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Showing papers on "Breaking wave published in 1977"


Journal ArticleDOI
TL;DR: In this article, an experimental investigation of the evolution of a nonlinear wave train on deep water is reported, and the initial stage of evolution is characterized by exponential growth of a modulational instability, as was first discovered by Benjamin'Feir.
Abstract: Results of an experimental investigation of the evolution of a nonlinear wave train on deep water are reported. The initial stage of evolution is found to be characterized by exponential growth of a modulational instability, as was first discovered by Benjamin ' Feir. At later stages of evolution it is found that the instability does not lead to wave-train disintegration or loss of coherence. Instead, the modulation periodically increases and decreases, and the wave train exhibits the Fermi–Pasta–Ulam recurrence phenomenon. Results of an earlier study of nonlinear wave packets by Yuen ' Lake, in which solutions of the nonlinear Schrodinger equation were shown to provide quantitatively correct descriptions of the properties of nonlinear wave packets, are applied to describe the experimentally observed wave-train phenomena. A comparison between the laboratory data and numerical solutions of the nonlinear Schrodinger equation for the long-time evolution of nonlinear wave trains is given.

365 citations


Journal ArticleDOI
TL;DR: In this paper, the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible.
Abstract: Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Pade approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Pade-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

322 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that a negative mean force arises from an asymmetry in the breaking waves, associated with a time-delay in the response to the change in depth.
Abstract: Water waves transport both energy and momentum, and any solid body which absorbs or reflects wave energy must absorb or reflect horizontal momentum also. Hence the body is subject to a mean horizontal force. In low waves, the force may be calculated immediately when the incident, reflected and transmitted wave amplitudes are known. For wave power devices the mean force can be large, so that anchoring presents practical problems. Experiments with models of the Cockerell wave-raft and the Salter ‘duck’ accurately confirm the predicted magnitude of the force at low wave amplitudes. For steeper waves, however, the magnitude of the force can be less than that given by linear theory. By experiments with submerged cylinders, it is shown that this is due partly to the presence of a free second harmonic on the down-wave side. In breaking waves, it is confirmed that the mean force on submerged bodies is sometimes reduced, and even reversed. An explanation is suggested in terms of the ‘wave set-up’ produced by breaking waves. Submerged cylinders act as a kind of double beach. A negative mean force arises from an asymmetry in the breaking waves, associated with a time-delay in the response to the change in depth. Similar arguments apply to submerged reefs and sand bars. Experiments with a model bar show that long low waves propel the bar towards the shore, whereas steep, breaking waves propel it seawards. This is similar to the observed behaviour of off-shore sand bars. The existence of a horizontal momentum flux (or radiation stress) in water waves is demonstrated by using it to propel a small craft.

106 citations


Journal ArticleDOI
TL;DR: In this article, the linear stability of an internal gravity wave of arbitrary amplitude in an unbounded stratified inviscid Boussinesq fluid is considered mathematically and the instability is governed by a Floquet system and treated by a generalization of the method of normal modes.
Abstract: The linear stability of an internal gravity wave of arbitrary amplitude in an unbounded stratified inviscid Boussinesq fluid is considered mathematically. The instability is shown to be governed by a Floquet system and treated by a generalization of the method of normal modes. Some properties of the Floquet system, and in particular those of its parametric instability, are analysed. The parametric instability is related to the theory of resonant wave interactions; and the surface of marginal stability in the control space of the amplitude and wavenumbers is shown to be describable by the catastrophe theory of Thom. Finally some results of numerical calculations of the marginal surface are shown. The main physical conclusion is to confirm that the internal gravity wave is unstable always, even when its amplitude is small and so its local Richardson number is large everywhere for all time. It is suggested, by various illustrations and arguments, that the methods developed in this paper are applicable to the instability of many symmetric nonlinear waves.

