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.

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.

Measuring Sea Surface Gravity Waves Using Smartphones

Ports 2019 ◽  
2019 ◽  
Author(s):  
Matheus de Paula Vieira ◽  
Pedro Veras Guimarães
Keyword(s):  
Gravity Waves ◽  
Sea Surface ◽  
Surface Gravity ◽  
Surface Gravity Waves

Sea Surface Gravity Waves Excited by Dynamic Ground Motions from Large Regional Earthquakes

2020 ◽  
Vol 91 (4) ◽  
pp. 2268-2277 ◽  
Author(s):  
Yoshihiro Ito ◽  
Spahr C. Webb ◽  
Yoshihiro Kaneko ◽  
Laura M. Wallace ◽  
Ryota Hino
Keyword(s):  
Gravity Waves ◽  
Seismic Waves ◽  
Ground Motions ◽  
Maximum Amplitude ◽  
Sea Surface ◽  
Surface Gravity ◽  
Accretionary Wedge ◽  
Low Velocity ◽  
Infragravity Waves ◽  
Surface Gravity Waves

Abstract Infragravity waves on the sea surface near coastlines are occasionally excited by static displacement caused by large local earthquakes and recorded as tsunamis. However, tsunamis induced by ground motions from seismic waves are rarely observed, especially far from earthquake focal areas. We investigated seafloor pressure variations in the infragravity band at the Hikurangi subduction zone following the M 7.8 Kaikōura and M 7.1 Te Araroa earthquakes. Anomalous infragravity waves were observed at 0.2–20 mHz at sites overlying a low-velocity accretionary wedge offshore of the east coast of New Zealand’s North Island accompanying the Rayleigh-wave arrivals. The maximum amplitude of these ultra-low-frequency waves was similar to the tsunami that propagated from the earthquake focal area hours later. The amplitude of the pressure signal from these waves observed offshore varied inversely with water depth, suggesting that sea surface gravity waves were excited by Rayleigh or Love waves amplified within the accretionary wedge.

On the phase velocity effect of nonlinear interactions between surface gravity waves

2002 ◽  
Vol 14 (7) ◽  
pp. 2109 ◽  
Author(s):  
Mitsuhiro Tanaka ◽  
Catherine Phan Van ◽  
Olivier Oldrini
Keyword(s):  
Phase Velocity ◽  
Gravity Waves ◽  
Surface Gravity ◽  
Nonlinear Interactions ◽  
Surface Gravity Waves ◽  
Velocity Effect

scholarly journals Observations and a Model of Undertow over the Inner Continental Shelf

2008 ◽  
Vol 38 (11) ◽  
pp. 2341-2357 ◽  
Author(s):  
Steven J. Lentz ◽  
Melanie Fewings ◽  
Peter Howd ◽  
Janet Fredericks ◽  
Kent Hathaway
Keyword(s):  
Gravity Waves ◽  
Vertical Structure ◽  
Surf Zone ◽  
Stokes Drift ◽  
Vertical Shear ◽  
Surface Gravity ◽  
Linear Wave ◽  
Surface Gravity Waves ◽  
Offshore Flow ◽  
Offshore Transport

Abstract Onshore volume transport (Stokes drift) due to surface gravity waves propagating toward the beach can result in a compensating Eulerian offshore flow in the surf zone referred to as undertow. Observed offshore flows indicate that wave-driven undertow extends well offshore of the surf zone, over the inner shelves of Martha’s Vineyard, Massachusetts, and North Carolina. Theoretical estimates of the wave-driven offshore transport from linear wave theory and observed wave characteristics account for 50% or more of the observed offshore transport variance in water depths between 5 and 12 m, and reproduce the observed dependence on wave height and water depth. During weak winds, wave-driven cross-shelf velocity profiles over the inner shelf have maximum offshore flow (1–6 cm s−1) and vertical shear near the surface and weak flow and shear in the lower half of the water column. The observed offshore flow profiles do not resemble the parabolic profiles with maximum flow at middepth observed within the surf zone. Instead, the vertical structure is similar to the Stokes drift velocity profile but with the opposite direction. This vertical structure is consistent with a dynamical balance between the Coriolis force associated with the offshore flow and an along-shelf “Hasselmann wave stress” due to the influence of the earth’s rotation on surface gravity waves. The close agreement between the observed and modeled profiles provides compelling evidence for the importance of the Hasselmann wave stress in forcing oceanic flows. Summer profiles are more vertically sheared than either winter profiles or model profiles, for reasons that remain unclear.

scholarly journals Freely Decaying Weak Turbulence for Sea Surface Gravity Waves

2002 ◽  
Vol 89 (14) ◽  
Author(s):  
M. Onorato ◽  
A. R. Osborne ◽  
M. Serio ◽  
D. Resio ◽  
A. Pushkarev ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Sea Surface ◽  
Surface Gravity ◽  
Weak Turbulence ◽  
Surface Gravity Waves

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.

Sign in / Sign up

Export Citation Format

Share Document