Short Wave Groups Research Articles

경사지형에서 파군에 의해 생성된 장파의 Bragg 반사

경사지형에서 파군에 의해 생성된 장파의 Bragg 반사

Long–wave forcing by the breaking of random gravity waves on a beach

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

Transmission of Long Waves Induced by Short-Wave Groups Through a Composite Breakwater

Theoretical findings and laboratory evidences are presented regarding the transmission of long waves induced by short-wave groups through the rubble base of an infinitely long composite breakwater. Multiple-scale perturbation method is applied in describing the long-wave fields in terms of velocity potential, and an analytical solution is derived for transmitted and reflected long waves induced by wave groups. Dependency of the reflection and transmission of free long waves on several parameters is examined through the numerical calculations. It is found that the linear friction factor, the rubble-base height and the modulation of short waves affect the transmission of free long waves significantly. Theoretical results are then compared with the results from laboratory experiments. It is shown that although the conventional rubble-mound breakwaters can reflect short wave energy efficiently, a significant part of the bound long-wave energy associated with shortwave groups is transmitted to the leeward side of the breakwater as free waves.

Short-Wave and Wave Group Scattering by Submerged Porous Plate

An analytical solution for waves propagating through a horizontal porous plate of finite thickness is obtained. The objective of the plate is to reduce the incident short-wave energy and the long-wave energy as well. Consequently, in this study the plate is analyzed in a global perspective [i.e., considering its response to obliquely incident short waves (both regular and irregular) and wave groups (with the consequent generation of free and locked long waves)]. To solve the propagation of regular and irregular waves, an eigenfunction expansion is used and the results are verified with experimental data showing good agreement. The propagation of a wave group past a horizontal porous plate is studied using a multiple-scale perturbation method, and an analytical solution is presented. The results show that the generated long waves are present on both sides of the plate and that maximum short-wave reflection is associated with maximum long-wave transmission.

Breakpoint generated surf beat induced by bichromatic wave groups

This paper presents new experimental data on 2-D surf beat generation by a time-varying breakpoint induced by bichromatic wave groups. The experimental investigation covers a broad range of wave amplitudes, short wave frequencies, group frequencies and modulation rates. The data include measurements of incident and outgoing wave amplitudes, breakpoint position, shoreline run-up and the cross-shore structure of both the short and long wave motion. Surf beat generation is shown to be in good agreement with theory [Symonds, G., Huntley, D.A., Bowen, A.J., 1982. Two dimensional surf beat: long wave generation by a time-varying breakpoint. J. Geophys. Res. 87, 492–498]. In particular, surf beat generation is dependent on the normalised surf zone width, which is a measure of the phase relationship between the seaward and shoreward breakpoint forced long waves, and linearly dependent on the short wave amplitude. The cross-shore structure of the long wave motion is also consistent with theory; at maximum and minimum surf beat generation, the mean breakpoint coincides with the nodal and anti-nodal points, respectively, for a free long wave standing at the shoreline. A numerical solution, using measured data as input, additionally shows that the phase relationship between the incident bound long wave and the outgoing breakpoint forced wave is consistent with the time-varying breakpoint mechanism.

Thermic structure and intense internal waves on the narrow continental shelf of the Black Sea

Measurements results of the thermic structure taken from the waters of the narrow continental shelf of the south coast of Crimea are discussed. Continuous observations were performed in July–August 1993, from a stationary oceanologic platform (depth 30 m) using an antenna with three temperature distribution sensors and two temperature gradient distribution sensors situated at the platform corners (in a 19×22 m plane) covering the thermocline completely. Probes were also made of the water layer down to the bottom using a CTD, and also the currents at 5, 10 and 20 m were observed. A continuous register of the sea level waves, wind and atmospheric pressure was taken. The thermic structure showed oscillations in three time-scales: synoptic, related to the surge phenomena (3–5 days); inertial (17–18 h) and short period (less than 1 h). The thermocline was completely extended with a strong negative setup, and was close to the bottom with a positive setup, possessing vertical gradients of up to 2°C/m. Inertial movements showed up in the current oscillations and also produced vertical displacements in the thermocline up to 8–10 m, happening constantly while the measurements were taken. These displacements were usually related to groups of intense internal short period waves with amplitudes of 4–9 m, periods of 14–28 min and wavelengths of 250–360 m. An intense movement, with diurnal period related to the breeze processes on the coast, was also found in the currents. The relationship between the parameters of the intense waves in groups and those of the medium dispersion and non-linearity as well as the parameters of the calculated solitons in the Korteweg and de Vries equation, are analyzed.

Numerical experiments on low-frequency fluctuations on a submerged coastal reef

Low-frequency fluctuations on a reef coast are studied through a numerical model based on nonlinear conservation equations of mass and momentum. The model is used to investigate the long wave generation and propagation phenomena under both breaking and non-breaking incident short wave groups. The effects of incident wave characteristics and reef topography on the long wave phenomena are discussed. The results show that the long wave elevations on reef coasts are substantial, which explains the large water level fluctuations observed at certain occasions.

