Wave Breaking Process Research Articles

Some statistics of sea noise

Surface‐derived ambient noise has been measured on a long‐term basis by the use of a bottom‐mounted narrow beam sonar, in depths of 65–80 m, over windspeeds 3–20 m/s, in frequency bands over 6–50 kHz. Results are presented as time histories and derived statistics. It is found that, after detection and smoothing, the noise power in a narrow beam fluctuates widely, “spikes” in time being identifiable with individual breaking waves. The statistics of fluctuation is found to depend on beamwidth, the coefficient of variation being typically 10/beamwidth in meters. Time autocorrelation functions of noise power are presented, which also depend on beamwidth and windspeed. The mean horizontal speed of the noise sources can be deduced and is approximately half the windspeed in a well‐developed sea. These results are interpreted in the light of known spectra of sea waves, and simple assumptions about the nature of the wave breaking process.

Irreversible Wave–Mean Flow Interactions in a Mechanistic Model of the Stratosphere

A wave-1 minor warming is simulated in a mechanistic, global, primitive equation model. The modification of the zonal flow by the rearrangement of potential vorticity on a middle stratopheric isentrope is compared in a fully nonlinear model and in a model with only one wave and the zonal flow (a quasi-linear model). The permanent rearrangement of potential vorticity during the wave episode is more intense and more localized meridionally in the fully nonlinear model, which is able to capture the process of planetary wave breaking in some detail. Additional experiments reveal that the differences between the quasi-linear and nonlinear models persist for a broad range of wave amplitudes, and that the quasi-linear model can qualitatively reproduce the modification of the zonal flow by the wave when the diffusive dissipation of the wave is enhanced. These results are discussed in the context of the theory of barotropic Rossby waves in shear flows, and in comparison with recent numerical simulations of the middle atmosphere.

The Effects of a Periodic Upstream Flow on Nonlinear Hydrostatic Mountain Waves

Abstract Steady, two-dimensional, hydrostatic, nonlinear mountain waves are examined within the context of Long's model. Both uniform and periodic upstream flows are considered. The well-known condition for a hydrostatic wave to break (convective instability), under uniform upstream conditions, is reviewed and a reinterpretation provided. Long's wave solution appropriate for periodic upstream conditions is introduced, and shown to satisfy the same wave-breaking condition that is appropriate for uniform upstream flow: overturning is associated with convective instability. Moreover, there is no obvious relationship between wave overturning and the upstream distribution of either the static stability or the Richardson number. In essence, the physical process of wave breaking, associated with this particular solution, is decoupled from details of the upstream profiles. However, the levels at which breaking occurs, and profiles of streamline displacements, are both affected by upstream conditions.

Optical fibre-grating pulse compression

Numerical simulation is used to consider non-linear pulse propagation in fibres and subsequent pulse compression in a dispersive delay line. It is shown that for small initial pulse powers the conventional non-linear Schrodinger equation (NSE) is quite accurate to describe the process of pulse propagation in fibres. In this case initially symmetrical pulses undergo squaring and spectral broadening in fibres, and frequency chirp is linearized over most of the pulse, while shapes of the pulse, spectrum and frequency chirp remain symmetrical at the output of the fibre. There is a certain optimum fibre lengthZopt which is determined by the initial pulse parameters and fibre characteristics for pulse compression in the dispersive delay line. When the fibre lengthZ>Zopt the optical wave breaking effect distorts the linearity of the frequency chirp and thus deteriorates the quality of the compressed pulse. The region of NSE approximation accuracy is determined. It is demonstrated that at increase of the initial pulse power (initial pulse width makes no difference) the NSE approximation becomes inaccurate. So the pulse dynamics in the fibre were described by the modified NSE derived in the higher-order approximation of the method of slowly varying amplitudes from Maxwell's equations. In this case the shock wave appears at the trailing edge of the pulse, which accelerates the wave breaking process. This results in a decrease of the optimum fibre length and deterioration of compressed pulse parameters, compared with the NSE case. Spectral windowing of the extreme Stokes components of the pulse spectrum permits significant improvement in the quality of the compressed pulse. The main features of the compression of pulses with asymmetrical initial shape are also considered.

