Three-Dimensional Surface Water Waves Governed by the Forced Benney-Luke Equation

2015 ◽  
Vol 135 (4) ◽  
pp. 447-465 ◽  
Author(s):  
Christopher W. Curtis ◽  
Samuel S. P. Shen
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Three Dimensional ◽  
Surface Water Waves ◽  
Dimensional Surface

An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves

2001 ◽  
Vol 428 ◽  
pp. 273-304 ◽  
Author(s):  
C. SWAN ◽  
I. P. CUMMINS ◽  
R. L. JAMES
Keyword(s):  
Experimental Study ◽  
Surface Water ◽  
Water Waves ◽  
Water Surface ◽  
Two Dimensional ◽  
Current Profile ◽  
Water Particle ◽  
Vorticity Distribution ◽  
Surface Water Waves ◽  
Dimensional Surface

This paper describes an experimental study of two-dimensional surface water waves propagating on a depth-varying current with a non-uniform vorticity distribution. The investigation is divided into two parts. The first concerns the ‘equilibrium’ conditions in which the oscillatory wave motion and the current co-exist. Measurements of the water-surface elevation, the water-particle kinematics, and the near-bed pressure fluctuations are compared to a number of wave and wave–current solutions including a nonlinear model capable of incorporating the vertical structure of the current profile. These comparisons confirm that the near-surface vorticity leads to an important modification of the dispersion equation, and thus affects the nature of the wave-induced orbital motion over the entire water depth. However, the inclusion of vorticity-dependent terms within the dispersion equation is not sufficient to define the combined wave–current flow. The present results suggest that vorticity may lead to a significant change in the water-surface profile. If a current is positively sheared, dU/dz > 0, with negative vorticity at the water surface, as would be the case in a wind-driven current, a wave propagating in the same direction as the current will experience increased crest–trough asymmetry due to the vorticity distribution. With higher and sharper wave crests there is a corresponding increase in both the maximum water-particle accelerations and the maximum horizontal water-particle velocities. These results are consistent with previous theoretical calculations involving uniform vorticity distributions (Simmen & Saffman 1985 and Teles da Silva & Peregrine 1988).The second part of the study addresses the ‘gradually varying’ problem in which there are changes in the current, the wavelength and the wave height due to the initial interaction between the wave and the current. These data show that there is a large and non-uniform change in the current profile that is dependent upon both the steepness of the waves and the vorticity distribution. Furthermore, comparisons between the measured wave height change and a number of solutions based on the conservation of wave action, confirm that the vorticity distribution plays a dominant role. In the absence of a conservation equation for wave action appropriate for nonlinear waves on a depth-varying current, an alternative approach based on the conservation of total energy flux, first proposed by Longuet-Higgins & Stewart (1960), is shown to be in good agreement with the measured data.

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.

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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