pulses in nonlinear-optical fibers

Abstract: A qualitative as well as quantitative investigation is made of the conditions for avoiding wave breaking during pulse propagation in optical fibers. In particular, it is shown that pulses having a parabolic intensity variation are approximate wave-breaking-free solutions of the nonlinear Schrodinger equation in the high-intensity limit. A simple expression for the compression factor of a fiber-grating compressor based on parabolic pulses is also derived.

Wave Breaking in Deep Water

Abstract: Every mariner is aware that dangerous large breaking water waves occur on the world's oceans. The scope of this review is somewhat greater. Wave breaking occurs at a large range of scales and we do not restrict ourselves to the deep ocean. "Deep water" in the context of water wave studies implies water sufficiently deep that the surface waves are unaffected by the direct effects of variations in bed topography. Thus even a small pond can support breaking deep-water waves. Shallow water breaking is reviewed in Peregrine (1983). Some comments on the visual aspect of breakers are in order, since direct observation still has a role to play in the study of this complex phenomenon. The most dramatic breakers are plunging breakers where the breaking commences by the wave overturning and forming a forward moving sheet of water which plunges down into the water in front causing splashes, air entrainment, and eddies. Although plunging breakers are common on beaches they are less common on deep water, so much so that some people have argued that they do not occur naturally. However, read Coles (1991) for a distillation of an experienced yachtsman's account of waves at sea. Most other breakers are described as spilling breakers. From their

Hurricane Spiral Bands

Abstract: The spiral bands that occur in tropical cyclones can be conveniently divided into two classes—outer bands and inner bands. Evidence is presented here that the outer bands form as the result of nonlinear effects during the breakdown of the intertropical convergence zone (ITCZ) through barotropic instability. In this process a zonal strip of high potential vorticity (the ITCZ shear zone or monsoon trough) begins to distort in a varicose fashion, with the potential vorticity (PV) becoming pooled in local regions that are connected by filaments of high PV. As the pooled regions become more axisymmetric, the filaments become thinner and begin to wrap around the PV centers. It is argued that inner bands form in a different manner. As a tropical cyclone intensifies due to latent heat release, the PV field becomes nearly circular with the highest values of PV in the cyclone center. The radial gradient of PV provides a state on which PV waves (the generalization of Rossby waves) can propagate. The nonline...

Convolution Method for Time-Dependent Beach-Profile Response

Abstract: A simple analytical solution is presented for approximating the time-dependent beach-profile response to severe storms. This solution is in the form of a convolution integral involving a time-varying erosion-forcing function and an exponential erosion-response function. The erosion-forcing function reflects changes in the nearshore water level and breaking wave height. In this paper, an idealized storm-surge hydrograph is considered from which an analytic solution is obtained for beach and dune erosion associated with severe storms such as hurricanes or northeasters. It is shown that for a given initial beach geometry and sediment size, the peak water level and the incipient breaking wave height determine the maximum erosion potential that would be achieved if the beach were allowed to respond to equilibrium. Because of the assumed exponential erosion rate, beach response obtained from the convolution method is found to lag the erosion forcing in time, and is damped relative to the maximum erosion potential such that only a fraction of the equilibrium response actually occurs.

Classification of breaking wave loads on vertical structures

Abstract: Measurements of impact pressures and forces together with simultaneous video records of the wave motion at and in front of caisson breakwaters were performed in a wave flume. Based on the results of this model study, criteria are developed for wave‐breaking and breaker‐type classification in the presence of vertical structures. As a result, four main breaker types are identified and discussed. The corresponding impact loads (pressure, pressure distribution, and total forces) are described. The results obtained suggest that the observed breaker shapes can now be identified by the recorded force histories, as well as by the impact pressure histories and distributions, without any use of the corresponding video pictures. The effect of the caisson front geometry on the impact forces is also briefly discussed. It is concluded that the shape of both the colliding breaker and structure front must be accounted for in the future prediction of impact loads.

