Showing papers on "Breaking wave published in 1971"

On the generation of long waves

Abstract: For relatively long waves generated by a piston-type wave maker, the classical linear wave-maker theory is extended to second order accuracy. Within the limits of validity of the theory, this agrees well with experimental results for the motion generated by a sinusoidally moving wave maker, and shows that secondary waves are associated with the existence of a second harmonic free wave. By giving the wave maker a motion that consists of a first and a second harmonic, it is shown that this free second harmonic wave may be eliminated, so that the generated wave is virtually of permanent form.

Mixing in the surf zone

Abstract: Two important mixing mechanisms are operative within the surf zone, each having distinctive length and time scales determined by the intensity of the waves and the dimensions of the surf zone The first is associated with the breaking wave and its bore, which produce rapid mixing in an on-offshore direction This mixing, when normalized and averaged over the surf zone width Xb, gives coefficients of eddy diffusivity of the order of HbXb/T where Hb and T are the breaker height and the period of the waves The second process is advective and is associated with the longshore and rip current systems in the nearshore circulation cell For constant longshore discharge of water between cells Qi, this process gives a concentration Nn in the nth cell down-current from a continuously injected source of dye of Nn=N0(Qi/Qm)n where N0 is the concentration leaving the injection cell, and Qm is the maximum longshore discharge within a cell As an approximation, the concentration decreases exponentially with distance y from the injection point when n is replaced by y/Y, where Y is the spacing between rip currents This relation gives an apparent longshore eddy mixing coefficient of the order of Y〈υi〉 where 〈υi〉 is the longshore current velocity Along ocean beaches HbXb/T and Y〈υi〉 are about 10 m2 sec−1 and 100 m2 sec−1 respectively

The mechanics of sand transport on beaches

Abstract: On steep-faced beaches where waves break and swash at an angle to the shoreline the littoral drift of beach material results from the saw-tooth motions of the sediment in the longshore direction. The sand moves forward obliquely to the shore under the incoming wave swash and then moves normal to the shoreline under the return flow. For such transport conditions a rational derivation leads to the relationship Ii=K(ECn)b sin αb cos αb, where Ii is the longshore transport rate of sediment expressed as an immersed weight, (ECn)b is the flux of wave energy at the breaker zone, αb is the angle the breaking wave makes with the shoreline, and K is a dimensionless proportionality coefficient. This often applied relationship, previously only intuitive, is therefore more rigorously established for special saw-tooth transport. It has recently been shown to also apply when the sediment is transported by a longshore current proportional to um sin αb, where um is the orbital velocity under the breaking waves. These are the two most important mechanisms by which sediment is transported along the shore under wave action, and hence the successful application of the above relationship can be expected. Deriving the relationship by two different approaches suggests that the ratio tan β cos αb/cf may be constant, where tan β is the beach slope, and cf is the coefficient of bottom friction. This helps to explain the observation that the longshore current is proportional to um sin αb and to account for the lack of dependence of the sand transport relationships on the beach slope. The profiles of variation of the longshore sand transport as a function of the distance seaward of the swash line are examined theoretically. The results conform with the field observations.

Run-up distributions of waves breaking on slopes

Abstract: Run-up of irregular waves which break on a slope is calculated by assuming that on the average the run-up of each wave with a given height and period equals the run-up of a periodic wave train of the same height and period. General expressions are derived for the distributions of the run-up and the wave steepness as functionals of an arbitrary joint distribution of the wave height and the square of the period. Explicit results are obtained for the case when these variates are jointly Rayleigh distributed with arbitrary degree of correlation. Some of the assumptions are verified by a comparison of the analytical results with previous experimental data.

Acoustic Doppler Measurements of Vertical Velocities in the Atmosphere

Abstract: Acoustic echo sounding techniques have been used to determine vertical velocities in the atmosphere during thermal plume activity and a nocturnal inversion. The existence of breaking wave formations within the inversion has been clearly established.

The Coupling of Momentum Between Internal Gravity Waves and Mean Flow: A Numerical Study

Abstract: A numerical model of internal gravity waves allows momentum transport by the waves to interact with the mean flow. Momentum deposited at a critical level develops a “shelf” in the mean flow. Mean flow acceleration Doppler-shifts the wave frequency, allowing more penetration of wave energy than expected from linear theory.

Laboratory investigation of air turbulence above simple water waves

Abstract: The structure of turbulent-shear flows above propagating waves is investigated experimentally in a wind and wave facility at the University of Florida. Wave-induced perturbations and their importance in transferring momentum to waves is a central question in this study. The turbulent air velocities were measured in the horizontal and vertical directions by using a two channel hot-film anemometer system. Turbulence measurements were obtained both in the presence and absence of mechanical waves with wave height =8.9 cm and wave speed =2.23 m/sec. Power spectra of air turbulence indicate the presence of significant wave-induced peaks in both the horizontal and vertical velocities at the frequency of mechanical wave. The peaks disappear in the absence of mechanical waves. Calculations of momentum transfer to waves based on the wave-induced Reynolds stress and on the measured growth rate of waves indicate that the interaction of surface waves with the turbulent flow above them produces significant momentum transfer in addition to the wave-induced stress.

