scholarly journals LABORATORY EXPERIMENTS OF BICHROMATIC WAVE GROUPS PROPAGATION ON A GENTLE SLOPE BEACH PROFILE AND ENERGY TRANSFER TO LOW AND HIGH FREQUENCY COMPONENTS

2017 ◽  
pp. 6 ◽  
Author(s):  
Enrique M Padilla ◽  
Jose M Alsina
Keyword(s):  
High Frequency ◽  
Wave Breaking ◽  
Low Frequency ◽  
Primary Wave ◽  
Wave Group ◽  
Wave Groups ◽  
Long Wave ◽  
Wave Conditions ◽  
Hf Wave ◽  
Nonlinear Energy

This work presents a first analysis of experimental data studying the influence of the frequency bandwidth on the propagation of bichromatic wave groups over a constant 1:100 beach slope. The use of a large spatial cross-shore resolution and Bi-Spectral analysis techniques allows the identification of nonlinear energy transfers along the propagation of wave groups. During wave-group shoaling, nonlinear coupling between the primary wave frequencies results in a larger growth of superharmonics for narrow-banded wave conditions, increasing the skewness of the wave and leading to eventual instabilities and earlier high frequency (hf) wave breaking compared to the broad-banded wave condition. Regarding the growth of low frequency (lf) component, the data analysis has shown a larger growth of the incident bound long wave (IBLW) for broad-banded wave conditions. It is generally assumed that the transferred energy from the primary wave components to subharmonics does not affect the short wave energy budget. Here, the opposite is hypothesised, and a larger growth of the IBLW for broad-banded wave conditions is accompanied of a larger reduction of the primary wave components, a reduced growth of hf components and, consequently, a reduction in the growth of hf wave asymmetry during wave group shoaling. Conversely for narrow-banded wave conditions, a reduced IBLW growth is associated with a larger growth of hf wave asymmetry. After hf wave breaking, within the low frequency domain (lf), the IBLW decays slightly for narrow-banded conditions, consistent with a reduction in radiation stress forcing. This involves a nonlinear energy transfer from the wave group frequency back to hf components. The remaining lf energy, Outgoing Free Long Wave (OFLW), reflects back at the shoreline. However, for broad-banded wave conditions, strong dissipation and minimal reflection of lf components occurs close to the shoreline, which might be caused by lf wave breaking.

scholarly journals Free and forced components of shoaling long waves in the absence of short wave breaking

2021 ◽  
Author(s):  
Stephanie Contardo ◽  
Ryan J. Lowe ◽  
Jeff E. Hansen ◽  
Dirk P. Rijnsdorp ◽  
François Dufois ◽  
...  
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Phase Relationship ◽  
Wave Model ◽  
Short Wave ◽  
Long Waves ◽  
Wave Group ◽  
Wave Groups ◽  
Long Wave ◽  
Complete Representations

AbstractLong waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free long generation, through breakpoint forcing and bound wave release mechanisms, we highlight the importance of an additional free long wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free long wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.

scholarly journals WAVE GROUPINESS AS A SOURCE OF NEARSHORE LONG WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 38 ◽  
Author(s):  
Jeffrey H. List
Keyword(s):  
Wave Amplitude ◽  
Cross Correlation ◽  
Surf Zone ◽  
Low Frequency ◽  
Long Waves ◽  
Progressive Wave ◽  
Wave Groups ◽  
Long Wave ◽  
Cross Correlation Analysis ◽  
Limited Usefulness

Data from a low energy swell-dominated surf zone are examined for indications that observed low frequency motions are simply group-forced bounded long waves. Time series of wave amplitude are compared to filtered long wave records through cross-spectral and cross-correlation analysis. These methods are found to have limited usefulness until long waves are separated into seaward and shoreward components. Then a clear picture of a rapidly shoaling bounded long wave emerges, with a minimum of nearly one fourth of the long wave amplitude being explainable by this type of motion close to shore. Through the zone in which waves were breaking, and incident wave amplitude variability decreased by 50%, the contribution from the bounded long wave continued to increase at a rate much greater than a simple shoaling effect. Also present are clear signs that this amplified bounded long wave is reflected from a position close to the shoreline, and is thus released from wave groups as a free, offshore-progressive wave.