A note on infragravity waves in the Arctic Ocean

Long‐period (20–50 s) surface‐gravity waves were recorded in the eastern Arctic (83°N, 10°E) using tiltmeters deployed on the ice and an acoustical current meter deployed a few meters below the ice during the spring of 1989. The waves caused ice tilt of a few microradians and horizontal velocity of the water just beneath the ice of order 10−4 m s−1. The unprecedented sensitivity of the velocity measurements is the result of a path‐averaging technique based on reciprocal transmission along 200‐m horizontal paths. The measurements indicate that infragravity waves and low‐frequency swell penetrate the Arctic Ocean through the Pram Strait and that they are freely propagating and not tied to groups of short waves. It is suggested that these waves could provide a method to measure ice thickness distribution in the Arctic Ocean.

Bar formation due to wave groups and associated long waves

Field observations reveal that waves propagating onto a beach from deeper water have a grouped structure. Associated with this pattern of alternating high and low waves is a long wave forced by radiation stress variations due to the changing short wave height. As the wave groups propagate onshore, the relationship between the variation in the short wave height and the long wave motion is complicated by breaking of the short waves, reflection of the long wave and the generation of a free long wave by time variation of the breakpoint position. Nevertheless, there may still be a fixed phase relation between the short-wave envelope and the long wave motion at any particular location, resulting in a net transport of sediment over the timescale of the short wave groups. This transport arises from sediment grains mobilised by short waves and moved by the long wave motion. Model predictions of wave group propagation onto a beach and the associated long wave motions are presented which suggest that sediment transport due to short-wave/long-wave coupling may result in the formation of a bar within the inner surf-zone and the possibility of additional bars further offshore, outside the surf-zone. This mechanism for bar formation may provide a new framework for understanding bar morphodynamics.

Edge waves forced by short-wave groups

On the basis of the theory for infragravity waves induced by short-wave groups developed by Schäffer (1993), three-dimensional infragravity waves are analysed. The theory relies on the linearized depth-integrated conservation equations for mass and momentum combined to give a second-order long-wave equation with forcing expressions in terms of the radiation stress. This forcing gives a dynamic set-up originating from oscillations of the break-point position and a dynamic set-down bound to the short-wave groups. For small angles of incidence leaky-mode solutions are found while trapped modes appear when the primary waves are sufficiently oblique. In the latter case resonant edge-wave excitation may occur. A semi-analytical steady-state solution for the infragravity motion is presented. The solution is restricted to periodicity along a plane beach connected to a shelf and valid only for small primary-wave modulations.

RESONANCE OF LONG WAVES IN A HARBOUR BY GROUPS OF SHORT WAVES

小規模な港湾において長周期振動を引き起こす原因を荒天時に不規則波群に伴って来襲する2次長周期波と考え, その応答特性を数値解析および水理実験によって調べた. 数値解については, 長方形湾に対して厳密である解析解とも比較することによって, 共振による長周期波の増幅率の予測に関する適用性を明らかにした. 同時に, 実際のスペクトルを想定した不規則波計算も行い, 狭帯スペクトルの仮定に基づく本解析方法の有用性を示した.

Infragravity waves induced by short-wave groups

A theoretical model for infragravity waves generated by incident short-wave groups is developed. Both normal and oblique short-wave incidence is considered. The depth-integrated conservation equations for mass and momentum averaged over a short-wave period are equivalent to the nonlinear shallow-water equations with a forcing term. In linearized form these equations combine to a second-order long-wave equation including forcing, and this is the equation we solve. The forcing term is expressed in terms of the short-wave radiation stress, and the modelling of these short waves in regard to their breaking and dynamic surf zone behaviour is essential. The model takes into account the time-varying position of the initial break point as well as a (partial) transmission of grouping into the surf zone. The former produces a dynamic set-up, while the latter is equivalent to the short-wave forcing that takes place outside the surf zone. These two effects have a mutual dependence which is modelled by a parameter K, and their relative strength is estimated. Before the waves break, the standard assumption of energy conservation leads to a variation of the radiation stress, which causes a bound, long wave, and the shoaling bottom results in a modification of the solution known for constant depth. The respective effects of this incident bound, long wave and of oscillations of the break-point position are shown to be of the same order of magnitude, and they oppose each other to some extent. The transfer of energy from the short waves to waves at infragravity frequencies is analysed using the depth-integrated conservation equation of energy. For the case of normally incident groups a semi-analytical steady-state solution for the infragravity wave motion is given for a plane beach and small primary-wave modulations. Examples of the resulting surface elevation as well as the corresponding particle velocity and mean infragravity-wave energy flux are presented. Also the sensitivity to the variation of input parameters is analysed. The model results are compared with laboratory experiments from the literature. The qualitative agreement is good, but quantitatively the model overestimates the infragravity wave activity. This can, in part, be attributed to the neglect of frictional effects.

