Nonlinear evolutions of surface gravity waves on fluid of finite depth

1992 ◽  
Vol 69 (4) ◽  
pp. 609-611 ◽  
Author(s):  
Y. Matsuno
Keyword(s):  
Gravity Waves ◽  
Finite Depth ◽  
Surface Gravity ◽  
Surface Gravity Waves

Nonlinear effects on shoaling surface gravity waves

1984 ◽  
Vol 311 (1515) ◽  
pp. 1-41 ◽  
Keyword(s):  
Wave Field ◽  
Gravity Waves ◽  
Fourier Coefficients ◽  
Nonlinear Models ◽  
Finite Depth ◽  
Surface Gravity ◽  
Spectral Energy ◽  
Frequency Space ◽  
Surface Gravity Waves ◽  
Wide Range

Two nonlinear models that describe the shoaling of unidirectional surface gravity waves are developed. Based on variants of Boussinesq’s equations, the models are cast as a set of coupled evolution equations for the amplitudes and phases of the temporal Fourier modes of the wave field. Triad interactions across the entire wind wave frequency band (0.05-0.25 Hz) provide the mechanism for cross spectral energy transfers and modal phase modifications as the waves propagate shoreward through the shoaling region (10-3 m depth). A field experiment, designed to test the operational validity of the nonlinear shoaling models, provided data on wave parameters over a wide range of conditions. Three representative data sets illustrating different initial spectral shapes and subsequent evolutions are compared with predictions of the nonlinear shoaling models and linear, finite-depth theory. Power spectral comparisons, as well as spectra of coherence and relative phase between model predictions and data, indicate that the nonlinear models accurately predict Fourier coefficients of the wave field through the shoaling region sets. Differences between the predictions of the various models are related to differences in the models' dispersion relations. Although generally inferior to the nonlinear models, linear, finite-depth theory accurately predicts Fourier coefficients in regions of physical and frequency space where nonlinear evolution of the power spectrum is not observed, thus verifying the validity of the linear, finite-depth dispersion relation in limited portions of physical and frequency space in the shoaling region.

Phase velocity and dispersion relations of surface gravity waves in shallow sea

1994 ◽  
Vol 45 (6) ◽  
pp. 993
Author(s):  
VA Kalmykov
Keyword(s):  
Phase Velocity ◽  
Gravity Waves ◽  
Experimental Studies ◽  
Finite Depth ◽  
Dispersion Relations ◽  
Sea Surface ◽  
Surface Gravity ◽  
Linear Wave ◽  
Shallow Sea ◽  
Surface Gravity Waves

Phase velocity and dispersion relations of surface gravity waves on the sea have been modelled by two numerical methods and the results compared with previous experimental studies. Wave nonlinearities cause deviations from linear wave relations and these deviations are seen on the sea surface in the form of sharply crested waves. The effects are amplified if wave steepness increases or wave spectra become narrower. When the effects of finite depth of water are included in the calculations, the deviations from linearity are found to increase significantly.

scholarly journals On the Lagrangian description of steady surface gravity waves

2007 ◽  
Vol 589 ◽  
pp. 433-454 ◽  
Author(s):  
DIDIER CLAMOND
Keyword(s):  
Gravity Waves ◽  
Order Approximation ◽  
Mathematical Formulation ◽  
Finite Depth ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Lagrangian Description ◽  
Perturbation Scheme ◽  
Third Order ◽  
Surface Gravity Waves

This paper concerns the mathematical formulation of two-dimensional steady surface gravity waves in a Lagrangian description of motion. It is demonstrated first that classical second-order Lagrangian Stokes-like approximations do not exactly represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time – in other words, without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of the same order.

scholarly journals Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth

2013 ◽  
Vol 716 ◽  
pp. 316-348 ◽  
Author(s):  
Fabrice Ardhuin ◽  
T. H. C. Herbers
Keyword(s):  
Gravity Waves ◽  
Rayleigh Waves ◽  
Seismic Noise ◽  
Noise Source ◽  
Finite Depth ◽  
Surface Gravity ◽  
Noise Generation ◽  
Surface Gravity Waves ◽  
Wave Induced ◽  
Depth Effects

AbstractOceanic pressure measurements, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 s, which is believed to be excited by ocean surface gravity waves. Most of this noise is explained by a nonlinear wave–wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical work on seismic noise focused on surface (Rayleigh) waves, and did not consider finite-depth effects on the generating wave kinematics. These finite-depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that were limited to vertical propagation only. Finally, the noise generation theory is also extended beyond the domain of Rayleigh waves, giving the first quantitative expression for sources of seismic body waves. In the limit of slow phase speeds in the ocean wave forcing, the known and well-verified gravity wave result is obtained, which was previously derived for an incompressible ocean. The noise source of acoustic, acoustic-gravity and seismic modes are given by a mode-specific amplification of the same wave-induced pressure field near zero wavenumber.

scholarly journals Wake angle for surface gravity waves on a finite depth fluid

2015 ◽  
Vol 27 (6) ◽  
pp. 061701 ◽  
Author(s):  
Ravindra Pethiyagoda ◽  
Scott W. McCue ◽  
Timothy J. Moroney
Keyword(s):  
Gravity Waves ◽  
Finite Depth ◽  
Surface Gravity ◽  
Surface Gravity Waves

scholarly journals Modeling and control of surface gravity waves in a model of a copper converter

2008 ◽  
Vol 32 (9) ◽  
pp. 1696-1710 ◽  
Author(s):  
Eduardo Godoy ◽  
Axel Osses ◽  
Jaime H. Ortega ◽  
Alvaro Valencia
Keyword(s):  
Gravity Waves ◽  
Surface Gravity ◽  
Modeling And Control ◽  
Copper Converter ◽  
Surface Gravity Waves ◽  
And Control
Sign in / Sign up

Export Citation Format

Share Document