Harbour resonance due to set-down beneath wave groups

1977 ◽  
Vol 79 (1) ◽  
pp. 71-92 ◽  
Author(s):  
E. C. Bowers
Keyword(s):  
Group Velocity ◽  
Wave System ◽  
Primary Wave ◽  
Natural Oscillations ◽  
Natural Period ◽  
Wave Groups ◽  
Long Period ◽  
Natural Modes ◽  
Long Wave ◽  
Harbour Resonance

Natural modes of water oscillation inside harbours are known to occur with periods of the order of minutes. It seems likely that these oscillations are excited by water fluctuations of similar period outside the harbour and an often quoted cause of such fluctuations is the phenomenon of surf beats. These are thought to be long waves which are reflected back out to sea when a primary wave system breaks upon a beach. In this paper it is shown theoretically that the natural oscillations of a harbour can be excited directly, without breaking of the primary wave system, by set-down beneath wave groups, which is a long-period disturbance travelling towards the shore line at the group velocity. This theory is in agreement with model experimental results which show that, when the group period is close to a natural period of the harbour, resonance will occur with the set-down behaving as if it were a real long wave.

Frequency spectra evolution of two-dimensional focusing wave groups in finite depth water

2011 ◽  
Vol 688 ◽  
pp. 169-194 ◽  
Author(s):  
Zhigang Tian ◽  
Marc Perlin ◽  
Wooyoung Choi
Keyword(s):  
Energy Transfer ◽  
Wave Breaking ◽  
Frequency Region ◽  
Breaking Wave ◽  
Two Dimensional ◽  
Spectral Bandwidth ◽  
Frequency Spectra ◽  
Wave Groups ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

AbstractAn experimental and numerical study of the evolution of frequency spectra of dispersive focusing wave groups in a two-dimensional wave tank is presented. Investigations of both non-breaking and breaking wave groups are performed. It is found that dispersive focusing is far more than linear superposition, and that it undergoes strongly nonlinear processes. For non-breaking wave groups, as the wave groups propagate spatial evolution of wave frequency spectra, spectral bandwidth, surface elevation skewness, and kurtosis are examined. Nonlinear energy transfer between the above-peak ($f/ {f}_{p} = 1. 2{{\ndash}}1. 5$) and the higher-frequency ($f/ {f}_{p} = 1. 5\text{{\ndash}} 2. 5$) regions, with ${f}_{p} $ being the spectral peak frequency, is demonstrated by tracking the energy level of the components in the focusing and defocusing process. Also shown is the nonlinear energy transfer to the lower-frequency components that cannot be detected easily by direct comparisons of the far upstream and downstream measurements. Energy dissipation in the spectral peak region ($f/ {f}_{p} = 0. 9\text{{\ndash}} 1. 1$) and the energy gain in the higher-frequency region ($f/ {f}_{p} = 1. 5\text{{\ndash}} 2. 5$) are quantified, and exhibit a dependence on the Benjamin–Feir Index (BFI). In the presence of wave breaking, the spectral bandwidth reduces as much as 40 % immediately following breaking and eventually becomes much smaller than its initial level. Energy levels in different frequency regions are examined. It is found that, before wave breaking onset, a large amount of energy is transferred from the above-peak region ($f/ {f}_{p} = 1. 2\text{{\ndash}} 1. 5$) to the higher frequencies ($f/ {f}_{p} = 1. 5\text{{\ndash}} 2. 5$), where energy is dissipated during the breaking events. It is demonstrated that the energy gain in the lower-frequency region is at least partially due to nonlinear energy transfer prior to wave breaking and that wave breaking may not necessarily increase the energy in this region. Complementary numerical studies for breaking waves are conducted using an eddy viscosity model previously developed by the current authors. It is demonstrated that the predicted spectral change after breaking agrees well with the experimental measurements.