Propagation and trapping of obliquely incident wave groups over a trench with currents

The analytical solutions of secord-order long waves generated by the diffraction of short wave groups by a combination of depth and current velocity discontinuities are presented. The incident wave groups consist of two co-linear short waves with slightly different frequencies. These incident short wave groups are reflected partially by the abrupt changes in depth and current velocity. The incident, reflected, and transmitted wave groups are accompanied by the second-order locked long waves, which propagate together with the wave envelopes of the short waves at their group velocity. Because of the discontinuity in the second-order free surface displacement of the locked long waves, free long waves are generated, which propagate at the shallow-water phase speed and in a direction different from those of short waves and wave envelopes. With certain combinations of angle of wave incidence, depth ratios and current velocity, the free long waves can be trapped in the vicinities of depth and current discontinuities. Several examples are given to illustrate the resonance of trapped free long waves.

Infragravity waves in the deep ocean

Energetic pressure fluctuations at periods longer than 30 s are a ubiquitous feature of pressure spectra from instruments sited on the deep seafloor in both the Atlantic and the Pacific oceans. We show these pressure fluctuations are caused by freely propagating ocean surface waves. The waves are generated in the near shore region along the entire coastline of an ocean basin through nonlinear transfer of energy from short‐period waves. This view contrasts with some earlier work, which described these long‐period pressure fluctuations as trapped waves tied to groups of short waves. We have constructed a model based on the average energy in the short (wind driven and swell) wave band along the North Atlantic coast to predict the energy in the long wave band at a site in the Atlantic. Maximum likelihood wave number‐frequency spectra calculated on data from an 11 element array in the North Pacific confirm that the long wave energy is confined to wave numbers corresponding to the surface gravity wave dispersion relation. We have used the wave number spectra to isolate particular regions of the Pacific Ocean which are sources of long wave energy. Energetic short‐period waves are incident on the coastline in these regions. Long waves are detected at the array which originate in the Gulf of Alaska, the northwestern Pacific, and at the southern tip of South America.

Bore-like surf beat in a reef zone caused by wave groups of incident short period waves

Resonant oscillation of sea surface elevation in coral reef zones is asserted to be excited by the change of radiation stress and breaking point due to the wave groups of incident short period waves. Numerical and laboratory experiments confirmed the generation of long period oscillation and its nonlinear deformation into the "bore-like or tsunami-like surf beat" with a steep forward face. A resonance diagram is prepared for a design criterion.

Long-Wave Generation Due to the Refraction of Short-Wave Groups over a Shear Current

The generation of long waves by short-wave groups propagating over a shear current is studied. The incident wave groups consist of two co-linear short waves with slightly different frequencies. These short waves are refracted by the shear currents. For certain angles of incidence caustics may exist and the short waves are reflected back by the shear current. Similarly, caustics could also appear in the wave envelope, which propagates in a different direction from that of the short waves. In the present paper, the treatment of caustics is not considered. In the region where the shear current vanishes, the short-wave groups are accompanied by locked long waves that propagate with the wave envelope of short waves at their group velocity. In the shear current region, the refraction effects not only separate the propagation directions of the short waves and the wave envelope but also generate free long waves, which propagate at the speed of.gh. The free long waves could also be trapped over the shear current region.

A note on long waves induced by short-wave groups over a shelf

The generation of long waves due to the refraction of wave groups over a shelf is reexamined. The appropriate boundary conditions for calculating the second-order mean free-surface displacement are discussed. Numerical results for a plane shelf are presented, which are different from those given by Mei & Benmoussa (1984).

Trapping and resonance of long shelf waves due to groups of short waves

Groups of short waves within a narrow frequency band are known to be accompanied by second-order long waves travelling at the group velocity of the predominant short waves. When the short waves are refracted by bottom topography, new long waves can be further radiated and propagated away from the topography at the shallow-water speed. Since over a long submarine ridge there can be trapped modes of long-period waves, incident groups of short waves can excite the trapped waves through a second-order mechanism. In this paper we study such excitations over a rectangular shelf which scatters the first-order short waves. By employing asymptotic methods we examine the transient excitation of the trapped long wave by both sinusoidal wave groups and wave packets. The effects of a small angular spread of the incident waves are also included.

Excitation of long internal waves by groups of short surface waves incident on a barrier

The effects of diffraction by a long barrier on second-order long waves forced by sinusoidally modulated short incident waves are examined for a two-layered model ocean. When the group velocity of the short waves lies between the phase velocities of the longest baroclinic and barotropic modes, long internal waves of the frequency equal to twice the modulational frequency of the short waves are found to radiate away from the edge ray which divides the geometrical shadow and the illuminated region. In particular the baroclinic wave can penetrate the shadow. This penetration occurs when the internal long wave is not resonated by short surface waves.

Fundamental research on a nonlinear diffraction problem of the long waves by a huge vertical circular cylinder

The objectives of present paper are to formulate the nonlinear diffraction problem for the long waves induced by a short wave groups using the multiple scales perturbation method and to find the effect of 2 nd-order long waves on the ocean structures.The governing equation for the 1 st-order zeroth harmonic potential is obtained by using the solvability condition of the boundary value problem for 3 rd-order zeroth harmonic potential. The formulas for the surface elevation of the 2 nd-order long waves induced by modulated short wave groups are derived analytically.Numerical results are presented for the case where the envelope of incident waves-train is a sine function and the influences of the long waves around a huge circular cylinder are considered.