scholarly journals On waves in the presence of vertical porous boundaries

1997 ◽  
Vol 39 (1) ◽  
pp. 104-120 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Finite Depth ◽  
Wave Source ◽  
Lack Of Information ◽  
Infinite Extent ◽  
Wave Maker ◽  
Incident Waves ◽  
Standard Techniques ◽  
Porous Boundaries ◽  
Effect Of Surface

AbstractIn this paper various wave motions in water of infinite depth containing vertical porous boundaries are determined when the water is of infinite extent on one or both sides. Initially surface tension is ignored and simple solutions for incident waves are obtained before going on to harder wave source and wave-maker solutions. A reduction method is developed to obtain solutions for two-sided boundaries from those for one-sided, which are obtained by standard techniques. The effect of surface tension that precludes simple solutions is also considered, although a present lack of information on dynamical edge behaviour for porous boundaries means that the formal mathematical solutions must be left in terms of arbitrary edge constants. In conclusion, some solutions are noted for finite depth.

scholarly journals The effect of surface tension in porous wave maker problems

1998 ◽  
Vol 39 (4) ◽  
pp. 539-556 ◽  
Author(s):  
A. Chakrabarti ◽  
T. Sahoo
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Eigenfunction Expansion ◽  
Mixed Type ◽  
Finite Depth ◽  
Time Harmonic ◽  
Surface Water Waves ◽  
Wave Maker ◽  
Porous Walls ◽  
Effect Of Surface

AbstractUsing a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

scholarly journals Scattering of water waves by rectangular thick barriers in presence of surface tension

2021 ◽  
Vol 23 (11) ◽  
pp. 30-55
Author(s):  
Gour Das ◽  
◽  
Rumpa Chakraborty ◽  
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Graphical Representation ◽  
Finite Depth ◽  
Approximation Technique ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Gegenbauer Polynomial ◽  
Incident Waves ◽  
Effect Of Surface

The influence of surface tension over an oblique incident waves in presence of thick rectangular barriers present in water of uniform finite depth is discussed here. Three different structures of a bottom-standing submerged barrier, submerged rectangular block not extending down to the bottom and fully submerged block extending down to the bottom with a finite gap are considered. An appropriate multi-term Galekin approximation technique involving ultraspherical Gegenbauer polynomial is employed for solving the integral equations arising in the mathematical analysis. The reflection and transmission coefficients of the progressive waves for two-dimensional time har- monic motion are evaluated by utilizing linearized potential theory. The theoretical result is validated numerically and explained graphically in a number of figures. The present result will almost match analytically and graphically with those results already available in the literature without considering the effect of surface tension. From the graphical representation, it is clearly visible that the amplitude of reflection coefficient decreases with increasing values of surface tension. It is also seen that the presence of surface tension, the change of width, and the height of the thick barriers affect the nature of the reflection coefficients significantly

EFFECTS OF SURFACE TENSION ON TRAPPED MODES IN A TWO-LAYER FLUID

2015 ◽  
Vol 57 (2) ◽  
pp. 189-203 ◽  
Author(s):  
S. SAHA ◽  
S. N. BORA
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Boundary Value Problems ◽  
Finite Depth ◽  
Trapped Modes ◽  
Trapped Waves ◽  
Linearized Theory ◽  
Horizontal Circular Cylinder ◽  
Effect Of Surface

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these.

scholarly journals The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

2017 ◽  
Vol 156 ◽  
pp. 526-533
Author(s):  
G.C. Hocking ◽  
H.H.N. Nguyen ◽  
T.E. Stokes ◽  
L.K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Effect Of Surface

On forced three-dimensional surface waves in a channel in the presence of surface tension

1974 ◽  
Vol 75 (3) ◽  
pp. 405-426 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Velocity Potential ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Vertical Plane ◽  
Dimensional Solution ◽  
Surface Slopes ◽  
Infinite Region ◽  
Wave Maker ◽  
Effect Of Surface

AbstractIn this paper wave-maker theory including the effect of surface tension is determined for three-dimensional motion of water in a semi-infinite rectangular channel with outgoing surface wave modes allowed for at infinity; the motion is generated by a harmonically oscillating vertical plane wave-maker at the end of the channel and the cases of both infinite and finite constant depth are treated. The solution of the boundary-value problem for the velocity potential is more complicated in the presence of surface tension due mainly to the additional effect of the channel walls at which the normal free surface slopes are prescribed—as also is the slope at the wave-maker—to ensure uniqueness. The simpler three-dimensional solution for a semi-infinite region—obtained long ago by Sir Thomas Havelock in the absence of surface tension for the case of infinite depth—is also noted.

On the evolution of disturbances at an inviscid interface

1981 ◽  
Vol 108 ◽  
pp. 159-170 ◽  
Author(s):  
P. N. Shankar
Keyword(s):  
Surface Tension ◽  
Finite Time ◽  
Mixed Boundary ◽  
Vortex Sheet ◽  
Major Effect ◽  
Interface Shape ◽  
Initial Value ◽  
Initial Shape ◽  
Infinite Extent ◽  
Effect Of Surface

The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, inviscid streams is considered in the framework of linearized analysis. Given the initial shape y = εη0(x) of the interface at t = 0 the objective is to calculate the interface shape η(x,t) for later times. First, it is shown that, if the vortex sheet is of infinite extent, if surface tension is absent and if the two streams are of the same density, the evolution is given by \[ \eta(x,t) = \epsilon(1-\alpha)^{-1}{\rm Re}[\{(1-\alpha)+(1+\alpha)i\}\eta_0\{x-{\textstyle\frac{1}{2}}((1+\alpha)+(1-\alpha)i)t\}], \] where α (≠ 1) is the ratio of the speeds of the streams, provided the initial interface shape εη0(x) is analytic and its Fourier transform decays sufficiently rapidly. An interesting consequence is that it is possible, under certain circumstances, for the interface to develop singularities after a finite time. Next it is shown that when the two streams move at the same speed (α = 1) the growth of η is given by \[ \eta(x,t) = \epsilon\eta_0(x-t)+\epsilon t\,d\eta_0(x-t)/dx \] with mild restrictions on η0(x). The major effect of surface tension, it is found, is to prevent the occurrence of singularities after a finite time, a distinct possibility in its absence. Finally the vortex sheet shed by a semi-infinite flat plate is considered. The unsteady mixed boundary-value problem is formally solved by using parabolic coordinates and Fourier-Laplace transforms.

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.

On the forced surface waves due to a vertical wave-maker in the presence of surface tension

1971 ◽  
Vol 70 (2) ◽  
pp. 323-337 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Surface Waves ◽  
Wave Motion ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Finite Depth ◽  
Cylindrical Wave ◽  
Constant Depth ◽  
Classical Wave ◽  
Wave Maker

AbstractThe classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.

scholarly journals Fundamental singularities in the theory of water waves with surface tension

1970 ◽  
Vol 2 (3) ◽  
pp. 317-333 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Water Waves ◽  
Potential Functions ◽  
Fundamental Wave ◽  
Harmonic Waves ◽  
Constant Depth ◽  
Wave Source ◽  
Time Harmonic ◽  
Effect Of Surface

In this paper the forms are obtained for the harmonic potential functions describing the fundamental wave-source and multipole singularities which pertain to the study of infinitesimal time-harmonic waves on the free surface of water when the effect of surface tension is included. Line and point singularities are considered for both the cases of infinite and finite constant depth of water. The method used is an extension of that which has been used to obtain these potentials in the absence of surface tension.

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