Observations on the evolution of wave modulation

2006 ◽  
Vol 463 (2077) ◽  
pp. 85-112 ◽  
Author(s):  
Hwung-Hweng Hwung ◽  
Wen-Son Chiang ◽  
Shih-Chun Hsiao
Keyword(s):  
Wave Breaking ◽  
Wave Train ◽  
Wave Spectrum ◽  
Wave Steepness ◽  
Carrier Wave ◽  
Wave Flume ◽  
Initial Wave ◽  
Wide Range ◽  
Wave Trains ◽  
Hydraulics Laboratory

A series of laboratory experiments on the long-time evolution of nonlinear wave trains in deep water was carried out in a super wave flume (300×5.0×5.2 m) at Tainan Hydraulics Laboratory of National Cheng Kung University. Two typical wave trains, namely uniform wave and imposed sideband wave, were generated by a piston-type wavemaker. Detailed discussions on the evolution of modulated wave trains, such as transient wavefront, fastest growth mode and initial wave steepness effect, are given and the results are compared with existing experimental data and theoretical predictions. Present results on the evolution of initial uniform wave trains cover a wide range of initial wave steepness ( ) and thus, greatly extend earlier studies that are confined only to the larger initial wave steepness region ( ). The amplitudes of the fastest growth sidebands exhibit a symmetric exponential growth until the onset of wave breaking. At a further stage, the amplitude of lower sideband becomes larger than the carrier wave and upper sideband after wave breaking, which is known as the frequency downshift. The investigations on the evolution of initial imposed sideband wave trains for fixed initial wave steepness but different sideband space indicate that the most unstable mode of initial wave train will manifest itself during evolution through a multiple downshift of wave spectrum for the wave train with the smaller sideband space. It reveals that the spectrum energy tends to shift to a lower frequency as the wave train propagates downstream due to the sideband instability. Experiments on initial imposed sideband wave trains with varied initial wave steepness illustrate that the evolution of the wave train is a periodic modulation and demodulation at post-breaking stages, in which most of the energy of the wave train is transferred cyclically between the carrier wave and two imposed sidebands. Meanwhile, the wave spectra show both temporal and permanent frequency downshift for different initial wave steepness, suggesting that the permanent frequency downshift induced by wave breaking observed by earlier researchers is not permanent. Additionally, the local wave steepness and the ratio of horizontal particle velocity to linear phase velocity at wave breaking in modulated wave group are very different from those of Stokes theory.

Nonlinear and Dissipative Characteristics of a Combined Random-Cnoidal Wave Field

2017 ◽  
Author(s):  
James M. Kaihatu ◽  
John T. Goertz ◽  
Samira Ardani ◽  
Alex Sheremet
Keyword(s):  
Wave Spectrum ◽  
Leading Edge ◽  
Dissipation Function ◽  
Indian Ocean Tsunami ◽  
Random Wave ◽  
Cnoidal Wave ◽  
State University ◽  
Large Wave ◽  
Wave Flume ◽  
Wave Trains

Images of the 2004 Indian Ocean tsunami at landfall shows a leading edge marked by short waves (“fission” waves). These waves appear to be cnoidal in shape and of a temporal and spatial scale in line with the longest swell present in the region, and may interact with the longer waves in the background random wave spectrum. As part of a comprehensive series of experiments, the Large Wave Flume at Oregon State University (USA) was used to generate and measure the properties of cnoidal, random, and combined cnoidal-random wave trains. Both the nonlinear energy transfer characteristics (via bispectral analysis) and dissipation characteristics (via a proxy dissipation function) are studied for all generated wave conditions. It is generally determined that the characteristics of the cnoidal wave dominate the combined cnoidal-random wave signals if the energy of the cnoidal wave is at least equal to that of the random wave.

scholarly journals Wind Sea and Swell Separation of 1D Wave Spectrum by a Spectrum Integration Method*

