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 The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water

2015 ◽  
Vol 20 (4) ◽  
pp. 835-855
Author(s):  
D.P. Majumder ◽  
A.K. Dhar
Keyword(s):  
Growth Rate ◽  
Evolution Equation ◽  
Gravity Waves ◽  
Fourth Order ◽  
Order Term ◽  
Spectral Width ◽  
Higher Order ◽  
Order Contribution ◽  
Fourth Order Term ◽  
The Stability

Abstract A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.

Non-normal stability analysis of a shear current under surface gravity waves

2008 ◽  
Vol 609 ◽  
pp. 49-58
Author(s):  
D. AMBROSI ◽  
M. ONORATO
Keyword(s):  
Growth Rate ◽  
Modal Analysis ◽  
Gravity Waves ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Surface Gravity ◽  
Horizontal Shear ◽  
Surface Gravity Waves ◽  
Shear Current ◽  
The Stability

The stability of a horizontal shear current under surface gravity waves is investigated on the basis of the Rayleigh equation. As the differential operator is non-normal, a standard modal analysis is not effective in capturing the transient growth of a perturbation. The representation of the stream function by a suitable basis of bi-orthogonal eigenfunctions allows one to determine the maximum growth rate of a perturbation. It turns out that, in the considered range of parameters, such a growth rate can be two orders of magnitude larger than the maximum eigenvalue obtained by standard modal analysis.

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

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.

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