Showing papers on "Breaking wave published in 1987"

The runup of solitary waves

Abstract: This is a study of the runup of solitary waves on plane beaches. An approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves. A series of laboratory experiments is described to support the theory. It is shown that the linear theory predicts the maximum runup satisfactorily, and that the nonlinear theory describes the climb of solitary waves equally well. Different runup regimes are found to exist for the runup of breaking and non-breaking waves. A breaking criterion is derived for determining whether a solitary wave will break as it climbs up a sloping beach, and a different criterion is shown to apply for determining whether a wave will break during rundown. These results are used to explain some of the existing empirical runup relationships.

Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

Abstract: To provide theoretical basis for the connection between observed radar scattering and wind-generated waves, a model for the response of surface waves in the gravity-capillary equilibrium region of the spectrum is proposed on the basis of a local (in wavenumber) balance between wind input and dissipation. The wind input function was constructed on the basis of laboratory observations of short-wave growth, while the dissipation function was developed from ideas of viscous dissipation and wave breaking in response to local accelerations and modified by kinematic effects of phase and group velocity differences. The model was exercised at L, C, X, and Ka bands to demonstrate the differences in wind speed and water temperature sensitivity.

Hyperbolic conservation laws with relaxation

Abstract: The effect of relaxation is important in many physical situations. It is present in the kinetic theory of gases, elasticity with memory, gas flow with thermo-non-equilibrium, water waves, etc. The governing equations often take the form of hyperbolic conservation laws with lower-order terms. In this article, we present and analyze a simple model of hyperbolic conservation laws with relaxation effects. Dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified. Stability criteria for diffusion waves, expansion waves and traveling waves are found and justified nonlinearly. Time-asymptotic expansion and the energy method are used in the analysis. For dissipative waves, the expansion is similar in spirit to the Chapman-Enskog expansion in the kinetic theory. For shock waves, however, a different approach is needed.

Nonlinear evolution of the Kelvin-Helmholtz instability in the high-latitude ionosphere. Interim report

Abstract: The nonlinear evolution of the electrostatic Kelvin-Helmholtz instability, resulting from velocity-sheared plasma flows perpendicular to an ambient magnetic field, was studied including Pedersen conductivity effects (i.e., ion-neutral collisions). The Kelvin-Helmholtz instability develops in a distinctly different manner in the nonlinear regime with Pedersen coupling than without it. Specifically, the Pedersen coupling effects, in conjunction with a neutral wind and density gradient, (1) result in an increased time scale for Kelvin-Helmholtz instability wave growth, (2) inhibit Kelvin-Helmholtz vortex formation, (3) lead to nonlinear structures that can be described as breaking waves, and (4) generate, in the nonlinear regime, small-scale turbulence by means of secondary instabilities growing on the primary waves. The spatial power spectra of the electrostatic potential and density fluctuations, and it is found that there is a tendency for the potential and density to become shallower when Pedersen conductivity effects are included. The results are compared with recent Dynamics Explorer satellite observations of velocity sheared plasma flows in the high-latitude, near-earth space plasma and good agreement is found.

Steepened magnetosonic waves at Comet Giacobini-Zinner

Abstract: Intense MHD waves at Comet Giacobini-Zinner were examined to investigate the mode and direction of wave propagation and thereby to provide important constraints on potential mechanisms for the wave origin in the vicinity of the comet. From observations of steepened wave forms, it is found that the waves must be propagating toward the sun but are blown back across the ICE spacecraft. The correlation between magnetic field magnitude and electron density enhancements indicates that these waves are fast magnetosonic mode emissions. The sense of rotation of the partial rotations are left-hand circularly polarized in the spacecraft frame, consistent with anomalously Doppler-shifted right-hand waves.