Wave and vortex dynamics on the surface of a sphere

Abstract: Motivated by the observed potential vorticity structure of the stratospheric polar vortex, we study the dynamics of linear and nonlinear waves on a zonal vorticity interface in a two-dimensional barotropic flow on the surface of a sphere (interfacial Rossby waves). After reviewing the linear problem, we determine, with the help of an iterative scheme, the shapes of steadily propagating nonlinear waves; a stability analysis reveals that they are (nonlinearly) stable up to very large amplitude. We also consider multi-vortex equilibria on a sphere: we extend the results of Thompson (1883) and show that a (latitudinal) ring of point vortices is more unstable on the sphere than in the plane; notably, no more than three point vortices on the equator can be stable. We also determine the shapes of finite-area multi-vortex equilibria, and reveal additional modes of instability feeding off shape deformations which ultimately result in the complex merger of some or all of the vortices. We discuss two specific applications to geophysical flows: for conditions similar to those of the wintertime terrestrial stratosphere, we show that perturbations to a polar vortex with azimuthal wavenumber 3 are close to being stationary, and hence are likely to be resonant with the tropospheric wave forcing; this is often observed in highresolution numerical simulations as well as in the ozone data. Secondly, we show that the linear dispersion relation for interfacial Rossby waves yields a good fit to the phase velocity of the waves observed on Saturn’s ‘ribbon’.

Basic wave mechanics : for coastal and ocean engineers

Abstract: Sea Surface Gravity Waves. Small Amplitude Wave Theory and Characteristics. Two-Dimensional Wave Transformation. Finite Amplitude Wave Theory. Three-Dimensional Wave Transformations. Wind-Generated Waves. Design Wave Determination. Wave-Structure Interaction. Long Waves. Laboratory Investigation of Surface Waves. Index.

Wave breaking signatures in noctilucent clouds

Abstract: Results of a recent modeling study of gravity wave breaking in three dimensions by Andreassen et al. and Fritts et al. showed wave saturation to occur via a three-dimensional instability oriented normal to the direction of wave propagation. The instability was found to occur at horizontal scales comparable to the depth of unstable regions within the wave field and to lead to substantial vertical displacements and tilting of isentropic surfaces. Because of strong similarities between the wave and instability structures in the simulation and the structure observed in noctilucent cloud layers near the summer mesopause, we have used these model results to compute the advective effects on cloud visibility and structure for a range of viewing angles and cloud layer widths. Our results show the gravity wave breaking signature to provide a plausible explanation of the observed structures and suggest that noctilucent cloud structures may be used in turn to infer qualitative properties of gravity wave scales, energy and momentum transports, and turbulence scales near the summer mesopause.

Hybrid frequency-domain kdv equation for random wave transformation

Abstract: This paper develops a hybrid model for random wave transformation by employing a modified spectral model of the KdV equation and a probabilistic bore-type wave breaking model, and compares the numerical predictions with experimental observations. Main results are as follows: 1) Original frequency-domain KdV equation overestimates energy densities, due to over-shoaling term by Green's law in the equation, even in a region where wave breaking is not seen; 2) Modification of the original KdV equation in order to represent shoaling for linear-dispersive component waves leads to better predictions in the non-breaking region; 3) Damping coefficients in the model equation, either estimated from measured spectral densities or the numerically predicted, are in inverse proportion to the water depth and in proportion to the square of frequency, similar to the viscous damping term of the Burgers equation; 4) The hybrid model developed here can predict transformations of random waves satisfactorily, as indicated by comparison of energy spectra, representative wave heights, periods, and crest heights.

Initiation of slugs in horizontal gas-liquid flows

Abstract: Experiments were conducted with air-water flow in a horizontal 0.095-m pipeline at atmospheric pressure to examine the mechanism by which slugs form in a stratified flow. A specially designed entrance box was used to avoid disturbances. In these experiments, at superficial gas velocities less than 3 m/s, the slugs are found to evolve from waves, with a length of about 0.085 m, that are generated by a Jeffreys mechanism. These waves grow in height and eventually double in wavelength by a nonlinear resonance mechanism. Depending on the height of the liquid, the growth can lead to a breaking wave or to a wave that fills the whole pipe cross section. At superficial gas velocities equal to or greater than 4 m/s capillary-gravity waves with a wide range of lengths are generated by a linear Kelvin-Helmholtz mechanism. These rapidly evolve into long waves outside the range of linear instability. If the liquid height is large enough, these waves can form slugs through a nonlinear Kelvin-Helmholtz instability that is aided by wave coalescence.