102 citations


Journal ArticleDOI
TL;DR: In this article, the authors measured the temporal and spatial development of short gravity waves in a linear wind-wave tank for wind speeds up to 15 m/s using microwave Doppler spectrometry.
Abstract: Temporal and spatial development of short gravity waves in a linear wind-wave tank has been measured for wind speeds up to 15 m/s using microwave Doppler spectrometry. Surface waves of wavelength 4·1 cm, 9·8 cm, 16·5 cm and 36 cm were observed as a function of fetch, wind speed and wind duration. The waves grew exponentially from inception until they were about 10 dB smaller than their maximum height, and the temporal growth and spectral transport (spatial growth) rates were about equal when the wave amplitude was sufficiently small. The amplitude of a short gravity wave of fixed wavelength was found to decrease substantially at winds, fetches or durations greater than those at which the short gravity wave was approximately the dominant wave; such phenomena are sometimes referred to as overshoot. The dominant short gravity wave was observed to reach a maximum amplitude which depended only on wavelength, showing that wave breaking induced by an augmented wind drift cannot be the primary limitation to the wave height. Waves travelling against the wind were observed for wavelengths of 9·8 cm, 16·5 cm and 36 cm and were shown to be generated by the air flow at low wind speeds.Measured initial growth rates for 16·5 cm and 36 cm waves were greater than expected, suggesting the existence of a growth mechanism in addition to direct transfer from the wind via linear instability of the boundary-layer flow. Initial temporal growth rates and spectral transport rates were compared to yield an experimental determination of the magnitude of the sum of nonlinear interactions and dissipation in short gravity waves. If the steady-state energy input in the neighbourhood of the dominant wave occurs at the measured initial temporal growth rates, then most of the energy input is locally dissipated; relatively little is advected away. Calculated gravitycapillary nonlinear energy transfer rates match those determined from initial growth rates for 9·8 cm waves and the gravity–capillary wave interaction continues to be significant for waves as long as 16·5 cm. For longer waves the gravity–capillary interaction is too small to bring the short gravity wave to a steady state when it is the dominant wave of the wind-wave system.

90 citations


Journal ArticleDOI
TL;DR: In this paper, the existence of solitary waves in a thin layer of viscous liquid which is running down a vertical surface under the action of gravity is investigated, and a solution of the problem of stationary waves is obtained by the method of expansion in the small parameter in two regions with subsequent matching and also by numerical integration method.
Abstract: Solitary waves in a thin layer of viscous liquid which is running down a vertical surface under the action of gravity are investigated. The existence of such waves was demonstrated in the experiments of [1, 2]. The difficulties that must be faced in a theoretical computation were also noted in these studies. Below a solution of the problem of stationary waves is obtained by the method of expansion in the small parameter in two regions with subsequent matching and also by a numerical integration method. It is shown that in each case a solution of solitary wave type exists along with the single-parameter family of periodic solutions (parameter—the wave number α). On decreasing the wave number, the periodic waves go over into a succession of solitary waves.

68 citations


Journal ArticleDOI
TL;DR: In this article, a review is concerned with wave propagation in plasmas where collisions may be neglected, and the relevant kinetic theory is described by the Vlasov equation, and general concepts of stability are discussed, including the conversion of wave energy from one kind of wave and linear coupling mechanisms.
Abstract: The review is concerned with wave propagation in plasmas where collisions may be neglected. The relevant kinetic theory is described by the Vlasov equation. Waves in the absence of a magnetic field are reviewed including Landau damping of electron waves and ion acoustic waves. The complications due to purely ballistic effects are described and the latter case includes the study of mixtures of ions. Thermal motion has little effect on electromagnetic waves with the exception of the anomalous skin effect. Beam-plasma interactions are reviewed and general concepts of stability are discussed. The conversion of wave energy from one kind of wave and linear coupling mechanisms are described. The importance of resonance cones is also noted.

52 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of surface wave breaking on the adjacent atmospheric boundary layer are examined and it is argued that the transition from aerodynamically smooth to rough flow in a neutral atmosphere corresponds to the onset of extensive small-scale wave breaking.
Abstract: The effects of surface wave breaking on the adjacent atmospheric boundary layer are examined. It is argued that the transition from aerodynamically smooth to rough flow in a neutral atmosphere corresponds to the onset of extensive small-scale wave breaking. The association of wave breaking with the generation of turbulence in the boundary layer above leads to the result that the friction velocity is approximately equal to the phase velocity of the breaking waves. It is argued that this approximate relationship holds even when the small-scale breaking waves are riding on a swell. The existence of a minimum phase velocity for surface waves then requires that there be a minimum friction velocity, in the neighborhood of 23 cm s−1 below which rough flow cannot occur. A result of Phillips and Banner (1974) which describes the limiting amplitude of small gravity waves under the action of wind drift and swell is used to derive a relationship between the roughness length and friction velocity which is a g...