On the spatial distribution of ocean bubbles

Abstract: Clouds of bubbles generated by breaking waves were detected with a vertically directed high-frequency echo sounder mounted on a submarine. Bubble concentration was inferred from a simple model of the bubble size distribution. The vertical and horizontal distribution of clouds is discussed in terms of wave-breaking processes, air-sea temperature differences, and subsurface motions which are thought to modulate the bubble concentration. Mean vertical profiles of bubble concentration decreased roughly exponentially with depth, with e-folding depths between 0.7 m and 1.5 m. The mean bubble concentration at the surface, N–0, was found to increase with the wind speed measured at 10 m above the surface, U10, as N–0∼U103.0±0.3. Various upper ocean dynamical processes are discussed in terms of their effects on the shapes and spacing of bubble plumes. The observations provide only weak evidence to support relationships between plume spacing and surface wave-breaking events and between plume spacing and the expected scale of Langmuir circulation.

Recession Rate of Glacial Till Bluffs

Abstract: The relationship between waves and recession rate of cohesive bluff shorelines consisting of glacial till is explained in physical terms as a function of wave-foreshore interaction. An equation is derived based on wave energy dissipation rate in the breaking zone and on wave shear stresses offshore of the breaking zone. Measured long-term recession rates of bluffs along the North Shore of Lake Erie are compared to hindcast long-term average wave power and related to the equations developed in this paper.

MHD wave breaking in the outer plasmasphere

Abstract: Empirical models of the average magnetospheric magnetic field, plasma density, and temperature distributions are used to construct a model of the distribution of MHD wave mode speeds within the magnetosphere. A persistent feature of the derived optical structure is a pronounced minimum of the wave speeds in the outer plasmasphere, i.e., a magnetospheric 'shoal'. This feature does not map along magnetic field lines, but is confined to the equatorial region, leading to a positive radial gradient of wave speeds near synchronous orbit. The breaking of earthward propagating disturbances in this region may play an essential role in the formation of the substorm injection boundary and in the creation of equatorially trapped warm ion distributions.

Instability and Breaking of a Solitary Wave

Abstract: The result of a linear stability calculation of solitary waves which propagate steadily along the free surface of a liquid layer of constant depth is examined numerically by employing a time-stepping scheme based on a boundary-integral method. The initial growth rate that is found for sufficiently small perturbations agrees with the growth rate expected from the linear stability calculation. In calculating the later ‘nonlinear’ stage of the instability, it is found that two distinct types of long-term evolution are possible. These depend only on the sign of the unstable normal-mode perturbation which is superimposed initially on the steady wave. The growth of the perturbation ultimately leads to breaking for one sign. Unexpectedly, for the opposite sign, there is a monotonic decrease in the total height of the wave. In this latter case there is a smooth evolution to a stable solitary wave of lesser amplitude but very nearly the same energy.

Observations of internal gravity waves under the Arctic pack ice

Abstract: Internal gravity waves measured under the Arctic pack ice were strikingly different from measurements at lower latitudes. The total wave energy, integrated over the internal wave frequency band, was lower by a factor of 0.03–0.07, and the spectral slope at high frequency was nearly −1 in contrast to the − 2 observed at lower latitudes. This result has implications for theoretical investigations of the generation, evolution, and destruction of internal waves and is also important for other processes, such as the propagation of sound, and the wave-induced turbulent diffusion of heat, plankton, and chemical tracers.

Observations of Small-Scale Mixing Processes in the Seasonal Thermocline, Part II: Wave Breaking

Abstract: Towed thermistor chain measurements are used to describe a large patch of ocean fine- and microstructure. In contrast to the relatively quiescent salt-fingering conditions of Part I, the 3-km long by 5–10-m high patch is in a frontal zone where background shear is enhanced by an inertial were (Mied et al.). It is conjectured that an embedded, coherent structure resembling a series of breaking waves is creating the smaller-scale activity. The waves have lengths of 30–50 m which are not incompatible with Kelvin-Helmholtz shear instabilities growing in an observed low-Richardson number layer. Ongoing mixing in the patch is inferred from large values of Cox number, fluctuation length scales which scale with the Cox number, and gradient microstructure spectra which increase as (wavenumber)+1 and are often unresolved at the higher values of Cox number.