Sediment suspension under waves and currents: time scales and vertical structure

Abstract: Field measurements of the vertical structure of near-bed suspended sediment concentrations were obtained from arrays of fast response optical backscatter suspended solids sensors to examine the time-dependent response of sediment resuspension to waves and currents and the constraints imposed by bedforms. Data were recorded from both a nonbarred, marine shoreface and a barred lacustrine shoreface, under both shoaling and breaking waves (significant heights of 0·25–1·50m; peak periods of 3 and 8 s) and in water depths of 0·5–5·0 m. Sediment concentrations are positively correlated with increasing elevation above the bed, but lagged in time. The time lag varies directly with separation distance between measurement locations and inversely with the horizontal component of the near-bed oscillatory velocity. Both the presence of wave groups and the settling velocities of the sediment particules in suspension influence the temporal changes in concentration at a given elevation. Sediment concentrations appear to respond more slowly to the incident wind-wave forcing with distance away from the bed as a result of two factors: (1) the sequential increase in concentration induced by a succession of large waves in a group; and (ii) the relative increase in finer sediments with smaller settling velocities. Bedforms interact with the near-bed horizontal currents to impose a distinct constraint upon the timing of suspension events relative to the phase of the fluid motion, and, therefore, the vertical structure of the suspended sediment concentration at a range of time scales. The near-bed concentrations appear to be strongly dependent upon the vertical convection of sediment associated with the ejection from the wave boundary layer of separation vortices generated in the lee of ripple crests. Concentration gradients in the presence of vortex ripples are large, as are the correlation between concentrations measured at different elevations within the fluid.

Wave-turbulence dynamics in the stably stratified boundary layer

Abstract: New data obtained at the Boulder Atmospheric Observatory are analyzed to obtain separation of wave, turbulence, and mean field necessary for a complete treatment of wave-turbulence interaction. The data were compared with a linear stability analysis of the background atmospheric state, showing good agreement between measured wave parameters (such as wavelength, period, and vector phase velocity) and the eigenvalues of the linear solution. The analysis of the budgets of wave heat flux and temperature variance revealed the essential role of wave-turbulence interaction in maintaining a large amplitude temperature wave and countergradient heat flux. A mechanism for the maintenance of turbulence by waves in strongly stratified boundary layers is described, which emphasizes that the time-mean Richardson number is an irrelevant parameter at such times.

Evolution of maximum amplitude of solitary waves on plane beaches

Abstract: This paper presents a study of the transformation of solitary waves on plane beaches. A series of laboratory experiments is presented to describe the amplitude evolution of long waves; these experiments suggest that at least four different regions exist for the functional variation of the maximum amplitude, two regions before and two regions after breaking. Linear theory is used to provide an expression for the growth of solitary waves evolving first over constant depth and then over a sloping bottom, including reflection. This result is shown to be equivalent to the wave evolution expression known as Green's law, and the limitations of Green's original derivation are discussed. Other existing analytical results and certain empirical relationships are used to produce a formulation consistent with the laboratory data with the objective to model the entire process of solitary wave evolution.

Statistics of Shear and Turbulent Dissipation Profiles in Random Internal Wave Fields

Abstract: Because breaking internal waves produces most of the turbulence in the thermocline, the statistics of ϵ, the rate of turbulent dissipation, cannot be understood apart from the statistics of internal wave shear. The statistics of ϵ and shear are compared for two sets of profiles from the northeast Pacific. One set, PATCHEX, has internal wave shear close to the Garrett and Munk model, but the other set, PATCHEX north, has average 10-m shear squared, 〈S210〉, about four times larger than the model. The 10-m, shear components, Sx and Sy, were measured between 1 and 9 MPa and referenced to a common stratification by WKB scaling. The scaled components, Sˆx and Sˆy, are found to be independent and normally distributed with zero means, as assumed by Garrett and Munk. This readily leads to analytic forms for the probability densities of Sˆ210 and Sˆ410. The observed probability densities of Sˆ210 and Sˆ410 are close to the predicted forms, and both are strongly skewed. Moreover, σlnSˆ210 and σlnSˆ410 are c...