48 citations


Journal ArticleDOI
TL;DR: In this article, the authors use a rather formal and perhaps narrow definition of separation and show that it does not occur where the shear stress is zero but only in conjunction with wave breaking, except in the presence of quite strong surface drift velocities in the water.
Abstract: Whether or not ‘separation’ occurs in the airflow over wind-generated water waves is partly a question of semantics but also has an important bearing on the wave generation process. In the present paper we use a rather formal and perhaps narrow definition of ‘separation’ and show that it does not occur where the shear stress is zero but only in conjunction with wave breaking. This is unlikely to happen except in the presence of quite strong surface drift velocities in the water. A similar connection between separation, surface drift and wave breaking has recently been established by Banner and Melville (1976).

46 citations


Journal ArticleDOI
TL;DR: In this paper, the amplitude, width and velocity variation of the solitons is studied, taking into account the ion thermal effects, and the results obtained are compared with those for plasmas with cold ions.
Abstract: Ion-acoustic waves in warm-ion plasma which includes some negative ions are studied using the properties of a modified Korteweg-de Vries equation. The equation, which describes the amplitude, width and velocity variation of the solitons is studied, taking into account the ion thermal effects. As in the case of a cold plasma, the warm negative ions also introduce a critical concentration at which the wave breaks up, which could play an important role in exploiting the ion-heating mechanism. The results obtained are compared with those for plasmas with cold ions.

43 citations


Journal ArticleDOI
TL;DR: In this paper, a non-linear Schrodinger equation for Langmuir waves is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics.
Abstract: A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy with negative energy waves explaining the different features of the two cases is outlined.

Journal ArticleDOI
TL;DR: In this article, the saturation range in the frequency spectrum of wind-generated waves is derived using linear wave theory as a spectral transfer function and the horizontal velocity spectrum Su(ω) ∝ ω−3.
Abstract: The saturation range in the frequency spectrum of wind-generated waves is rederived. Laboratory and theoretical work show that wave breaking is the result of kinematic instability, suggesting that wave celerity is the governing parameter in the saturation range. Using similarity arguments, a general formulation is rederived giving the wave profile spectrum Sη(ω) ∝ ω−5 in deep water as derived by Phillips and Sη(ω) ∝ ω−3 in shallow water. The velocity spectrum in the saturation range is derived using linear wave theory as a spectral transfer function. In both deep and shallow water the horizontal velocity spectrum Su(ω) ∝ ω−3. Wave and velocity measurements made in deep and shallow water are presented showing agreement with theory.

Journal ArticleDOI
Akira Hasegawa1
01 Aug 1977
TL;DR: In this paper, the kinetic properties of the Alfven wave, which originates from the finite perpendicular wavelength effects, have been shown for both linear and nonlinear regime, and the wave can be excited in a plasma either by drift wave instability or resonant mode conversion of surface magnetohydrodynamic wave.
Abstract: Kinetic properties of the Alfven wave, which originate from the finite perpendicular wavelength effects, are shown for both linear and nonlinear regime. The wave accompanies a parallel electric field and can propagate in the direction perpendicular to the ambient magnetic field. The kinetic Alfven wave can be excited in a plasma either by drift wave instability or resonant mode conversion of a surface magnetohydrodynamic wave.

Journal ArticleDOI
TL;DR: In this article, the importance of wave period to the stability of sloping-faced wave protection structures (permeable and impermeable) is discussed, and a risk criterion in the design for stability and wave run-up is given using the joint distribution of wave heights and periods.

01 Dec 1977
TL;DR: In this paper, measurements of wave processes, wave-driven currents, and sediment distribution have been made in several fringing reef systems, and the results show that wave height and wave period are typically reduced by about 50% as waves pass over the reef crest.
Abstract: : Measurements of wave processes, wave-driven currents, and sediment distribution have been made in several fringing reef systems. Wave height and wave period are typically reduced by about 50% as waves pass over the reef crest. This decrease depends primarily upon reef crest water depth, so that wave conditions in the back-reef lagoon show significant changes over a single tide cycle. Wave-driven currents tend to flow continuously onshore over the reef crest. Their velocity is greatest near low tide, when wave breaking is most intense. Current in the lagoon moat generally showed a tendency to drain the lagoon except during brief intervals near flooding tide when a weak current reversal occurred. Sediment distribution in the lagoon displays a pattern that reflects current patterns in the lagoon and wave characteristics at the lagoon shoreline. (Author)

Journal ArticleDOI
TL;DR: In this paper, it was shown that a deep water limit for cnoidal wave shoaling exists and the nature of this limit and the behaviour of the waves close to it are analyzed.