2012 ◽  
Vol 29 (1) ◽  
pp. 116-128 ◽  
Author(s):  
Paul A. Hwang ◽  
Francisco J. Ocampo-Torres ◽  
Héctor García-Nava
Keyword(s):  
Integration Method ◽  
Wave Spectrum ◽  
Peak Frequency ◽  
External Information ◽  
Wave Steepness ◽  
Wave Age ◽  
Wide Range ◽  
Wave Development ◽  
Wave Conditions ◽  
Wind Sea

Abstract In an earlier paper by Wang and Hwang, a wave steepness method was introduced to separate the wind sea and swell of the 1D wave spectrum without relying on external information, such as the wind speed. Later, the method was found to produce the unreasonable result of placing the swell–sea separation frequency higher than the wind sea peak frequency. Here, the following two factors causing the erratic performance are identified: (a) the wave steepness method defines the swell–sea separation frequency to be equal to the wind sea peak frequency with a wave age equal to one, and, (b) for more mature wave conditions, the peak frequency of the wave steepness function may not continue monotonic downshifting in high winds if the high-frequency portion of the wave spectrum has a spectral slope milder than −5. Conceptually, the swell–sea separation frequency should be placed between the swell and wind sea peak frequencies rather than at the wind sea peak frequency. Furthermore the wind sea wave age can vary over a considerable range, thus factor a above can lead to incorrect results. Also, because the slope of the wind sea equilibrium spectrum is typically close to −4, factor b becomes a serious restriction in more mature wave conditions. A spectrum integration method generalized from the wave steepness method is presented here for wind sea and swell separation of the 1D wave spectrum without requiring external information. The new spectrum integration method works very well over a wide range of wind wave development stages in the ocean.

scholarly journals Drag of the Water Surface at Very Short Fetches: Observations and Modeling

2008 ◽  
Vol 38 (9) ◽  
pp. 2038-2055 ◽  
Author(s):  
Guillemette Caulliez ◽  
Vladimir Makin ◽  
Vladimir Kudryavtsev
Keyword(s):  
Wind Stress ◽  
Wave Breaking ◽  
Wind Wave ◽  
Wind Forcing ◽  
Wave Steepness ◽  
Surface Drag ◽  
Wave Fields ◽  
Wind Speeds ◽  
Dominant Wave ◽  
Wide Range

Abstract The specific properties of the turbulent wind stress and the related wind wave field are investigated in a dedicated laboratory experiment for a wide range of wind speeds and fetches, and the results are analyzed using the wind-over-waves coupling model. Compared to long-fetch ocean wave fields, wind wave fields observed at very short fetches are characterized by higher significant dominant wave steepness but a much smaller macroscale wave breaking rate. The surface drag dependence on fetch and wind then closely follows the dominant wave steepness dependence. It is found that the dimensionless roughness length z*0 varies not only with wind forcing (or inverse wave age) but also with fetch. At a fixed fetch, when gravity waves develop, z*0 decreases with wind forcing according to a −1/2 power law. Taking into account the peculiarities of laboratory wave fields, the WOWC model predicts the measured wind stress values rather well. The relative contributions to surface drag of the equilibrium-range wave-induced stress and the airflow separation stress due to wave breaking remain small, even at high wind speeds. At moderate to strong winds, the form drag resulting from dominant waves represents the major wind stress component.

scholarly journals An Experimental and Theoretical Study of Wave Damping due to the Elastic Coating of the Sea Surface

2020 ◽  
Vol 8 (8) ◽  
pp. 571
Author(s):  
Igor Shugan ◽  
Ray-Yeng Yang ◽  
Yang-Yih Chen
Keyword(s):  
Sea Surface ◽  
Thin Elastic Plate ◽  
Intermediate Water ◽  
Elastic Plates ◽  
Wave Flume ◽  
Flexible Plates ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Motion Characteristics ◽  
Hydraulics Laboratory