SPECTRAL WAVE MODELLING IN TIDAL INLET SEAS: RESULTS FROM THE SBW WADDEN SEA PROJECT

2011 ◽  
Vol 1 (32) ◽  
pp. 44 ◽  
Author(s):  
Ap Van Dongeren ◽  
Andre Van der Westhuysen ◽  
Jacco Groeneweg ◽  
Gerbrant Van Vledder ◽  
Joost Lansen ◽  
...  
Keyword(s):  
Wave Height ◽  
Wave Breaking ◽  
Wadden Sea ◽  
Low Frequency ◽  
Wave Model ◽  
Finite Depth ◽  
Transformation Model ◽  
Wave Transformation ◽  
Sea Waves ◽  
Wave Conditions

Over the last five years a research program has been carried out to assess the performance of the spectral wave model SWAN in the Wadden Sea so that it may be used for the transformation of offshore wave conditions to wave boundary conditions near the sea defenses (dikes and dunes). The assessment was done on the basis of extensive wave measurements conducted in Ameland inlet and the Dutch Eastern Wadden Sea, as well as relevant data from lakes and estuaries. After a first round of assessment, we found that SWAN performed reasonably well for storm conditions but three aspects required further attention. Firstly, focusing on the main channel, SWAN formulations needed to be modified in order to eliminate overprediction of the significant wave height in opposing currents. Secondly, the primary spectral peak of North Sea waves penetrating into the inlet was underpredicted. Best results were obtained when the refraction of low-frequency waves was limited and the bottom friction coefficient was set at a lower value than the current default for wind seas. Thirdly, over the tidal flats the computed ratio of integral wave height over water depth showed an apparent upper limit using the conventional Battjes and Janssen (1978) depth-limited wave breaking formulation, because the wave growth over finite depth is hampered by the present formulation of depth-induced wave breaking. The problem has been solved using a new breaker formulation. All these improvements have lead to a wave transformation model with which reliable wave conditions in the Wadden Sea and related complex areas can be determined.

scholarly journals Investigation of High-Frequency Internal Wave Interactions with an Enveloped Inertia Wave

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
B. Casaday ◽  
J. Crockett
Keyword(s):  
Internal Wave ◽  
High Frequency ◽  
Wave Breaking ◽  
Large Scale ◽  
Critical Level ◽  
Low Frequency ◽  
Small Scale ◽  
Wave Interactions ◽  
Frequency Wave ◽  
Action Density

Using ray theory, we explore the effect an envelope function has on high-frequency, small-scale internal wave propagation through a low-frequency, large-scale inertia wave. Two principal interactions, internal waves propagating through an infinite inertia wavetrain and through an enveloped inertia wave, are investigated. For the first interaction, the total frequency of the high-frequency wave is conserved but is not for the latter. This deviance is measured and results of waves propagating in the same direction show the interaction with an inertia wave envelope results in a higher probability of reaching that Jones' critical level and a reduced probability of turning points, which is a better approximation of outcomes experienced by expected real atmospheric interactions. In addition, an increase in wave action density and wave steepness is observed, relative to an interaction with an infinite wavetrain, possibly leading to enhanced wave breaking.

scholarly journals Generation, Transformation, and Scattering of Long Waves Induced by a Short-Wave Group over Finite Topography

2011 ◽  
Vol 41 (10) ◽  
pp. 1842-1859 ◽  
Author(s):  
Qingping Zou
Keyword(s):  
Analytical Solutions ◽  
Wave Train ◽  
Short Wave ◽  
Long Waves ◽  
Wave Group ◽  
Wave Groups ◽  
Long Wave ◽  
Wave Orbital Velocity ◽  
Variable Water ◽  
Horizontal Bottom