Longshore Current on a Barred Beach: Field Measurements and Calculation

Abstract: Measurements of the longshore current on a barred beach made during the 1990 Duck Experiment on Low-Frequency and Incident-Band Longshore and Across-Shore Hydrodynamics (DELILAH) field data collection project conducted at Duck, North Carolina, revealed an unexpected and persistent broad peak in the current velocity in the trough between the nearshore bar and the shore. This paper introduces longshore current and associated wave measurements from DELILAH together with a numerical model capable of describing the field observations. An existing numerical model of the mean current is modified to include a general transport equation for the mean turbulent kinetic energy created by wave breaking, and Reynolds stress components needed to calculate the longshore current and mean water level are reexpressed to include the turbulent momentum transport. In comparison to predictions from the original model, the modified model produces much improved agreement with the measured current velocity on the barred profiles in the field measurements and with the velocity profile and mean water level generated on a uniformly sloping laboratory beach by monochromatic waves. Three forms of a bottom friction coefficient are examined, and the open-channel-flow Manning friction coefficient is selected because of best agreement and consistency. Values of the Manning friction coefficient required to calibrate the model agree with values normally assigned to the related bottom roughness in open-channel flow.

Longshore current and wave height modulation at tidal frequency inside the surf zone

Abstract: Data were acquired continuously during the 19-day DELILAH nearshore experiment with a specific objective of examining variability of the longshore current at tidal frequencies. It is hypothesized that breaking wave heights inside the surf zone are strong functions of the depth which are modulated by the tidal variations, and since radiation stress is a function of the wave height, longshore currents are forced at the tidal frequency inside the surf zone. The measured longshore current variations at tidal frequency are the same order of magnitude as the mean longshore current variations for moderate wave height conditions, indicating that the tide is a dominant mechanism associated with longshore current variability. Simulations of the magnitude and phase of the longshore current variability with tide elevation using the model by Thornton and Guza (1986) are used to explain observations. The measured tidal elevation and longshore current are in phase in the inner surf zone and out of phase in the outer surf zone as predicted by the model, verifying the hypothesis.

Energy Loss by Breaking waves

Abstract: Observations of the frequency of wind wave breaking in deep water are combined with laboratory estimates of the rate of energy loss a from single breaking wave to infer the net rate of energy transfer to the mixed layer from breaking waves, as a function of wind speed. Breaking waves with wavelengths much shorter than the dominant waves can contribute energy at a rate that is a significant fraction of the total turbulent kinetic energy dissipation rate in the ocean surface mixed layer.

Vertical wave barriers: wave transmission and wave forces

Abstract: Wave interaction with a vertical slotted wave barrier, also called a wave screen or slit-type breakwater, is considered. A theoretical analysis is presented based on application of the continuity, momentum, and energy equations to flow through the slots in the breakwater, accounting for head losses associated with flow constriction and re-expansion. As a result, relatively simple expressions are found for the wave transmission coefficient and for the wave forces on the wall. These are then verified by laboratory experiments with regular waves.

The underwater sound generated by heavy rainfall

Abstract: The underwater acoustic signature of heavy rainfall is very different from that of light rainfall. During heavy rainfall sound levels are observed to rise with increasing rainfall rate at all frequencies monitored (4–21 kHz) and the 15‐kHz spectral peak observed during light rainfall is absent. The sound levels are most highly correlated (r≊0.8) with heavy rainfall rate for frequencies less than 10 kHz. Lower correlations between sound levels and heavy rainfall rate were observed for frequencies above 10 kHz under several different conditions. When wind speed exceeds 10 m/s, wave breaking mixes bubbles downward and creates a layer of bubbles. This bubble layer attenuates subsequent surface‐generated sound (from the raindrop splashes) for frequencies above 10 kHz. Extremely heavy rainfall (total rainfall above 150 mm/h) also generates a subsurface bubble layer. This rainfall‐generated bubble layer is evidence of rainfall‐induced turbulent mixing of the ocean surface layer and has implications for air/sea e...