Resonant reflection of surface water waves by periodic sandbars

1985 ◽  
Vol 152 ◽  
pp. 315-335 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Resonance Condition ◽  
Nonlinear Effects ◽  
Sea Bottom ◽  
Strong Reflection ◽  
Weak Reflection ◽  
Surface Water Waves ◽  
Wave Induced ◽  
Incident Waves ◽  
Resonant Reflection

One of the possible mechanisms of forming offshore sandbars parallel to a coast is the wave-induced mass transport in the boundary layer near the sea bottom. For this mechanism to be effective, sufficient reflection must be present so that the waves are partially standing. The main part of this paper is to explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met. For constant mean depth and simple harmonic waves this resonance has been studied by Davies (1982), whose theory, is however, limited to weak reflection and fails at resonance. Comparison of the strong reflection theory with Heathershaw's (1982) experiments is made. Furthermore, if the incident waves are slightly detuned or slowly modulated in time, the scattering process is found to depend critically on whether the modulational frequency lies above or below a threshold frequency. The effects of mean beach slope are also studied. In addition, it is found for periodically modulated wave groups that nonlinear effects can radiate long waves over the bars far beyond the reach of the short waves themselves. Finally it is argued that the breakpoint bar of ordinary size formed by plunging breakers can provide enough reflection to initiate the first few bars, thereby setting the stage for resonant reflection for more bars.

Formation of sand bars under surface waves

2000 ◽  
Vol 416 ◽  
pp. 315-348 ◽  
Author(s):  
JIE YU ◽  
CHIANG C. MEI
Keyword(s):  
Evolution Equation ◽  
Water Waves ◽  
Layer Structure ◽  
Effective Diffusivity ◽  
Sand Bars ◽  
Surface Water Waves ◽  
Concurrent Processes ◽  
Bed Stress ◽  
Forced Diffusion ◽  
Wave Induced

A quantitative theory is described for the formation mechanism of sand bars under surface water waves. By assuming that the slopes of waves and bars are comparably gentle and sediment motion is dominated by the bedload, an approximate evolution equation for bar height is derived. The wave field and the boundary layer structure above the wavy bed are worked out to the accuracy needed for solving this evolution equation. It is shown that the evolution of sand bars is a process of forced diffusion. This is unlike that for sand ripples which is governed by an instability. The forcing is directly caused by the non-uniformity of the wave envelope, hence of the wave-induced bottom shear stress associated with wave reflection, while the effective diffusivity is the consequence of gravity and modified by the local bed stress. During the slow formation, bars and waves affect each other through the Bragg scattering mechanism, which consists of two concurrent processes: energy transfer between waves propagating in opposite directions and change of their wavelengths. Both effects are found to be controlled locally by the position of bar crests relative to wave nodes. Comparison with available laboratory experiments is discussed and theoretical examples are studied to help understand the coupled evolution of bars and waves in the field.

Bragg scattering of water waves by a doubly periodic seabed

1988 ◽  
Vol 192 ◽  
pp. 51-74 ◽  
Author(s):  
Mamoun Naciri ◽  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Transverse Direction ◽  
Resonance Condition ◽  
Phase Matching ◽  
Two Dimensional ◽  
Bragg Scattering ◽  
Reflected Waves ◽  
One Dimensional ◽  
Resonant Reflection ◽  
Bed Waves

We extend the recent work on Bragg scattering of water waves by one-dimensional parallel bars of sinusoidal profile to two-dimensional, doubly sinusoidal bed waves. The resonance condition governing the phase matching between the incident, scattered and bed waves is now more complicated and a much richer variety of resonant reflection can occur. In particular, for one normally incident wave there can be two reflected waves forming a standing wave in the transverse direction. Solutions for a wide strip of bed waves are discussed for incident water waves satisfying approximately the Bragg resonance condition. Modifications for a two-dimensional array of hemispheroids are also given. Possible application to the design of submerged breakwaters is suggested.

scholarly journals Wave-Induced Accelerations of a Fish-Farm Elastic Floater: Experimental and Numerical Studies

2014 ◽  
Author(s):  
Peng Li ◽  
Odd M. Faltinsen ◽  
Marilena Greco
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Nonlinear Effects ◽  
Fish Farm ◽  
Frequency Domain Method ◽  
Frequency Dependency ◽  
Numerical Studies ◽  
Vertical Accelerations ◽  
Steep Waves ◽  
Wave Induced

Numerical simulations and experiments of an elastic circular collar of a floating fish farm are reported. The floater model without netting structure is moored with nearly horizontal moorings and tested in regular deep-water waves of different steepnesses and periods without current. Local overtopping of waves were observed in steep waves. The focus here is on the vertical accelerations along the floater in the different conditions. The experiments show that higher-order harmonics of the accelerations matter. A 3D weak-scatter model with partly nonlinear effects as well as a 3D linear frequency-domain method based on potential flow are used. From their comparison against the measurements, strong 3D and frequency dependency effects as well as flexible floater motions matter. The weak-scatter model can only partly explain the nonlinearities present in the measured accelerations.

Current effects on resonant reflection of surface water waves by sand bars

1988 ◽  
Vol 186 ◽  
pp. 501-520 ◽  
Author(s):  
James T. Kirby
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Multiple Scale ◽  
Periodic Wave ◽  
Sand Bars ◽  
Linear Waves ◽  
Surface Water Waves ◽  
Wave Trains ◽  
Resonant Reflection ◽  
A Current

The effect of currents flowing across a bar field on resonant reflection of surface waves by the bars is investigated. Using a multiple-scale expansion, evolution equations for the amplitudes of linear waves are derived and used to investigate the reflection of periodic wave trains with steady amplitude for both normal and oblique incidence. The presence of a current is found to shift resonant frequencies by possibly significant amounts and is also found to enhance reflection of waves by bar fields due to the additional effect of the perturbed current field.

scholarly journals A NUMERICAL STUDY OF THE IMPORTANCE OF NONLINEAR EFFECTS FOR FABRY-PEROT RESONANCE OF WATER WAVES

2018 ◽  
pp. 26
Author(s):  
Michel Benoit ◽  
Jie Zhang
Keyword(s):  
Water Waves ◽  
Numerical Study ◽  
Wave Train ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Resonance Phenomenon ◽  
Linear Wave ◽  
Flat Bottom ◽  
Fabry Perot ◽  
Incident Waves

When a regular wave train propagates over a patch of periodic bottom corrugations on an otherwise flat bottom (with still water depth h), the so called Bragg resonance phenomenon can appear, leading to a significant reflection of the incident waves due to the presence of the ripple patch. This effect is maximum when the wavelength of the surface waves (noted A = 2n/k) is twice that of the bottom ripples (noted Ab = 2n/kb). This phenomenon has been studied both experimentally (e.g. Davies & Heathershaw, 1984) and theoretically within the linear wave theory framework (e.g. Mei, 1985; Dalrymple & Kirby, 1986).

scholarly journals Wave-Induced Accelerations of a Fish-Farm Elastic Floater: Experimental and Numerical Studies

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Peng Li ◽  
Odd M. Faltinsen ◽  
Marilena Greco
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Fish Farm ◽  
Frequency Domain Method ◽  
Frequency Dependency ◽  
Numerical Studies ◽  
Vertical Accelerations ◽  
Steep Waves ◽  
Wave Induced

Numerical simulations and experiments of an elastic circular collar of a floating fish farm are reported. The floater model without netting structure is moored with nearly horizontal moorings and tested in regular deep-water waves of different steepnesses and periods without current. Local overtopping of waves was observed in steep waves. The focus here is on the vertical accelerations along the floater in the different conditions. The experiments show that higher-order harmonics of the accelerations matter. A three-dimensional (3D) weak-scatter model with partly nonlinear effects as well as a 3D linear frequency-domain method based on potential flow are used. From their comparison against the measurements, strong 3D and frequency dependency effects as well as flexible floater motions matter. The weak-scatter model can only partly explain the nonlinearities present in the measured accelerations.

scholarly journals Multiple stopbands and wavefield asymmetry of surface water waves in non-Bragg structures

AIP Advances ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 015215
Author(s):  
Joshua-Masinde Kundu ◽  
Ting Liu ◽  
Jia Tao ◽  
Jia-Yi Zhang ◽  
Ya-Xian Fan ◽  
...  
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Bragg Structures ◽  
Surface Water Waves

Defect modes in non-Bragg resonant structures for guided surface water waves

Wave Motion ◽  
2021 ◽  
pp. 102766
Author(s):  
Joshua-Masinde Kundu ◽  
Ting Liu ◽  
Jia Tao ◽  
Bo-Yang Ma ◽  
Jia-Yi Zhang ◽  
...  
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Defect Modes ◽  
Resonant Structures ◽  
Surface Water Waves

The Stochastic Parametric Mechanism for Growth of Wind-Driven Surface Water Waves

2008 ◽  
Vol 38 (4) ◽  
pp. 862-879 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Surface Water ◽  
Growth Rates ◽  
Atmospheric Pressure ◽  
Water Waves ◽  
Wave Amplitude ◽  
Pressure Fluctuations ◽  
Theoretical Understanding ◽  
Wave Growth ◽  
Atmospheric Pressure Fluctuations ◽  
Surface Water Waves

Abstract Theoretical understanding of the growth of wind-driven surface water waves has been based on two distinct mechanisms: growth due to random atmospheric pressure fluctuations unrelated to wave amplitude and growth due to wave coherent atmospheric pressure fluctuations proportional to wave amplitude. Wave-independent random pressure forcing produces wave growth linear in time, while coherent forcing proportional to wave amplitude produces exponential growth. While observed wave development can be parameterized to fit these functional forms and despite broad agreement on the underlying physical process of momentum transfer from the atmospheric boundary layer shear flow to the water waves by atmospheric pressure fluctuations, quantitative agreement between theory and field observations of wave growth has proved elusive. Notably, wave growth rates are observed to exceed laminar instability predictions under gusty conditions. In this work, a mechanism is described that produces the observed enhancement of growth rates in gusty conditions while reducing to laminar instability growth rates as gustiness vanishes. This stochastic parametric instability mechanism is an example of the universal process of destabilization of nearly all time-dependent flows.

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