scholarly journals Cyclic gravity waves in deep water

1983 ◽  
Vol 25 (1) ◽  
pp. 2-15 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Wave Height ◽  
Gravity Waves ◽  
Deep Water ◽  
Fourier Transforms ◽  
Surface Displacement ◽  
Surface Boundary ◽  
Surface Boundary Conditions ◽  
Method Of Solution ◽  
Nonlinear Surface ◽  
The Waves

AbstractNumerical evidence is presented for the existence of unsteady periodic gravity waves of large height in deep water whose shape changes cyclically as they propagate. It is found that, for a given wavelength and maximum wave height, cyclic waves with a range of cyclic periods exist, with a steady wave of permanent shape being an extreme member of the range. The method of solution, using Fourier transforms of the nonlinear surface boundary conditions, determines the irrotational velocity field in the water and the water surface displacement as functions of space and time, from which properties of the waves are demonstrated. In particular, it is shown that cyclic waves are closer to the point of wave breaking than are steady permanent waves of the same wave height and wavelength.

Wave Kinematics Computed With the Nonlinear Schro¨dinger Method for Deep Water

1999 ◽  
Vol 121 (2) ◽  
pp. 126-130 ◽  
Author(s):  
K. Trulsen
Keyword(s):  
Time Series ◽  
Gravity Waves ◽  
Deep Water ◽  
Water Wave ◽  
Surface Displacement ◽  
Horizontal Position ◽  
Two Dimensional ◽  
Limited Bandwidth ◽  
Wave Kinematics ◽  
The Waves

The nonlinear Schro¨dinger method for water wave kinematics under two-dimensional irregular deepwater gravity waves is developed. Its application is illustrated for computation of the velocity and acceleration fields from the time-series of the surface displacement measured at a fixed horizontal position. The method is based on the assumption that the waves have small steepness and limited bandwidth.

The interaction of deep-water gravity waves and an annular current: linear theory

1993 ◽  
Vol 248 ◽  
pp. 153-172 ◽  
Author(s):  
Marius Gerber
Keyword(s):  
Linear Theory ◽  
Gravity Waves ◽  
Deep Water ◽  
Large Scale ◽  
Ray Theory ◽  
Velocity Parameter ◽  
Dimensional Parameters ◽  
The Waves ◽  
Angle Parameter

The interaction of linear, steady, axisymmetric deep-water gravity waves with preexisting large-scale annular currents has been investigated. Waves originating inside the annulus as well as waves approaching the annulus from the outside were studied. Exact linear ray solutions were obtained and involve two non-dimensional parameters, a radius-angle parameter and a velocity parameter. For opposing currents the linear solutions also allow the derivation of radii at which the waves are blocked, reflected at a linear caustic or stopped by the current. Various examples of rays interacting with an annular current are presented to illustrate aspects of the solutions obtained. In particular, the behaviour of the ray solutions at blocking, reflection and stopping is investigated. Linear ray theory is shown to fail at caustics and caustic solutions are briefly discussed.

Refraction of gravity waves by weak current gradients

2001 ◽  
Vol 442 ◽  
pp. 157-159 ◽  
Author(s):  
KRISTIAN B. DYSTHE
Keyword(s):  
Surface Waves ◽  
Group Velocity ◽  
Gravity Waves ◽  
Deep Water ◽  
Current Velocity ◽  
Water Surface ◽  
Simple Formula ◽  
Vertical Component ◽  
Weak Current ◽  
The Waves

When deep water surface waves cross an area with variable current, refraction takes place. If the group velocity of the waves is much larger than the current velocity we show that the curvature of a ray, χ, is given by the simple formula χ = ζ/vg. Here ζ is the vertical component of the current vorticity and vg is the group velocity.

scholarly journals On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

2000 ◽  
Vol 42 (2) ◽  
pp. 277-286 ◽  
Author(s):  
A. Chakrabarti
Keyword(s):  
Surface Water ◽  
Boundary Conditions ◽  
Water Waves ◽  
Surface Boundary ◽  
Transmission Coefficients ◽  
Sharp Discontinuity ◽  
Surface Boundary Conditions ◽  
Method Of Solution ◽  
Surface Water Waves ◽  
Carleman Type

AbstractClosed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

Interactions of Gravity Waves Generated by a Moving Source With the Shelf: Laboratory Experiment