Abstract Second-order analytical solutions are constructed for various long waves generated by a gravity wave train propagating over finite variable depth h(x) using a multiphase Wentzel–Kramers–Brillouin (WKB) method. It is found that, along with the well-known long wave, locked to the envelope of the wave train and traveling at the group velocity Cg, a forced long wave and free long waves are induced by the depth variation in this region. The forced long wave depends on the depth derivatives hx and hxx and travels at Cg, whereas the free long waves depend on h, hx, and hxx and travel in the opposite directions at . They interfere with each other and generate free long waves radiating away from this region. The author found that this topography-induced forced long wave is in quadrature with the short-wave group and that a secondary long-wave orbital velocity is generated by variable water depth, which is in quadrature with its horizontal bottom counterpart. Both these processes play an important role in the energy transfer between the short-wave groups and long waves. These behaviors were not revealed by previous studies on long waves induced by a wave group over finite topography, which calculated the total amplitude of long-wave components numerically without consideration of the phase of the long waves. The analytical solutions here also indicate that the discontinuity of hx and hxx at the topography junctions has a significant effect on the scattered long waves. The controlling factors for the amplitudes of these long waves are identified and the underlying physical processes systematically investigated in this presentation.

scholarly journals ON THE INITIATION OF NEARSHORE MORPHOLOGICAL RHYTHMICITY

2011 ◽  
Vol 1 (32) ◽  
pp. 47
Author(s):  
Matthieu Andreas De Schipper ◽  
Roshanka Ranasinghe ◽  
Ad Reniers ◽  
Marcel Stive
Keyword(s):  
Numerical Model ◽  
Wave Period ◽  
Wave Group ◽  
Initiation Time ◽  
Length Scales ◽  
Long Wave ◽  
Storm Wave ◽  
Wave Conditions

Nearshore rhythmicity is often initiated in the period just after a storm where the subtidal bar is turned alongshore uniform. The initiation time as well as the length scales of the created rhythmicity varies from one storm period to another. Here we show that the post-storm wave conditions are related to the initiation of the morphological rhythmicity. Narrow-banded and long wave period, both proxies for swell waves, are often found to be present priorto the initiation of rhythmicity. Furthermore, numerical model computations illustrate that swell waves induce significantly larger wave group induced velocities on the bar. These findings imply that the arrival of swell waves can initiate and stimulate the nearshore morphological rhythmicity.

scholarly journals SEPARATION OF LOW-FREQUENCY WAVES BY AN ANALYTICAL METHOD

2011 ◽  
Vol 1 (32) ◽  
pp. 64
Author(s):  
Yuxiang Ma ◽  
Guohai Dong ◽  
Xiaozhou Ma
Keyword(s):  
Fluid Mechanics ◽  
Gravity Waves ◽  
Present Method ◽  
Low Frequency ◽  
Wave Generation ◽  
Coastal Engineering ◽  
Wave Groups ◽  
International Conference ◽  
Long Wave ◽  
Low Frequency Waves