Journal ArticleDOI
TL;DR: In this paper, a model has been constructed to predict the horizontal distance of shoreline recession that occurs when a beach and nearshore zone in dynamic equilibrium is subjected to a rise in water level.
Abstract: A model has been constructed to predict the horizontal distance of shoreline recession that occurs when a beach and nearshore zone in dynamic equilibrium is subjected to a rise in water level. The horizontal distance of shoreline recession (X) is inversely proportioned to the angle of the nearshore slope seaward from breaking waves ($$\phi$$), and directly proportioned to the rise in water level (a): $$X = a/Tan \phi$$ The volume of sediment eroded from the beach is equal to the volume of sediment deposited in the nearshore up to and including the position where waves break: Xh = ab where h is the vertical distance from the foreshore crest to the foreshore base, and b is the distance from the foreshore base to the position of breaking waves.

Journal ArticleDOI
TL;DR: Tucker and Green as discussed by the authors presented a model for predicting the time-dependent vertical thermal structure of lakes, which has a basic structure similar to those of Kraus and Turner (1967) and Denman (1973).
Abstract: A model for predicting the time-dependent vertical thermal structure of lakes is presented. Radiative heating with depth, mixing induced by the surface wave field, and turbulent energy exchanges arc included as lake-averaged processes. The model was designed to be applicable to a wide range of lake sizes. Comparison of predictions with horizontally averaged observations from Lake Ontario during IFYGL and unaveraged (local) observations from Llyn Cwellyn, Wales, show good agreement. The depth of the summer thermocline in lakes is correlated with the size of the lake because of the more vigorous wind induced surface motion resulting from increased fetch. We present here a one-dimensional lake thermocline model in which this fetch dependence is parameterized in terms of the fetch-limited wave field. The model has a basic structure similar to those of Kraus and Turner (1967) and Denman ( 1973). Although our theoretical framework and general assumptions are similar to theirs, we have changed considerably the representation of important physical processes such as mixing due to surface waves and turbulent kinetic energy dissipation. Input variables required for the model are basin size (shoreline configuration, mean depth), solar radiation attenuation coefficient for the lake, wind speed and direction, air temperature and atmospheric water vapor pressure (or any convenient humidity variable) at some specified height above the lake surface, cloud cover, and an initial temperature profile. As has been noted by others (e.g. Kitaigorodskiy and Miropolskiy 1970; Linden 1975; Sundaram 1973) the KrausTurner model involves several sweeping assumptions not generally confirmed either in nature or in experimental studies. The ‘Study supported in part by the University of Michigan Sea Grant Program, maintained by NOAA, U.S. Dept. of Commerce. ’ Contribution 229 from the Department of Atmospheric and Oceanic Science, University of Michigan. key assumptions are neglect of mean flow, the assumption of a homogeneous surface layer, and the assumption that the energy available to increase the potential energy of the water column is proportional to the surface energy input, rwsfc, where r is surface stress and wsfc is a surface velocity scale, The turbulent exchange processes appear to depend also on lake size (Blanton 1973). Previous models of lake thermoclines have not included the effects of lake size on turbulence in the epilimnion; we describe methods to introduce this dependence. Also we present an alternative to the third assumption of the Kraus-Turner model, based on consideration of the dissipation of turbulent energy gained from the shear flow, wave breaking, and convection; implications and consequences of the first two assumptions are discussed later. To demonstrate the generality of the model for different sized basins, we have compared its predictions with observations from two lakes, one with a surface area of 1 km2, the other of 1.8 x lo* km2. For the smaller lake ( Llyn Cwellyn : Darbyshire and Colclough 1972), the available data only allow a l-day simulation over a period when strong winds significantly altered thermal structure. For the larger lake (L,. Ontario: IFYGL data), a much longer integration was possible. The basic parameters of the model are identical for both simulations. Symbols used in the text are given in Table 1. We thank R, L. Pickett and F. Rodante for providing edited versions of the IFYGL data. LIMNOLOGY AND OC.EANOGRAPEIY 687 JULY 1977, V. 22(4) 688 Tucker and Green Table 1. List of symbols. Table 1. Continued. __._ -.-_--_-----I--.-. --. .-. . . --.._ _ -__--_.-.. ..-.--...--. ____ __ ___.._. -_--_.----.__ -----_-.---