A shallow water spectral wave model

A shallow water spectral wave prediction model based on a numerical solution of the radiative transfer equation is presented. The model is second generation and uses a simple yet effective representation for the nonlinear source term. In addition, the model pays particular attention to the shallow water processes of refraction, shoaling, bottom friction, and wave breaking. The flexibility of the model is demonstrated by an intercomparison with field data from a number of tropical cyclones. The turning winds from such storms provide a demanding test of model physics. The comparisons are in both deep and shallow water.

A NEW PARAMETER FOR WAVE BREAKING WITH OPPOSING CURRENT ON SLOPING SEA BED

Opposing currents affect the wave breaking processes. The condition of wave breaking caused by opposing currents in deep water is described by the ratio of the wave celerity to the velocity of the opposing current(Yu(1952)). For the wave breaking caused by the opposing currents in shallow water on a flat bed, the equation given by Miche(1951) for the breaking criteria without current remains available (Iwagaki et al.(1980)). However, it is the breaking of shoaling wave in the presence of opposing current on a uniform slope, which is of concern in this paper. Sakai et al.(1981) showed that the wave breaking affected by opposing currents on a sloping sea bed is characterized by a normalized unit width discharge q*, as well as an incident wave steepness Ho/Lo and a slope of sea bed S, where q* is defined as q*= q/g2T3; q: a unit width discharge, g; the gravitational acceleration, T: a wave period. They proposed diagrams for the breaker height and the breaking depth as a function of these three parameters. The breaker index curves in their diagrams show the relationships between the breaker height (or the breaking depth) and q* for waves with particular values of Ho/Lo and S, and it is much more convenient to give a general expression for the breaker indices for arbitrary conditions of q*, Ho/Lo and S. The purpose of this study is to formulate the effects of these parameters on wave breaking, based on the results of systematic experiments performed by the authors, and to derive an empirical and simplified expression for the breaker height and depth in the presence of opposing currents.

Model and prototype tests for wave impact and run-up on a uniform 1:4 slope, by A. Führböter

The comprehensive article explores wave impacts and wave run-up in the tank and in a 1:10 model (FfihrbSter, 1986). The research undertaken has merits within a limited range. Wave versus slope interaction however depends highly upon the detailed character of the wave breaking which among other things is a function of G=tan~/Hx/-H-~o (Losada and Gimenez Curto, 1979; Giinbak, 1979; Sawaragi et al., 1983; Bruun et al., 1985). The author does not discuss details of the wave-breaking process itself including the great number of wave-breaking modes on a slope, even within the limited range of G under consideration producing chaotic forms (p. 68). This does not infer that his results for the narrow range of G-values of his tests (1.05 < G < 1.29) are not valid with the reservations given by himself, but it means that great care should be exercised with respect to extrapolation of the results outside the limited range of G-values. Wave geometries, reflections and 3-D effects, unavoidable in a 5-m-wide prototype test section, are not discussed. Downrush thickness is mentioned but not defined in detail in terms of time and space. The interest is concentrated on impact pressures not momentum, as admitted by the author. This makes it even more difficult to transfer or extrapolate results to practice, even within the narrow range of Gvalues. The large scattering of results therefore is understandable. Compare e.g. KirgSz (1978), who showed that just a small difference in wave geometry may produce very large variances in pressure. Similar results were obtained by Goda (1985). See also a recent review by Jansen (1986). A main shortcoming of the results, however, is the lack of consideration to resonance-effects. Resonance occurs when uprush + downrush periods equal the wave period (see Giinbak, 1979; Sawaragi et al., 1983; Bruun et al., 1985). Practical G-values for resonance on a smooth slope are in the range 2 < G < 3. For permeable (mound) slopes semi-resonance occurs (Sawaragi et al., 1983). The author explains and shows in figures that his tests refer to impacts

Natural self-cleaning of oil-polluted beaches by waves

Changes in the magnitude of oil pollution on five prototype study beaches on Israel's northern Mediterranean coast had been monitored at 2- to 4-weekly intervals from 21 November 1980 to 19 March 1981. Statistical analyses of these changes were employed to rank the beaches in order of decreasing self-cleaning capacity. Records of storm-induced wave data records for the winter of 1980–1981 were correlated to incidence of change in the magnitude of subsurface tarball pollution and the rate of emplaced fuel sample dissipation on the study beaches. Specific wave breaking processes, overtopping of offshore obstacles and wave refraction were singled out as accelerating or retarding wave energy transfer to the polluted beaches. Attribution of the occurrence of specific local littoral processes to observed change in beach pollution magnitude made it possible to assess potential oil spill damage. Elucidation of the causative processes provided theoretical corroboration for beach sensitivity ranking established earlier by statistical analysis.