A new method for separating low-frequency waves in time domain is proposed by constructing the analytical signals of the measured waves. Using three simultaneous wave records, the time series of incident bound, free and reflected low-frequency waves can be obtained by the present method. This method is only suitable for separating monochromatic low-frequency waves. The applicability of the method is examined by numerical tests. The results show that the present method can give accurate results over sloping beaches when water depth (kh) is larger than 0.2. Then, the present method is used to study an experiment of low-frequency waves over a mild slope beach. References Bakkenes, H.J. 2002. Observation and separation of bound and free low-frequency waves in the nearshore zone, in Faculty of Civil Engineering and Geosciences. Delft University of Technology: Delft. Baldock, T.E., D.A., Huntley, P.A.D., Bird, T.O., Hare, and G.N., Bullock. 2000. Breakpoint generated surf beat induced by bichromatic wave groups. Coastal Engineering. 30 (2-4): 213-242. http://dx.doi.org/10.1016/S0378-3839(99)00061-7 Battjes, J.A., Bakkenes, H.J., Janssen, T.T., van Dongeren, A.R. 2004. Shoaling of subharmonic gravity waves. J. Geophys. Res., 109(C2): C02009. http://dx.doi.org/10.1029/2003JC001863 Bowers, E.C. 1977. Harbour resonance due to set-down beneath wave groups. Journal of Fluid Mechanics. 79: 71-92. http://dx.doi.org/10.1017/S0022112077000044 Cohen, L. 1995. Time Frequency Analysis: Theory and Applications. Prentice Hall Englewood Cliffs, New Jersey. Dong, G.H., X.Z., Ma, M., Perlin, Y.X., Ma, B., Yu, and G., Wang. 2009. Experimental Study of long wave generation on sloping bottoms. Coastal Engineering, 56(1), 82-89. http://dx.doi.org/10.1016/j.coastaleng.2008.10.002 Kamphuis, J.W. 2000. Designing for low frequency waves. Proceedings of 27th International Conference on Coastal Engineering. Sydney, Australian. 1434-1447. Kostense, J.K. 1984. Measurements of surf beat and set-down beneath wave groups. Proceedings of 19th International Conference on Coastal Engineering. Houston, USA. 724-740. Longuet-Higgins, M.S. and R.W., Stewart. 1962. Radiation stress and mass transport in gravity waves with application to 'surfbeat'. Journal of Fluid Mechanics. 13: 481-504 http://dx.doi.org/10.1017/S0022112062000877 Mallat, S. 1999. A Wavelet Tour of Signal Processing. Academic Press. PMCid:407895 Nagai, T., N., Hashimoto, T., Asai, et al. 1994. Relationship of a moored vessel in a harbor and a long wave caused by wave groups. Proceedings of 17th International Conference on Coastal Engineering. Kobe, Japan. 847-861. Schäffer, H.A. 1993. Second-orderwavemaker theory for irregularwaves.Ocean Engineering. 23 (1), 47–88. http://dx.doi.org/10.1016/0029-8018(95)00013-B Symonds, G.D.A., D.A., Huntley, and A.J., Bowen. 1982. Two-dimensional surf beat-long-wave generation by a time-varying breakpoint. Journal of Geophysical Research. 87(C1): 492-498. http://dx.doi.org/10.1029/JC087iC01p00492 Yu, J. and C.C., Mei. 2000. Formation of sand bars under surface waves. Journal of Fluid Mechanics. 416: 315-348. http://dx.doi.org/10.1017/S0022112000001063

scholarly journals The Role of Transient Eddies in North Pacific Blocking Formation and Its Seasonality

2020 ◽  
Vol 77 (7) ◽  
pp. 2453-2470 ◽  
Author(s):  
Jaeyoung Hwang ◽  
Patrick Martineau ◽  
Seok-Woo Son ◽  
Takafumi Miyasaka ◽  
Hisashi Nakamura
Keyword(s):  
North Pacific ◽  
High Frequency ◽  
Wave Breaking ◽  
Low Frequency ◽  
Heat Fluxes ◽  
Background Flow ◽  
Budget Analysis ◽  
The Cross ◽  
A Minor

AbstractThe mechanism of North Pacific (NP) blocking formation is investigated by conducting a reanalysis-based budget analysis of the quasigeostrophic geopotential tendency equation. It is confirmed that the amplification of NP blocking anomalies primarily results from vorticity fluxes with a minor contribution of heat fluxes. In winter, the cross-frequency vorticity fluxes, resulting from interactions between high-frequency eddies and the slowly varying background flow, dominate the blocking formation. The cross-frequency vorticity fluxes, however, become substantially weaker and comparable to the low-frequency vorticity fluxes in summer. This seasonality indicates that the mechanism of NP blocking formation varies with seasons due to the different background flow. It is further found that NP blocking formation is not sensitive to the region of formation (i.e., western vs eastern NP) nor to the type of wave breaking (i.e., cyclonic vs anticyclonic wave breaking).

Sign in / Sign up

Export Citation Format

Share Document