Journal ArticleDOI
TL;DR: In this paper, diffraction of cnoidal waves around a large vertical circular cylinder is investigated, and first approximations are derived for the velocity potential of the flow field and consequently for the wave loading on the cylinder.
Abstract: The diffraction of cnoidal waves around a large vertical circular cylinder is investigated. First approximations are derived for the velocity potential of the flow field and consequently for the wave loading on the cylinder. The forces may be appreciably larger than predicted on the basis of shallow water sinusoidal wave theory, and the consequences on the design of large offshore structures in shallow water are assessed. The possibility of extending the theory to a second approximation is examined.

Journal ArticleDOI
TL;DR: In this paper, the stability of a finite-amplitude Rossby wave on a β-plane with respect to a small amplitude perturbation is examined, and the parametric instability exhibited by the system is examined analytically and numerically.
Abstract: The stability of a finite-amplitude Rossby wave on a β-plane with respect to a small amplitude perturbation is examined. Normal modes are defined, without further approximation, by a third-order Floquet system. The parametric instability exhibited by the system is examined analytically and numerically. When the amplitude of the Rossby wave tends to zero this instability is shown to be analogous to the resonant interaction of the Rossby wave with components of the perturbation. The stability of a Rossby wave is seen to depend upon two parameters, M and ξ. The parameter M is proportional to the amplitude of the Rossby wave and ξ is its orientation on the β-plane. Curves of marginal stability in the (M, ξ) space are found numerically.

Journal ArticleDOI
TL;DR: In this paper, it was shown that gravity waves in a latitudinally sheared zonal flow exhibit critical latitude behaviour where the wave frequency matches the Brunt-Vaisala frequency.
Abstract: Using the B-plane approximation we formulate the equations which govern small perturbations in a rotating atmosphere and describe a wide class of possible wave motions, in the presence of a background zonal flow, ranging from ‘moderately high’ frequency acoustic-gravity-inertial waves to ‘low’ frequency planetary-scale (Rossby) waves. The discussion concentrates mainly on the propagation properties of Rossby waves in various types of latitudinally sheared zonal flows which occur at different heights and seasons in the earth’s atmosphere. However, it is first shown that gravity waves in a latitudinally sheared zonal flow exhibit critical latitude behaviour where the ‘intrinsic ’ wave frequency matches the Brunt-Vaisala frequency (in contrast to the case of gravity waves in a vertically sheared flow where a critical layer exists where the horizontal wave phase speed equals the flow speed) and that the wave behaviour near such a latitude is similar to that of Rossby waves in the vicinity of their critical latitudes which occur where the ‘intrinsic’ wave frequency approaches zero. In the absence of zonal flow in the atmosphere the geometry of the planetary wave dispersion equation (which is described by a highly elongated ellipsoid in wave-number vector space) implies that energy propagates almost parallel to the /--planes. This feature may provide a reason why there seems to be so little coupling between planetary scale motions in the lower and upper atmosphere. Planetary waves can be made to propagate eastward, as well as westward, if they are evanescent in the vertical direction. The W.K.B. approximation, which provides an approximate description of wave propagation in slowly varying zonal wind shears, shows that the distortion of the wave-number surface caused by the zonal flow controls the dependence of the wave amplitude on the zonal flow speed. In particular it follows that Rossby waves propagating into regions of strengthening westerlies are intensified in amplitude whereas those waves propagating into strengthening easterlies are diminished in amplitude. A classification of the various types of ray trajectories that arise in zonal flow profiles occurring in the Earth’s atmosphere, such as jet-like variations of westerly or easterly zonal flow or a belt of westerlies bounded by a belt of easterlies, is given, and provides the conditions giving rise to such phenomena as critical latitude behaviour and wave trapping. In a westerly flow there is a tendency for the combined effects on wave propagation of jet-like variations of B and zonal flow speed to counteract each other, whereas in an easterly flow such variations tend to reinforce each other. An examination of the reflexion and refraction of Rossby waves at a sharp jump in the zonal flow speed shows that under certain conditions wave amplification, or over-reflexion, can arise with the implication that the reflected wave can extract energy from the background streaming motion. On the other hand the wave behaviour near critical latitudes, which can be described in terms of a discontinuous jump in the ‘wave invariant’, shows that such latitudes can act as either wave absorbers (in which case the mean flow is accelerated there) or wave emitters (in which case the mean flow is decelerated there).