Experiments on Saline Wedge

Abstract: Detailed measurements on the internal flow structure of the arrested saline wedge over a horizontal bottom have been performed together with observations of its overall appearance. The experiments covered a channel Reynolds number range between 4,000 and 10,000 and a densimetric Froude number range between 0.39 and 0.49. Measurements included overall shape, internal circulation, velocity, density and gradient Richardson number profiles, entrainment rates, and shear stresses. The major portion of the saline wedge, excluding the wedge tip and the exit regions, is a quasi‐equilibrium region in which internal flow properties are nearly similar. The flow dynamics are controlled by the turbulent freshwater overflow with a downward cascading process of energy toward the salt layer. Conditions at the two major internal dividing lines, the density interface and the zero velocity line, are elucidated. The density interface is a highly stable zone with intermittent wave breaking, mixing, and entrainment. The zone is...

Bubble clouds and temperature anomalies in the upper ocean

Abstract: The processes of mixing in the upper few metres of the ocean are poorly known and largely unqualified1 but are a vital element in ocean–atmosphere interaction, playing a key part in the transfer and dispersion of heat, gases and nutrients. Here we report results from a towed instrument used to measure simultaneously water temperature and the sound scattered from bubble clouds produced by breaking waves. Dominant features in the records are correlated, intense sound scattering (or bubble clouds) being associated with warmer water and large positive temperature gradients with the onset of increased scattering. The observations provide a more complete picture of the structure and nature of bubble clouds and establish their assocition with dynamical processes of turbulent diffusion in the upper ocean boundary layer.

Attenuation of wind waves by monomolecular sea slicks and the Marangoni Effect

Abstract: Previous observations of wind wave damping by monomolecular surface films (“slicks”) have shown a pronounced energy detraction (“dip”) in the short gravity wave range of the wind wave spectra. In this work, wind wave tunnel experiments with mechanically generated water waves have supplied experimental evidence which clearly shows that this dip is predominantly caused by the film-induced “Marangoni effect.”

Adjustment of Reflective Beaches to Waves

Abstract: A new mode of beach response to changes in wave height is identified for reflective beaches where waves break close to the shoreline. This response involves vertical adjustment of the beach face morphology, especially the beach step. It is found that profile relief varies with wave height rather than inversely to it as expected from existing models. As a result the characteristic steep reflective profile can be maintained under certain conditions, during periods of beach erosion. A field program which included surveys of 67 beach profiles on a persistently reflective beach measured vertical adjustments of the beach step and associated wave and sediment conditions. Based on these data a model is developed to describe the changes in the amplitude of the beach step related to changes in breaker height and sediment size. It was found that as breaker height increases the step height increases, while the surf zone width remains constant. Larger grain sizes and changes in grain size across the beach face are also associated with larger step heights. This step adjustment model implies that if wave height increases, under the range of conditions observed, the resultant increase in step amplitude and associated deepening of the nearshore will be sufficient to delay wave breaking, allowing a reflective profile to be maintained. Therefore the model can account for the environmental conditions which produce changes in step heights and favour the maintenance of a reflective system. The model also implies that a threshold exists between this mode and the conventionally recognised mode of beach response and therefore differentiates between transient reflective profiles, and those of less mobile reflective beach systems.

On the Representation of Rossby Wave Critical Layers and Wave Breaking in Zonally Truncated Models.

Abstract: A detailed comparison is made between the Stewartson-Warn-Warn analytical solution for a fully nonlinear, nondiffusive Rossby-wave critical layer and a new analytical solution for the corresponding zonally truncated, “wave-mean” or “quasi-linear” problem in which the motion is represented by the zonal mean and a single zonal harmonic only The effect of adding harmonics one by one is also considered The results illustrate the extent to which zonally truncated models, which inevitably miss certain aspects of the fluid behavior, nevertheless contrive to mimic some important dynamical features of the evolution of the nonlinear critical layer, particularly the absorption-reflection behavior The zonally truncated and fully nonlinear models predict almost the same reflection coefficient up to the time Tr when a state of perfect reflection is first reached, and the predicted values of Tr itself differ by only 5% The agreement deteriorates only subsequently, during the first overreflecting stage The

Skewness in the nearshore zone: A comparison of estimates from Marsh‐McBirney current meters and colocated pressure sensors

