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.

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.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves

2002 ◽  
Vol 450 ◽  
pp. 201-205 ◽  
Author(s):  
ELIEZER KIT ◽  
LEV SHEMER
Keyword(s):  
Gravity Waves ◽  
Fourth Order ◽  
Deep Water ◽  
Evolution Equations ◽  
Velocity Potential ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Zakharov Equation ◽  
Dimensional Version

A spatial two-dimensional version of the Zakharov equation describing the evolution of deep-water gravity waves is used to derive two fourth-order evolution equations, for the amplitudes of the surface elevation and of the velocity potential. The scaled form of the equations is presented.

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.

scholarly journals On the appearance of internal wave attractors due to an initial or parametrically excited disturbance

2013 ◽  
Vol 714 ◽  
pp. 283-311 ◽  
Author(s):  
Janis Bajars ◽  
Jason Frank ◽  
Leo R. M. Maas
Keyword(s):  
Gravity Waves ◽  
Normal Modes ◽  
Internal Gravity Waves ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Boussinesq Model ◽  
Resonant Modes ◽  
The Waves ◽  
Shaped Domain ◽  
Parametric Forcing

AbstractIn this paper we solve two initial value problems for two-dimensional internal gravity waves. The waves are contained in a uniformly stratified, square-shaped domain whose sidewalls are tilted with respect to the direction of gravity. We consider several disturbances of the initial stream function field and solve both for its free evolution and for its evolution under parametric excitation. We do this by developing a structure-preserving numerical method for internal gravity waves in a two-dimensional stratified fluid domain. We recall the linearized, inviscid Euler–Boussinesq model, identify its Hamiltonian structure, and derive a staggered finite difference scheme that preserves this structure. For the discretized model, the initial condition can be projected onto normal modes whose dynamics is described by independent harmonic oscillators. This fact is used to explain the persistence of various classes of wave attractors in a freely evolving (i.e. unforced) flow. Under parametric forcing, the discrete dynamics can likewise be decoupled into Mathieu equations. The most unstable resonant modes dominate the solution, forming wave attractors.

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.

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