On the laboratory generation of two-dimensional, progressive, surface waves of nearly permanent form on deep water

2006 ◽  
Vol 559 ◽  
pp. 413 ◽  
Author(s):  
DIANE M. HENDERSON ◽  
MATTHEW S. PATTERSON ◽  
HARVEY SEGUR
Keyword(s):  
Surface Waves ◽  
Deep Water ◽  
Two Dimensional ◽  
Permanent Form

The effect of a fixed vertical barrier on surface waves in deep water

1947 ◽  
Vol 43 (3) ◽  
pp. 374-382 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Integral Equation ◽  
Surface Waves ◽  
Deep Water ◽  
Vertical Plane ◽  
Standing Waves ◽  
Simple Type ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Vertical Barrier ◽  
The Mean

In this paper the two-dimensional reflection of surface waves from a vertical barrier in deep water is studied theoretically.It can be shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined, apart from a motion consisting of simple standing waves. In the cases considered here the normal velocity is prescribed on a part of the vertical plane and is taken to be unknown elsewhere. From the condition of continuity of the motion above and below the barrier an integral equation for the normal velocity can be derived, which is of a simple type, in the case of deep water. We begin by considering in detail the reflection from a fixed vertical barrier extending from depth a to some point above the mean surface.

The offshore vortex train

1994 ◽  
Vol 276 ◽  
pp. 113-124 ◽  
Author(s):  
N. Matsunaga ◽  
K. Takehara ◽  
Y. Awaya
Keyword(s):  
Surface Waves ◽  
Deep Water ◽  
Water Waves ◽  
Wave Breaking ◽  
Two Dimensional ◽  
Regular Surface ◽  
Formation Region ◽  
Vortex Merging ◽  
Run Up ◽  
Vortex Movement

A row of two-dimensional vortices forms in an offshore zone when regular surface waves run up a sloping flat bed. This vortex row is called the offshore vortex train. The vortices begin to appear near the breaking point. Moving in the offshore direction, they develop and increase their horizontal lengthscale through vortex merging. After reaching a particular offshore location, however, they decay rapidly. The formation region of the vortex train has been investigated on the basis of visual experiments for three bed slopes. Its formation does not depend on the type of wave breaking but is observed when the steepness of deep-water waves is smaller than 4.2 × 10−2. The horizontal lengthscale of the vortices and the velocities of the vortex movement have also been evaluated empirically.

scholarly journals Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method

2021 ◽  
Vol 9 (1) ◽  
pp. 76
Author(s):  
Duoc Nguyen ◽  
Niels Jacobsen ◽  
Dano Roelvink
Keyword(s):  
Surface Waves ◽  
Deep Water ◽  
Surf Zone ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Successful Implementation ◽  
Random Waves ◽  
Mean Motion ◽  
Generalized Lagrangian

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

Action of an adverse current on the shape of deep water surface waves

1995 ◽  
Vol 18 (6) ◽  
pp. 438-444 ◽  
Author(s):  
P. Bonmarin ◽  
F. Bartholin ◽  
A. Ramamonjiarisoa
Keyword(s):  
Surface Waves ◽  
Deep Water ◽  
Water Surface

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 short surface waves due to a half-immersed circular cylinder oscillating on water of infinite depth

1982 ◽  
Vol 384 (1787) ◽  
pp. 333-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Usual Method ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Small Kernel ◽  
Rolling Mode ◽  
Incident Waves ◽  
Plausible Argument ◽  
Fixed Cylinder

In this paper we examine two-dimensional short surface waves in water of infinite depth produced by various modes of oscillation of a half-immersed circular cylinder. The usual method, which depends on finding the potential on the cylinder from an integral equation with a small kernel, is here replaced by one that uses instead the known value of the potential for incident waves in the presence of the fixed cylinder. Thus we are able to determine three-term asymptotic expansions for both the heaving and the swaying modes that improve on earlier forms, and, for the heaving mode, to refine the interpolation with previous numerical calculations and confirm in principle the result obtained elsewhere by a plausible argument. The rolling mode also can actually be included by superposition of the heaving and swaying modes for this cylinder.

scholarly journals Deep Water Ship-Waves

1906 ◽  
Vol 25 (1) ◽  
pp. 562-587 ◽  
Author(s):  
Lord Kelvin
Keyword(s):  
Deep Water ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Present Communication ◽  
Ship Waves ◽  
Horizontal Bottom

§§ 32–64. Canal Ship-Waves.§ 32. To avoid the somewhat cumbrous title “Two-dimensional,” I now use the designation “Canal † Waves” to denote waves in a canal with horizontal bottom and vertical sides, which, if not two-dimensional in their source, become more and more approximately two-dimensional at greater and greater distances from the source. In the present communication the source is such as to render the motion two-dimensional throughout; the two dimensions being respectively perpendicular to the bottom, and parallel to the length of the canal: the canal being straight.

Statistical properties of Rayleigh waves due to scattering by topography

1967 ◽  
Vol 57 (1) ◽  
pp. 83-90
Author(s):  
J. A. Hudson ◽  
L. Knopoff
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Seismic Noise ◽  
Forward Scattering ◽  
Statistical Properties ◽  
Body Waves ◽  
Simplified Model ◽  
Two Dimensional ◽  
Especial Reference ◽  
The Earth

abstract The two-dimensional problems of the scattering of harmonic body waves and Rayleigh waves by topographic irregularities in the surface of a simplified model of the earth are considered with especial reference to the processes of P-R, SV-R and R-R scattering. The topography is assumed to have certain statistical properties; the scattered surface waves also have describable statistical properties. The results obtained show that the maximum scattered seismic noise is in the range of wavelengths of the order of the lateral dimensions of the topography. The process SV-R is maximized over a broader band of wavelengths than the process P-R and thus the former may be more difficult to remove by selective filtering. An investigation of the process R-R shows that backscattering is much more important than forward scattering and hence topography beyond the array must be taken into account.

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