Journal ArticleDOI
TL;DR: In this article, the spectral and cospectral analyses of velocity and temperature fluctuations were made to establish the characteristic features of the waves Flow visualization photographs of smoke released during the breaking of a wave are also presented Comparison between the turbulent energies present during and after breaking of the wave indicates enormous mixing and dispersion occurring during breaking.
Abstract: Observations are presented for internal gravity waves and their breaking at a height of 235 m over the ocean in surface-based inversions which are formed because of the advection of warm air over cold water The spectral and cospectral analyses of velocity and temperature fluctuations were made to establish the characteristic features of the waves Flow visualization photographs of smoke released during the breaking of a wave are also presented Comparison between the turbulent energies present during and after breaking of a wave indicates enormous mixing and dispersion occurring during breaking

Book ChapterDOI
01 Jan 1977
TL;DR: In this paper, the authors investigated the effect of bay resonance on the wave formation of large tsunamis and showed that a weak bore may be formed close to shore if the head wave of a tsunami is a positive wave, while there may be no bore formation at all if the negative wave forms the front.
Abstract: Scale parameters of large tsunamis suggest that non-linearity of waves is important only within a short distance of about a half wavelength from the shoreline.The Carrier-Greenspan transformation of the non-linear shallow-water equations on a uniformly sloping beach is elucidated to give a set of linear equations analogous to the linearized equations of the original non-linear equations, and an explicit form of the wave-breaking criterion is given.Although a weak bore (or an undular bore) may be formed close to shore if the head wave of a tsunami is a positive wave, there may be no bore formation at all if the negative wave forms the front.The maximum run-up of a tsunami is caused mostly by the non-breaking wave enhanced by the effect of bay resonance.

BookDOI
01 Jan 1977
TL;DR: A survey of theoretical research into tsunamis and observations of actual tsunami in Japan can be found in this article, where a real bathymetry model is used to simulate tsunami generation and propagation in the ocean.
Abstract: Summary.- Some classical water-wave problems in varying depth.- Linear transport methods for long surface waves in canals, bays and oceans.- Diffraction of gravity waves by ray methods.- Experimental studies of wave refraction.- Summary.- Survey of theoretical research into tsunamis and observations of actual tsunamis in Japan.- Numerical simulation of tsunami generation and propagation in the ocean with a real bathymetry.- Local behaviour of tsunamis.- Cylindrical solitary waves.- Summary.- Shoaling waves : Numerical solution of exact equations.- Wave-wave interactions near the shore.- Surf and run-up.- Laboratory study of a stationary oblique plunging breaker for surfboard testing.- On breaking waves.- Summary.- The dynamics of waves on currents over a weakly varying bed.- Finite-amplitude waves on non-uniform currents.- Triple roots and cusped caustics for surface gravity waves.- Summary.- Ondes internes evanescentes a l'infini dans un milieu liquide stratifie en rotation.- The interaction of surface and internal tides with boundary currents.- Along the strait in thirty six days.- Summary.- Difframon of shelf waves by an irregular coast-line.- The non-linear generation of shelf waves.- Resonance of shelf waves near islands.- Nonlinear aspects of shelf waves and mean currents.- Continental shelf waves in the presence of a sheared geostrophic current.- Generation of shelf waves on the East Australian coast by wind stress.- Long waves on the Southern Ocean.