Energy transfer among internal gravity modes: Weak and strong interactions

The general characteristics of the energy spectrum for internal gravity waves in the ocean are well known from the large body of recent experimental observations. The theoretical understanding has not developed at the same rate, perhaps due to the limitation of linear or quasi‐linear theories, which can cope only with weak interaction processes and are inadequate for representing the more violent and sporadic wave breaking processes present in nature. A detailed study of energy transfer among two‐dimensional internal gravity modes in a fully nonlinear regime was performed. Wave‐wave interactions and overturning were included in the solutions of a two‐dimensional numerical model, and the results are presented here. A background spectrum of finite amplitude, random internal gravity wave field was generated by a long time integration of a two‐dimensional model with random body forcing. Over this background field, two sets of experiments were performed: spike‐random, where energy at low, medium, and high wave numbers were introduced and integrated in time, and band‐random, where energy was introduced over a band of wave numbers instead of introducing only discrete modes. The results can be summarized as follows. Multiple triad interactions will result in a filling of the energy spectrum when energy is introduced in a particular band of wave numbers. For bands where the energy level is high enough to result in nonlinear time scales of only a few intrinsic periods, wave‐wave interactions (resonant and nonresonant) provide the mechanism for filling the spectrum. The energy transfer becomes more and more rapid with increasing energy, and no universal spectrum appears to result from these processes. As the energy input increases, energy will accumulate in high wave numbers until localized instabilities (over‐turning) occur. From that point on, these high wave numbers will remain at a saturation such that any additional energy input at the saturated band, either directly or via wave‐wave interactions, will result in localized mixing. On the other hand, additional energy input at bands other than the saturated band will result in an increase of low and medium wave band energy (via wave‐wave interactions) until an equilibrium level is achieved. The equilibrium level of any particular band will depend on the high wave number bands being saturated. For instance, any energy above the equilibrium at low wave numbers will produce localized mixing in physical space almost instantaneously. This does not mean that the low wave numbers are saturated, as their energy levels can be much lower than a saturation level. What takes place at or near an equilibrium level is that the contributions from high and low wave numbers result in localized regions in physical space where the criterion for instability is almost met. In fact, this superposition effect means that low and medium wave numbers are far from meeting any breaking criterion when taken individually, yet cannot tolerate any additional input energy when in the presence of a saturated band of high wave numbers. It was found also that the dissipation is approximately constant over the wave numbers and small compared with the large transfer of energy between neighboring waves. However, if bands of waves are considered, very little energy is transferred between neighboring bands above the equilibrium level. Rather, a direct cascade of energy from low to high wave numbers occurs due to localized instabilities which result in overturning, and it is this amount of energy flux which is dissipated by the high wave numbers.

PHYSICAL PROCESSES AND SEDIMENT FLUX THROUGH REEF-LAGOON SYSTEMS

Studies of physical processes in reef-lagoon systems continue to emphasize the importance of waves and wave-induced currents at the reef crest as agents of sediment transport to backreef environments. These across-the-reef currents are also largely responsible for driving backreef lagoon circulation. Rapid energy transformations associated with the process of wave breaking at the reef crest are responsible for strong reef-normal surge currents. Estimates of energy loss, as determined by wave height changes caused by wave breaking, can be as high as 70-80%' for discontinuous reefs and &gt;90% for continuous examples. The amount of energy loss is related to depth of water over the reef crest, a function of reef topography and tidal regime. Low-tide conditions promote the greatest incident wave modification and attenuation as a result of increased breaking-wave intensity. Under trade-wind conditions found in the Caribbean, surge currents of 50-80 cm/sec for durations of 2-6 sec are common in a low to moderate wave-energy setting (4-6 sec input waves, 40- 50 cm average heights). Sediments through the sand sizes up to pebbles are easily transported lagoonward by these periodic bursts of energy. Flow in shallow backreef lagoons (generally

Cold plasma wavebreaking in the presence of an electromagnetic driver

Nonlinear electron plasma oscillations driven by an electromagnetic wave are investigated. An improved, self-consistent Lagrangian description of the resonant interaction is derived. The modifications to the simple capacitor plate or uniform electrostatic driver model previously employed are calculated and shown to have a negligible effect on the wavebreaking process for laser intensities I&amp;lt;1017 W cm−2 in the case of Nd lasers.