Flexible plates or membranes located on the sea surface can be effective for attenuation waves approaching the beach. The most efficient structures should be found through comprehensive research using developed experiments and theory. Our experimental work was focused on the wave propagation and attenuation passing through floating elastic structures. The experiments were conducted at the wave flume of Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan. The experiment mainly analyzes the reflection coefficient, transmission coefficient and energy loss of the regular wave of intermediate water depth after passing through the elastic structure under different wave steepness and other different wave conditions. Our experiments also explore the comparison of energy dissipation effects and the differences in motion characteristics between different elastic plates and different plate fixing methods. Three elastic materials were tested in the experiments: Latex, cool cotton and polyvinyl chloride (PVC). A model of a thin elastic plate covering the sea surface was used to evaluate the effectiveness of the structure of the wave barrier. The results of experiments carried out in the wave flume were compared with theoretical predictions in a wide range of generated waves.

scholarly journals Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation

2010 ◽  
Vol 40 (9) ◽  
pp. 1917-1941 ◽  
Author(s):  
Fabrice Ardhuin ◽  
Erick Rogers ◽  
Alexander V. Babanin ◽  
Jean-François Filipot ◽  
Rudy Magne ◽  
...  
Keyword(s):  
Wind Speed ◽  
Wave Height ◽  
Wave Breaking ◽  
Wave Spectrum ◽  
Remote Sensing Data ◽  
Ocean Waves ◽  
Breaking Waves ◽  
Global Ocean ◽  
Short Waves ◽  
Wide Range

Abstract New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. The wave energy balance is verified in a wide range of conditions and scales, from the global ocean to coastal settings. Wave height, peak and mean periods, and spectral data are validated using in situ and remote sensing data. Some systematic defects are still present, but, overall, the parameterizations probably yield the most accurate estimates of wave parameters to date. Perspectives for further improvement are also given.

Nonlinear Generation of Narrow-Banded Wave Trains

2019 ◽  
Author(s):  
Anatoliy Khait ◽  
Lev Shemer
Keyword(s):  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Wave Train ◽  
Complex Surface ◽  
Nls Equation ◽  
Wave Flume ◽  
Domain Of Applicability ◽  
Wave Trains ◽  
Driving Signal

Abstract Analytic method for nonlinear wave generation by a wavemaker that is somewhat different from the nonlinear theory of Schäffer is proposed. The method that is based on the Nonlinear Schrödinger (NLS) equation and the nonlinear boundary condition at the wavemaker is free of 2nd order limitation inherent to the existing wavemaker theories. Advantages offered by the NLS model allowed simplification of the expressions for determination of the wavemaker driving signal and thus made them easily applicable in practice. The nonlinear correction to the wavemaker driving signal is calculated from the complex surface elevation envelope obtained as a solution of the NLS equation at the prescribed location in the wave flume. The domain of applicability of the generation method was determined on the basis of numerous experiments in the wave flume. A very good generation of the required wave train shape was obtained for sufficiently narrow-banded wave trains.

Experimental Study on Changes of Sloping Sandy Bed Profile under Breaking Waves

2012 ◽  
Vol 212-213 ◽  
pp. 163-168
Author(s):  
Yun Pan ◽  
Yong Zhou Cheng ◽  
Qing Feng Li ◽  
Wen Cheng Wang
Keyword(s):  
Wave Breaking ◽  
Orbital Motion ◽  
Breaking Waves ◽  
Coastal Structures ◽  
Wave Flume ◽  
Sand Ripple ◽  
Wide Range ◽  
Wave Heights ◽  
Formation And Evolution ◽  
Sand Bar