Journal ArticleDOI
TL;DR: In this paper, a wave analysis method is proposed for deriving amplitude function of elementary waves composing nonstantionary wave pattern generated by a ship which is forced to oscillate and is running on a calm water with forward velocity.
Abstract: Wave analysis is proposed for deriving amplitude function of elementary waves composing nonstantionary wave pattern generated by a ship which is forced to oscillate and is running on a calm water with forward velocity. The purpose of this wave analysis is especially to verify the validity of theory of resistance increase in waves in predicting the structure of nonstationary wave pattern due to an oscillating ship.Wave analysis method proposed here is similar to that which is used in research on stationary wave making resistance theory and is called Newman-Sharma method. Wave patterns generated by an oscillating ship, however, vary with time in contrast with those in stationary wave making and accordingly a process is devised for eliminating time factor and for deriving wave amplitude and phase distribution in space available for analysis. With this process we can easily extract space distribution information of amplitude and phase of nonstationary waves from wave height data which are obtained with repeating measurements a few times at only a point in model basin.From the results of wave analysis of measured wave pattern compared with theory we can conclude that slender body theory can predict wave amplitude function distribution fairly good. And a little interaction effects between stationary and nonstationary waves are observed.

Journal ArticleDOI
TL;DR: In this paper, the authors found that the energetic isotropic turbulence generated by a waterfall of low head was developed in part through the unstable two-phase flow of entrained air bubbles and the resulting turbulent field had a turbulent Reynolds number of ≳2×104 and maintained a self-similar structure throughout the decay period studied.
Abstract: The energetic isotropic turbulence generated by a waterfall of low head was found to be developed in part through the unstable two‐phase flow of entrained air bubbles. The resulting turbulent field had a turbulent Reynolds number of ≳2×104 and maintained a self‐similar structure throughout the decay period studied. The present study may provide some insight into the structure of turbulence produced by the breaking waves over the ocean.

01 Jun 1977
TL;DR: In this paper, the authors derived models for determining the conditions under which breaking waves will disperse an oil slicks on the ocean from simple considerations, and the results indicated that a 3 m significant wave height sea state will tend to initiate globular dispersion and that breaking waves of large crest lengths are essential for a surface dispersion to take place.
Abstract: : Limiting sea state condition for the globular dispersion of oil slicks on the ocean have been obtained from simple considerations. Models have been derived for determining the conditions under which breaking waves will disperse an oil slick. Two types of dispersions are considered, viz., surface dispersion and globular dispersion within the water column, with emphasis on the latter type of dispersion. The results indicate that a 3 m significant wave height sea state will tend to initiate globular dispersion and that breaking waves of large crest lengths are essential for a surface dispersion to take place. The depth of penetration of globules of oil formed under breaking waves is calculated to be relatively shallow. The large number of assumptions made and their effects on the results are discussed. Several of the unknown physical parameters of importance are identified and recommendations have been made for experimental determination of some of these parameters. (Author)

Patent
06 Apr 1977
TL;DR: In this paper, the power source frequency element only, which includes no trouble wave elements, is supplied to the load apparatys by second winding, in this way, no danger wave effect is given at all to the power apparatus.
Abstract: PURPOSE:The power source frequency element only, which includes no trouble wave elementsis supplied to the load apparatys by second winding. In this way, no trouble wave effect is given at all to the load apparatus.

Journal ArticleDOI
TL;DR: In this article, large amplitude atmospheric waves were observed at eight stations on a ground level pressure record, on vertical incidence ionograms, and on Faraday rotation records over the southern part of Africa.
Abstract: On July 1, 1973, large amplitude atmospheric waves occurred simultaneously in the troposphere and ionosphere over the southern part of Africa. The waves were observed at eight stations on a ground level pressure record, on vertical incidence ionograms, and on Faraday rotation records. Both a Fourier and a band filter analysis show significant wave amplitudes in two narrow period bands around 85 and 65 min, respectively. The waves were excited at low heights near the south coast of Africa and propagated toward the equator with horizontal phase trace speeds of the order of the lower atmosphere sound speed. An analysis of surface weather maps indicates that there was a close spatial and temporal coincidence of the observed waves and nongeostrophic winds, confirming the hypothesis that atmospheric waves may be generated during geostrophic adjustment processes. Wave calculations in a realistic model atmosphere over a rigid surface show that the observed wave properties can be best explained in terms of the Lamb mode. An energy estimate confirms that the nongeostrophic disturbance could in fact provide the energy necessary to explain the amplitudes and the period of occurrence of the observed waves.

Journal ArticleDOI
TL;DR: In this article, the authors studied the special class of quasi-simple wave solutions for the system of partial differential equations governing inviscid acoustic gravity waves. And they showed that these traveling wave solutions do not admit shocks.
Abstract: The special class of quasi‐simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically.