Surface water waves over a shallow canopy

2015 ◽  
Vol 768 ◽  
pp. 572-599 ◽  
Author(s):  
Benlong Wang ◽  
Xiaoyu Guo ◽  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Wave Attenuation ◽  
Multiple Scale ◽  
Small Scale ◽  
Vegetation Canopy ◽  
Unit Cells ◽  
Surface Water Waves ◽  
Slow Evolution ◽  
Scale Motion ◽  
Vertical Cylinders

The dynamics of water waves passing over a vegetation canopy is modelled theoretically. To simplify the geometry, we examine a periodic array of vertical cylinders fixed on a slowly varying seabed. The macroscale behaviour of wave attenuation is predicted based on microscale dynamics between plants. Interstitial turbulence is modelled by Reynolds equations with a locally constant eddy viscosity determined by energy considerations. Using the asymptotic method of multiple-scale expansions, the slow evolution of waves is derived by considering the coupling with the small-scale motion in the canopy. After numerical solution of the canonical boundary-value problem in a few unit cells, predictions of macroscale effects such as wave attenuation are made and compared with laboratory experiments. The counteracting effects of shoaling and dissipation are discussed for different vegetation densities.

scholarly journals Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders

2017 ◽  
Vol 813 ◽  
pp. 508-527 ◽  
Author(s):  
Luke G. Bennetts ◽  
Malte A. Peter ◽  
Fabien Montiel
Keyword(s):  
Water Waves ◽  
Solution Method ◽  
Bloch Wave ◽  
Linear Potential ◽  
Bloch Waves ◽  
Anderson Localisation ◽  
Attenuation Rate ◽  
Surface Water Waves ◽  
Finite Line ◽  
Vertical Cylinders

Linear potential-flow theory is used to study loads imposed on finite line arrays of rigid, bottom-mounted, surface-piercing, vertical cylinders by surface water waves. Perturbations in the cylinder locations are shown to damp the resonant loads experienced by the unperturbed array. A relationship is established between the damping and the phenomenon of Anderson localisation. Specifically, the Rayleigh–Bloch waves responsible for the resonant loads are shown to attenuate along the array when perturbations are introduced, resulting in localisation when the attenuation rate is sufficiently large with respect to the array length. Further, an efficient solution method for line arrays is introduced that captures the Rayleigh–Bloch wave modes supported by unperturbed arrays from the scattering characteristics of an individual cylinder.

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 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.

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.

scholarly journals Surface water waves as saddle points of the energy

2003 ◽  
Vol 17 (2) ◽  
pp. 199-220 ◽  
Author(s):  
B. Buffoni ◽  
�. S�r� ◽  
J.F. Toland
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Saddle Points ◽  
Surface Water Waves

Numerical study of surface water waves generated by mass movement

2013 ◽  
Vol 45 (5) ◽  
pp. 055506 ◽  
Author(s):  
Belgacem Ghozlani ◽  
Zouhaier Hafsia ◽  
Khlifa Maalel
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Numerical Study ◽  
Mass Movement ◽  
Surface Water Waves
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