2003 ◽  
Author(s):  
Yakov Afanasyev ◽  
Vasily Korabel
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Laboratory Experiments ◽  
Phase Speed ◽  
Critical Value ◽  
Total Reflection ◽  
Supercritical Regime ◽  
Subcritical Regime ◽  
Moving Storm ◽  
The Waves

Rapidly moving storm crossing the shelf from shallow water to deep water can generate tsunami-like waves which can cause local flooding and damage to docks when the waves hit the coast. We report on laboratory experiments to examine the reflection of waves generated by a moving disturbance from the shelf. Experiments are performed in a two-layer fluid consisting of a layer of oil based ferrofluid lying on top of a layer of water with step bottom. The disturbance is generated by a permanent magnet moving above the surface of ferrofluid. Digital images of the flow are analyzed to obtain the evolution of the wave field. The experimental flows demonstrate two distinct regimes, namely subcritical when the speed of the magnet is less than the phase speed of the wave, and supercritical when the speed of the magnet is greater than the phase speed of the wave. In subcritical regime the disturbance is localized and its size is determined by the spatial extent of the forcing. In supercritical regime the waves form two beams extending at “Mach angle” with respect to the direction of motion. Oblique wave incident on the shelf can experience total reflection if the angle between the wave front and the shelf is greater than a critical value.

scholarly journals DETERMINATION OF THE WAVE HEIGHT IN NATURE FROM MODEL TESTS SUPPLEMENTED BY CALCULATION

2011 ◽  
Vol 1 (6) ◽  
pp. 12
Author(s):  
J. G.H.R. Diephuis ◽  
J. G. Gerritze
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Deep Water ◽  
Bottom Topography ◽  
Model Tests ◽  
Small Scale ◽  
Wave Characteristics ◽  
Sea Bottom ◽  
The Waves

This paper deals with the problem of determining the wave characteristics in shallow water from those in deep water. In general this can be done by means of a refraction calculation. If the sea bottom topography is too irregular the height of the waves can be determined by means of a small-scale refraction model. In both cases, however, some additional effects have to be taken into account, viz. the influence of the bottom friction and the influence of the wind.

Nonlinear dynamic pressure beneath waves in water of large and intermediate depth

2021 ◽  
Author(s):  
Anna Kokorina ◽  
Alexey Slunyaev ◽  
Marco Klein
Keyword(s):  
Gravity Waves ◽  
Pressure Field ◽  
Dynamic Pressure ◽  
Surface Displacement ◽  
Weakly Nonlinear ◽  
Pressure Fields ◽  
Component Theory ◽  
Theoretical Predictions ◽  
Weakly Nonlinear Waves ◽  
The Waves

<p>The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure fields beneath the waves are compared with the theoretical predictions based on different approximations for modulated potential gravity waves. The performance of different theories to reconstruct the pressure field from the known surface displacement time series (the direct problem) is investigated. A new two-component theory for weakly modulated weakly nonlinear waves is proposed, which exhibits the best capability among the considered. Peculiarities of the vertical modes of the nonlinear pressure harmonics are discussed.</p><p> </p><p>The work was supported by the RFBR projects 19-55-15005 and 20-05-00162 (AK).</p>

scholarly journals A study of the waves and boundary layers due to a surface pressure on a uniform stream of a slightly viscous liquid of finite depth

2006 ◽  
Vol 2006 ◽  
pp. 1-24
Author(s):  
Arghya Bandyopadhyay
Keyword(s):  
Numerical Study ◽  
Surface Displacement ◽  
Finite Depth ◽  
Surface Boundary ◽  
Long Distance ◽  
Surface Boundary Layer ◽  
Linear Waves ◽  
Propagating Waves ◽  
The Waves ◽  
Asymptotic Forms

The 2D problem of linear waves generated by an arbitrary pressure distributionp0(x,t)on a uniform viscous stream of finite depthhis examined. The surface displacementζis expressed correct toO(ν)terms, for small viscosityν, with a restriction onp0(x,t). Forp0(x,t)=p0(x)eiωt, exact forms of the steady-state propagating waves are next obtained for allxand not merely forx≫0which form a wave-quartet or a wave-duo amid local disturbances. The long-distance asymptotic forms are then shown to be uniformly valid for largeh. For numerical and other purposes, a result essentially due to Cayley is used successfully to express these asymptotic forms in a series of powers of powers ofν1/2orν1/4with coefficients expressed directly in terms of nonviscous wave frequencies and amplitudes. An approximate thickness of surface boundary layer is obtained and a numerical study is undertaken to bring out the salient features of the exact and asymptotic wave motion in question.

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