The wave breaking forces can exacerbate sediment transport, and lead to erosion of the seabed, coastal deformation and destruction of coastal structures. The experiment is carried out in a wave flume with a 1:30 sloping sandy seabed. A wide range of measurements from the regular wave runs are reported, including time series of wave heights, changes of bed profile. The video records are analysed to measure the time development of the seabed form and the characteristics of the orbital motion of the sand in the wave breaking region. The location and wave height at wave breaking point is measured by experiment. Formation and evolution of sand ripple and sand bar are studied under the breaking waves. It is found that effect of bed surface on wave breaking zone is more significant than wave non-breaking.

scholarly journals On the Evolution of Different Types of Green Water Events

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1148
Author(s):  
Jassiel V. H. Fontes ◽  
Irving D. Hernández ◽  
Edgar Mendoza ◽  
Rodolfo Silva ◽  
Eliana Brandão da Silva ◽  
...  
Keyword(s):  
Water Surface ◽  
Early Stage ◽  
Dam Break ◽  
Green Water ◽  
Wave Steepness ◽  
Wave Flume ◽  
Initial Stage ◽  
Different Types ◽  
Wave Trains ◽  
First Time

Green water events may present different features in the initial stage of interaction with the deck of a structure. It is therefore important to investigate the evolution of different types of green water, since not all the events interact with the deck at the same time. In this paper, the evolution of three types of green water events (dam-break, plunging-dam-break, and hammer-fist) are studied. The water surface elevations and volumes over the deck in consecutive green water events, generated by incident [wave trains in a wave flume, were analyzed using image-based methods. The results show multiple-valued water surface elevations in the early stage of plunging-dam-break and hammer-fist type events. Detailed experimental measurements of this stage are shown for the first time. The effect of wave steepness on the duration of the events, maximum freeboard exceedance, and volumes were also investigated. Although the hammer-fist type showed high freeboard exceedances, the plunging-dam-break type presented the largest volumes over the deck. Some challenges for further assessments of green water propagation are reported.

scholarly journals On kinematics of very steep waves

2013 ◽  
Vol 1 (2) ◽  
pp. 1487-1506
Author(s):  
L. Shemer
Keyword(s):  
Wave Breaking ◽  
Wide Spectrum ◽  
Wave Train ◽  
Vertical Acceleration ◽  
Wave Group ◽  
Wave Steepness ◽  
Large Wave ◽  
Wave Parameters ◽  
Steep Waves ◽  
Group Velocities

Abstract. Experiments on extremely steep waves generated in a large wave tank by focusing of a broad-banded wave train serve as a motivation for the theoretical analysis of the conditions leading to wave breaking. Particular attention is given to the crest of the steepest wave where both the horizontal velocity and the vertical acceleration attain their maxima. Analysis is carried out up to the 3rd order in wave steepness. The apparent, Eulerian and Lagrangian accelerations are computed for wave parameters observed in experiments. It is demonstrated that for a wave group with a wide spectrum, the crest propagation velocity differs significantly from both the phase and the group velocities of the peak wave. Conclusions are drawn regarding the applicability of various criteria for wave breaking.

Periodic waves in shallow water

1973 ◽  
Vol 59 (4) ◽  
pp. 625-644 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Wave Train ◽  
Surface Displacement ◽  
Finite Amplitude ◽  
Periodic Waves ◽  
Linear Superposition ◽  
Initial Wave ◽  
Regularized Long Wave Equation ◽  
Spatially Periodic ◽  
Uniform Channel ◽  
Wave Trains

An investigation is made into the evolution, from a sinusoidal initial wave train, of long periodic waves of small but finite amplitude propagating in one direction over water in a uniform channel. The spatially periodic surface displacement is expanded in a Fourier series with time-dependent coefficients. Equations for the Fourier coefficients are derived from three sources, namely the Korteweg–de Vries equation, the regularized long-wave equation proposed by Benjamin, Bona & Mahony (1972) and the relevant nonlinear boundary-value problem for Laplace's equation. Solutions are found by analytical and by numerical methods, and the three models of the system are compared. The surface displacement is found to take the form of an almost linear superposition of wave trains of the same wavelength as the initial wave train.

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