Abstract: Many of the field studies that have undertaken an investigation of surf zone dynamics (e.g., Nearshore Sediment Transport Study, Canadian Coastal Sediment Study) have relied on Marsh-McBirney electromagnetic current meters to measure the velocity field. Data from these instruments have been used to compute higher order moments of the velocity field, which are used as an input in many sediment transport models. However, recent laboratory measurements by Aubrey and Trowbridge (1985) have raised questions regarding the suitability of Marsh-McBirney current meters for surf zone studies and the accuracy of higher order velocity moments. Fortunately, colocated pressure and velocity measurements were made during field programs. In effect, this provides a calibration check in the field of the performance of these instruments. A cross-spectral analysis indicates that colocated Marsh-McBirney current meter measurements are highly coherent; this is true for measurements from inside and outside the surf zone. As a result, normalized skewness estimates computed (with the aid of the bispectrum) from these colocated current meter measurements differ by only a few percent. A cross-spectral analysis between colocated pressure and velocity measurements show a similar distribution of variance for wind wave frequencies. Observed differences between normalized skewness estimates from colocated pressure and velocity measurements are shown to be consistent with the theoretical expectation that pressure has a nonlinear dependence on velocity. These results suggest that the Marsh-McBirney current meter is suitable for the estimation of nondimensional velocity moments, even in breaking wave conditions.

Properties of short-crested waves in water of finite depth

Abstract: Short-crested waves are defined as propagating surface gravity waves which are doublyperiodic in the horizontal plane. Linearly, the short-crested wave system we consider occurs when two progressive wavetrains of equal amplitude and frequency are propagating at an angle to each other. Solutions are calculated via a computer-generated perturbation expansion in wave steepness. Harmonic resonance affects the solutions but Pade approximants can be used to estimate wave properties such as maximum wave steepness, frequency, kinetic energy and potential energy. The force exerted by waves being reflected by a seawall is also calculated. Our results for the maximum depth-integrated onshore wave force in the standing wave limit are compared with experiment. The maximum force exerted on a seawall occurs for a steep wave in shallow water incident at an oblique angle. Results are given for this maximum force.

Internal waves and whitecaps

Abstract: There are numerous reports of internal waves being 'made visible' on the sea surface by their effect on the surface-wave field and the production of bands of steeper, often breaking, waves separated by zones of relatively calm water1–5. The effect is sometimes quite dramatic. There are accounts of a 'low roar' as the bands of breaking waves, 'walls of white water', pass a vessel6. The bands are sometimes visible from aircraft7, on ships, radar8,9 and are observed from satellites10–15. In the Bay of Biscay 'boils' have been reported on the sea surface in the calm zones, and appear to be related to pulses of nutrients from the thermocline16. The position of the roughest water has been commonly reported to be above the part of the internal wave in which the thermocline is most rapidly falling3,5 (as sketched in Fig. 1) except in very light winds (<3.5 m s−1), when this appears generally to be the calmest zone16. There are, however, few simultaneous observations of surface and internal waves and none, to our knowledge, which has both quantified the frequency of the breaking waves and established their position relative to the internal waves. Here we have used an upward-pointing side-scan sonar to obtain a sub-surface view of bands of rough water and whitecaps on the sea surface associated with internal waves travelling on a pycnocline. The sonar provides a means to measure the surface currents induced by the internal waves, the position, or phase, of the surface-wave breaking relative to the internal waves, and to quantify the frequency of wave breaking. The effect of wave breaking caused by wave–current interaction is to transfer momentum from the surface waves to the currents, with a phase which tends to diminish the internal waves in the cases studied. The enhanced turbulence caused by wave breaking may be effective in mixing or eroding the pycnocline.

