On the theory of steady progressive waves on the surface of a fluid of infinite depth

1962 ◽  
Vol 26 (5) ◽  
pp. 1284-1292
Author(s):  
V.M Bagin
Keyword(s):  
Infinite Depth ◽  
Progressive Waves

scholarly journals On the scattering of waves by nearly hard or soft incomplete vertical barriers in water of infinite depth

1998 ◽  
Vol 39 (3) ◽  
pp. 293-307
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Perturbation Theory ◽  
Infinite Depth ◽  
Hard Limit ◽  
Vertical Barriers ◽  
Progressive Waves ◽  
Porous Barriers

AbstractIn this paper the scattered progressive waves are determined due to progressive waves incident normally on certain types of partially immersed and completely submerged vertical porous barriers in water of infinite depth. The forms are approximate only, and are obtained using perturbation theory for nearly hard or soft barriers having high and low porosities respectively. The results for arbitrary porosity are difficult to obtain, in contrast to the well known hard limit of impermeable barriers.

scholarly journals On wave motion in a two-layered liquid of infinite depth in the presence of surface and interfacial tension

1994 ◽  
Vol 35 (3) ◽  
pp. 302-322 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Free Surface ◽  
Interfacial Tension ◽  
Vertical Wall ◽  
Small Time ◽  
Underlying Assumption ◽  
Wave Source ◽  
Infinite Depth ◽  
Surface And Interface ◽  
All Solutions ◽  
Progressive Waves

AbstractIn this paper various two-dimensional motions are determined for waves in a stratified region of infinite total depth with a free surface containing two superposed liquids, allowing for the effects of surface and interfacial tension. The fundamental set of wave-source potentials for the two layers is used to construct the set of slope potentials that produce discontinuous free-surface and interface slopes. The latter potentials are then utilized to obtain the potentials for waves due to both heaving vertical plates and incident progressive waves against a vertical wall. The underlying assumption of small time-harmonic motion pertains, described by a pair of velocity potentials for the two layers satisfying coupled linearized boundary-value problems, and all solutions are obtained in terms of their matching basic solutions. The technique for applying Green's theorem in the two layers is developed for use with the wave-source potentials, which themselves are found to obey a generalised reciprocity principle. Familiar results for a single liquid of infinite depth are hereby extended, but the new feature emerges of there being two types of progressive waves in all solutions. For ease of presentation the solutions are obtained for a particular relationship between surface and interfacial tension.

The effect of surface tension on the progressive waves due to incomplete vertical wave-makers in water of infinite depth

1991 ◽  
Vol 435 (1894) ◽  
pp. 293-319 ◽  
Keyword(s):  
Surface Tension ◽  
Reduction Method ◽  
Edge Condition ◽  
Infinite Depth ◽  
Transmitted Waves ◽  
Time Harmonic ◽  
Vertical Barriers ◽  
Wave Maker ◽  
Progressive Waves ◽  
Effect Of Surface

In this paper the influence of surface tension is allowed for in deriving formulas that determine the velocity potentials describing the outgoing progressive waves for two-dimensional time-harmonic motion due to both partially immersed and completely submerged vertical wave-makers in water of infinite depth. For this purpose an effective reduction method is developed to extend a known method suitable only in the absence of surface tension. The two results are used to find the reflected and transmitted waves due to waves incident upon partially immersed and completely submerged fixed vertical barriers, after reformulation as wave-maker problems; and to find the outgoing waves due to a partially immersed vertical hinged plate as a standard example. Certain edge-slope constants needed for the partially immersed wave-maker problem are evaluated using an appropriate dynamical edge condition.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

Progressive waves in non-ideal gases

2014 ◽  
Vol 67 ◽  
pp. 285-290 ◽  
Author(s):  
K. Ambika ◽  
R. Radha ◽  
V.D. Sharma
Keyword(s):  
Ideal Gases ◽  
Progressive Waves

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.

Progressive Waves in Materials Exhibiting Long Range Memory

1976 ◽  
Vol 30 (1) ◽  
pp. 31-41 ◽  
Author(s):  
J. M. Greenberg ◽  
S. Hastings
Keyword(s):  
Long Range ◽  
Progressive Waves
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