Effect of long internal waves on the evolution of deep-water surface gravity waves

1982 ◽  
Vol 25 (3) ◽  
pp. 411 ◽  
Author(s):  
Yan-Chow Ma
Keyword(s):  
Internal Waves ◽  
Gravity Waves ◽  
Deep Water ◽  
Water Surface ◽  
Surface Gravity ◽  
Surface Gravity Waves

scholarly journals The effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline

1998 ◽  
Vol 40 (2) ◽  
pp. 190-206
Author(s):  
Sudebi Bhattacharyya ◽  
K. P. Das
Keyword(s):  
Growth Rate ◽  
Evolution Equation ◽  
Gravity Waves ◽  
Fourth Order ◽  
Deep Water ◽  
Water Surface ◽  
Spectral Width ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
The Stability

AbstractThe effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline is studied. A previously derived fourth order nonlinear evolution equation is used to find a spectral transport equation for a narrow band of surface gravity wave trains. This equation is used to study the stability of an initially homogeneous Lorentz shape of spectrum to small long wave-length perturbations for a range of spectral widths. The growth rate of the instability is found to decrease with the increase of spectral widths. It is found that the fourth order term in the evolution equation produces a decrease in the growth rate of the instability. There is stability if the spectral width exceeds a certain critical value. For a vanishing bandwidth the deterministic growth rate of the instability is recovered. Graphs have been plotted showing the variations of the growth rate of the instability against the wavenumber of the perturbation for some different values of spectral width, thermocline depth, angle of perturbation and wave steepness.

scholarly journals Nonlinear Spectral Synthesis of Soliton Gas in Deep-Water Surface Gravity Waves

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Pierre Suret ◽  
Alexey Tikan ◽  
Félicien Bonnefoy ◽  
François Copie ◽  
Guillaume Ducrozet ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Surface ◽  
Spectral Synthesis ◽  
Surface Gravity ◽  
Surface Gravity Waves

Radiation of internal waves from groups of surface gravity waves

2017 ◽  
Vol 829 ◽  
pp. 280-303 ◽  
Author(s):  
S. Haney ◽  
W. R. Young
Keyword(s):  
Internal Waves ◽  
Energy Flux ◽  
Gravity Waves ◽  
Three Dimensions ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Fourth Power ◽  
Buoyancy Frequency ◽  
Surface Gravity Waves ◽  
Short Period

Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This ‘Stokes pumping’ creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.

scholarly journals The formation of strip-like vortex motion by surface gravity waves

2021 ◽  
Vol 2056 (1) ◽  
pp. 012033
Author(s):  
A V Poplevin ◽  
S V Filatov ◽  
A A Levchenko
Keyword(s):  
Gravity Waves ◽  
Wave Vector ◽  
Water Surface ◽  
Vortex Flow ◽  
Vortex Motion ◽  
Surface Contamination ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
Measured Dependence ◽  
Effect Of Surface

Abstract We studied experimentally the generation of vortex flow by non-collinear gravity waves with a frequency of 2.34 Hz. The vortices formed on the water surface have the form of stripes, the width L=π/(2k sin θ) of which is determined by the wave vector k and the angle between them, and the length is determined by the size of the system. We demonstrate that the measured dependence Ω(t) can be described within the recently developed model that considers the Eulerian contribution to the generated vortex flow and the effect of surface contamination.

Surface Gravity Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Water Surface ◽  
Wave Pattern ◽  
The Body ◽  
Surface Gravity ◽  
Shallow Water Waves ◽  
Ship Waves ◽  
Surface Gravity Waves ◽  
Basic Fluid

This chapter deals with the underlying mathematics of surface gravity waves, defined as gravity waves observed on an air–sea interface of the ocean. Surface gravity waves, or surface waves, differ from internal waves, gravity waves that occur within the body of the water (such as between parts of different densities). Examples of gravity waves are wind-generated waves on the water surface, as well tsunamis and ocean tides. Wind-generated gravity waves on the free surface of the Earth's seas, oceans, ponds, and lakes have a period of between 0.3 and 30 seconds. The chapter first describes the basic fluid equations before discussing the dispersion relations, with a particular focus on deep water waves, shallow water waves, and wavepackets. It also considers ship waves and how dispersion affects the wave pattern produced by a moving object, along with long and short waves.

Sign in / Sign up

Export Citation Format

Share Document