A note on lee wave structures in stratified flow over three-dimensional obstacles

Abstract: An experimental study of the spanwise structure of lee waves generated behind a surface mounted obstacle in linearly stratified flow is described. Attention is concentrated, first, on the conditions under which lee wave breaking always occurs and, second, on the rate at which the wave amplitudes decay across the span. Although only one particular body shape was used—one which promoted boundary layer separation in all cases—it is argued that the form of the results should be generally applicable. The data are compared where possible with the implications of linear theory for a circular hill or a long ridge. DOI: 10.1111/j.1600-0870.1987.tb00290.x

Bubbles between the wave trough and wave crest levels

Abstract: In order to estimate ocean-atmosphere mass transfer fluxes controlled by aerosol generation the bubble population at the interface has to be known. This information is usually inferred from measurements at a given depth below the water surface and from broad assumptions about the variation of bubble population with depth. However, recent measurements are not consistent with the usually assumed bubble population variation, and a direct investigation in the immediate vicinity of the interface appears to be necessary. Measurements above the minimum wave trough are difficult because a sensor level is alternately in the air and in the water. We have used a laser-based single-particle technique to investigate this zone for different breaking wave fields generated in a wind-water simulation facility. The main bubble population characteristics, common to the different breaking wave fields investigated, are as follows: a roughly invariant size distribution characterized by a spectrum slope of approximately −2, concentrations rapidly increasing upward, following approximately an exponential law, and clustered distributions at the different measurement levels. These results, consistent with equivalent measurements below the wave trough level, correspond to bubble generation zone characteristics suggested in a previous investigation and provide further evidence of the existence of a universal bubble distribution at the interface of breaking wave fields. Very high bubble concentrations, up to 1010 bubbles of diameter larger than 60 μ per cubic meter (nearly 10,000-fold the value just below the trough level), are observed at the crest levels.

Laboratory Study of Steep and Breaking Deep Water Waves

Abstract: Measurements are presented here of the onset of breaking of deep water waves. The results of recent experiments conducted at NRL to study the growth of steep waves to breaking in a convergent chann...

Dynamics and Tracer Transport in the Middle Atmosphere: An Overview of Some Recent Developments

Abstract: Our present understanding of dynamics and tracer transport in the middle atmosphere, and of the concepts needed for modelling them, is discussed in the light of recent developments. Included are comments on wave, mean-flow interaction theory and its relationship to the generalized concept of wave breaking, on the gravity wave “turbulent Prandtl number” and associated questions connected with wave-turbulence inhomogeneityj on the possibility of focusing and self-tuning resonant effects in the wintertime planetary-scale Rossby wave field, on the downward influence of wave dissipation regions on diabatic circulations and stratosphere-troposphere mass exchange rates, on the diabatic impermeability of isentropic surfaces to (Rossby-Ertel) potential vorticity and the new view this gives of the zonally asymmetric diabatic circulation, and on some implications for the representation of dynamical feedback processes in low-order models of the middle atmosphere, including models with artificial lower boundary conditions.

Sediment transport concentrations and sediment transport in case of irregular non-breaking waves with a current

Abstract: In many coastal, engineering problems the sediment transport plays a part. A transport gradient causes accretion or erosion. Various models, such as that of Bijker, Engelund and Hansen (van de Graaff and van Overeem, 1979) and Nielsen (1985) are available to estimate the sediment transport rate if the hydraulic and environmental conditions (wave height, current velocity and direction, sediment size) are known. Since reliable data under field conditions are extremely scarce, the reliability of these models is not known, while also no understanding of the basic relations between the sediment transport, current velocity and wave height can be obtained. To extend the knowledge of the basic phenomena, a laboratory study was carried out. Fluid velocities and sediment concentrations have been measured in case of irregular non-breaking waves alone, and in combination with following or opposing currents.

Solitary waves in the resonant phenomenon between a surface gravity wave packet and an internal gravity wave

Abstract: A two‐layer inviscid incompressible fluid system of intermediate depth is considered. A multiple‐scales perturbation technique is applied to the basic equations and boundary conditions for a two‐layer fluid system to derive a system of weakly nonlinear partial integrodifferential equations governing the resonant interaction between a surface gravity wave packet and an internal gravity wave at an intermediate depth, providing a bridge between the existing shallow and deep fluid theories. The convolution integral term in these equations accounts for the dispersion in the lower‐layer fluid. An iterative fast Fourier transform scheme is developed to find solitary wave solutions to this system of equations. The overtaking collision of two pairs of solitary waves, simulated using a spectral method, is found to be inelastic. It is found that the amplitude of the solitary waves changes slightly after the collision. The phase shifts these solitary waves undergo was calculated numerically.