The breaking of water waves

Abstract: A steady progressive wave of maximum amplitude can be defined as a wave that has a corner flow at its crest An analytical examination of the response of such a corner flow to certain perturbations gives a realistic description of the breaking of a spilling breaker In particular it is shown that breaking will occur in the direction of propagation of the wave

Energy spectrum of small‐scale internal gravity waves

Abstract: The breaking of internal gravity waves is the source that generates turbulence in the atmosphere and the ocean (CAT and DOT). Thus the internal gravity waves reach a limiting amplitude. Evidence of saturation from two spectra taken at different locations and the assumption that the breaking of these waves is due to the generation of local unstable stratification permit us to derive an expression of the energy spectrum that explains fairly well the shape of the observed spectrum.

Forces due to waves on submerged structures

Abstract: Existing theories on wave forces on large submerged structures are reviewed. The equations regarding wave forces and moments on piles do not apply because inertial forces are predominant on a submerged structure which has a principle horizontal dimension equal or larger than the vertical dimension. Several models of simple geometric structures were installed in a two-dimensional laboratory wave tank. The magnitude of the vertical and horizontal loads on the structure by the wave action were determined experimentally. Values of coefficient of inertia were obtained for experimental data. Results of data wer plotted in dimensionless form to provide a correlation between ratios of wave length to water depth, wave height to wave length, and dimensionless force for a number of different shapes of structures. Measurements were also obtained for one of the models of forces due to irregular, wind-generated waves. Comparison between forces caused by regular waves and irregular waves was made. It is concluded that forces due to waves, particularly due to irregular waves generated by wind are highly variable, but results presented may be sufficient for preliminary designs.

Experiments on Horizontal Water Particle Velocity at Water Surface of Near Breaking Waves

Abstract: As a breaking limit of progressive waves, many conditions have been proposed. One of them is that the water particle velocity at the wave crest is equal to the wave celerity.To examine this condition experimentally, the wave profile and the horizontal water particle velocity at the water surface near the crest of breaking waves were measured. These waves progress and break on a very gentle slope beach (1/200), which may be regarded as horizontal bottom.Experimental results of the wave profile and the horizontal water particle velocity at the water surface near the crest of breaking waves are presented and compared with theoretical values, and the breaking condition of progressive waves is examined experimentally.

The interaction between a vertical cylinder and regular waves

Abstract: The huge amount of offshore activities in recent years has increased the need of reliable data concerning the wave loading on vertical cylinders. A review is given of different methods, according to which the wave forces on a vertical circular cylinder can be calculated. Numerical results of these methods are compared with the results of model experiments. The wave diffraction around a cylindrical object was calculated with the potential theory and is compared with measurements of the wave amplitude.

Directional energy distribution of wind waves

Abstract: Two-dimensional ocean wave spectrum developing under the atmospheric surface pressure fluctuations is linearly correlated with that of wind pressure itself, so that angular distribution of energy of ocean surface waves can be determined by directional properties of surface pressure fluctuations with the same frequency to the surface wave.

Irregular Wave Action on Rubble-Mound Breakwaters

Abstract: An investigation was undertaken to compare the effect of regular and irregular waves on a rubble-mound breakwater model. During the experiments water depth, breakwater, and wave characteristics were kept constant; wave heights were varied. Experiments were conducted to determine the damage in terms of the displaced number of stones. It was concluded that the damage on a rubble-mound break-water is related to the energy of the attacking wave. Experiments revealed that relating the damage to the total energy is inaccurate. Consequently, this concept was replaced by a relationship between the damage and the effective energy, which is the part of the energy including the energy of waves higher than the design wave. Therefore, it was shown experimentally that the effective energy determines the different the different effects of regular and irregular wave action on the breakwater. It was shown that regular waves have the same effect as the irregular waves when the significant wave heights equal the heights of regular waves.

Viscous Effect on Waves Reflected Nearly Parallel to the Boundary

Abstract: The anomalous laws of wave reflection from a rigid plane surface in an inviscid, rotating, stratified Boussinesq fluid are due to the anisotropic feature of the wave motion. The singularity of the reflection process in the inviscid linear analysis, where the reflected wave amplitude becomes very large when the ray of the reflected wave is nearly parallel to the reflection boundary, is studied for the limiting cases by considering viscous boundary effect on wave motion. As the angle that the reflected wave (ray) makes with the wall becomes very small, the effect of boundary layer on wave reflection becomes significant. In the nonsingular case, the boundary layer thickness is ∼R−1/2 where R ( = n/νκ2) is the wave Reynolds number. A thicker boundary layer, R−1/3 is needed for the critical wave reflection and only within this layer is singularity removed. Two‐dimensional waves were generated in the laboratory by vertically oscillating a small wave‐making flap inside a clear Plexiglas container. The wave prope...

Surface wave momentum and energy velocities.

Abstract: REYNOLDS1 defined the energy velocity associated with a simple periodic wave train on the surface of deep water as the phase velocity multiplied by the ratio of the energy transmitted across a fixed vertical plane during one wave period to the energy of the waves per wavelength. In other words, the energy velocity is the velocity of a moving vertical plane across which, on average, no energy is transmitted. For waves of small amplitude this velocity is half the phase speed (see also ref. 2). Starr and Platzman3 extended the Reynolds concept to the case of waves of finite height, without mathematical approximation or further physical assumptions. The ratio already mentioned of energy transmitted, Et, to the energy per wavelength, E, is now Et/E=½ + 5e/2E, where e is the excess of kinetic over potential energy per wavelength, which vanishes for waves of small amplitude4. The phase speed for finite waves, multiplied by the ratio, gives the energy velocity which, for the highest waves, is 11/17 (or about 0.647) of this speed (see also Handbuch der Physik5 for a review of this and background material).