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.

Note on the reflexion of water waves at a wall in the presence of surface tension

1982 ◽  
Vol 92 (2) ◽  
pp. 369-374 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Wave Motion ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Time Harmonic ◽  
Initial Assumption ◽  
Effect Of Surface

AbstractIn this note we examine the influence of surface tension on surface waves incident against a fixed vertical plane wall. The motion is time harmonic and is determined by making the initial assumption that the free-surface slope at the wall is prescribed. From the unique solution obtained for the velocity potential, the parameter involved in this specification can be determined, for small laboratory-scale waves at least, using some longstanding experimental results on meniscus behaviour at a moving contact line. The effect of surface tension is to produce a motion wherein reflexion from the wall is not complete and there is a local disturbance, in contrast to the classical standing-wave motion in the absence of surface tension.

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.

scholarly journals A cylindrical wave-maker problem in a liquid of finite depth with an inertial surface in the presence of surface tension

1991 ◽  
Vol 33 (1) ◽  
pp. 111-121
Author(s):  
N. K. Ghosh
Keyword(s):  
Surface Tension ◽  
Circular Cross Section ◽  
Finite Depth ◽  
Angular Frequency ◽  
Cylindrical Wave ◽  
Forced Oscillations ◽  
Radial Coordinate ◽  
Time Harmonic ◽  
Inertial Surface ◽  
Wave Maker

AbstractThe problem of generation of waves in a liquid of uniform finite depth with an inertial surface composed of a thin but uniform distribution of disconnected floating particles, due to forced axisymmetric motion prescribed on the surface of an immersed vertical cylindrical wave-maker of circular cross section under the influence of surface tension at the inertial surface, is discussed. The techniques of Laplace transform in time and the modified Weber transform involving Bessel functions in the radial coordinate have been employed to obtain the velocity potential. The steady-state development to the potential function as well as the inertial surface depression due to time-harmonic forced oscillations of the wave-maker are deduced. It is found that the presence of surface tension at the inertial surface ensures the propagation of time-harmonic progressive waves of any angular frequency.

An explicit Hamiltonian formulation of surface waves in water of finite depth

1992 ◽  
Vol 237 ◽  
pp. 435-455 ◽  
Author(s):  
A. C. Radder
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Hamiltonian Formulation ◽  
Vertical Plane ◽  
Finite Depth ◽  
Short Wave ◽  
Linear Dispersion ◽  
Energy Functionals ◽  
Canonical Variables ◽  
Wave Nonlinearity

A variational formulation of water waves is developed, based on the Hamiltonian theory of surface waves. An exact and unified description of the two-dimensional problem in the vertical plane is obtained in the form of a Hamiltonian functional, expressed in terms of surface quantities as canonical variables. The stability of the corresponding canonical equations can be ensured by using positive definite approximate energy functionals. While preserving full linear dispersion, the method distinguishes between short-wave nonlinearity, allowing the description of Stokes waves in deep water, and long-wave nonlinearity, applying to long waves in shallow water. Both types of nonlinearity are found necessary to describe accurately large-amplitude solitary waves.

Generation and Propagation of Long-Crested Finite-Depth Surface Waves: Comparison Between the Corresponding Results From Numerical Models and a Wave Tank

2008 ◽  
Author(s):  
M. Hasanat Zaman ◽  
Wade Parsons ◽  
Okey Nwogu ◽  
Wooyoung Choi ◽  
R. Emile Baddour ◽  
...  
Keyword(s):  
Surface Waves ◽  
Numerical Solutions ◽  
Numerical Models ◽  
Finite Depth ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Surface Elevation ◽  
Ocean Engineering ◽  
Measured Time ◽  
Wave Maker

The evolution of long-crested surface waves subject to side-band perturbations is investigated with two different numerical models: a direct solver for the Euler equations using a non-orthogonal boundary-fitted curvilinear coordinate system and an FFT-accelerated boundary integral method. The numerical solutions are then validated with laboratory experiments performed in the NRC-IOT Ocean Engineering Basin with a segmented wave-maker operating in piston mode. The numerical models are forced by a point measurement of the free surface elevation at a wave probe close to the wave-maker and the numerical solutions are compared with the measured time-series of the surface elevation at a few wave probe locations downstream.

Forced gravity waves in two-layered fluids with the upper fluid having a free surface

2003 ◽  
Vol 81 (4) ◽  
pp. 675-689 ◽  
Author(s):  
H H Sherief ◽  
M S Faltas ◽  
E I Saad
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Harmonic Wave ◽  
Density Ratio ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids ◽  
Lower Fluid ◽  
Wave Maker

The steady-gravity wave motion is considered for two immiscible layers of incompressible and nonviscous fluids in the presence of a porous wave maker immersed vertically in the two fluids, the upper fluid having a free surface and the lower fluid is of infinite depth. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the wave maker. Also the scattering of a harmonic wave incident normally to the wave maker is considered and the reflection and transmission coefficients are obtained. The case when the lower fluid is of finite depth is also considered. The results are plotted for different values of porosity and different values of the density ratio. PACS Nos.: 47.35.+i, 47.55.Hd, 47.55.Mh

The scattering of surface waves by a vertical plane barrier

1969 ◽  
Vol 66 (2) ◽  
pp. 417-422 ◽  
Author(s):  
R. J. Jarvis ◽  
B. S. Taylor
Keyword(s):  
Surface Waves ◽  
Small Amplitude ◽  
Vertical Plane ◽  
Finite Depth ◽  
Infinite Depth ◽  
Plane Barrier

AbstractIn this paper we use a method due to Williams(1) to discuss the scattering of surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending indefinitely downwards from a 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 surface waves by a half immersed circular cylinder in fluid of finite depth

1985 ◽  
Vol 8 (1) ◽  
pp. 113-125
Author(s):  
Birendranath Mandel ◽  
Sudip Kumar Goswami
Keyword(s):  
Integral Equation ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Velocity Potential ◽  
Finite Depth ◽  
Reflection Coefficients ◽  
Infinite Depth ◽  
Transmission And Reflection Coefficients ◽  
Linearized Theory ◽  
Transmission And Reflection

A train of surface waves is normally incident on a half immersed circular cylinder in a fluid of finite depth. Assuming the linearized theory of fluid under gravity an integral equation for the scattered velocity potential on the half immersed surface of the cylinder is obtained. It has not been found possible to solve this in closed form even for infinite depth of fluid. Our purpose is to obtain the asymptotic effect of finite depth “h” on the transmission and reflection coefficients when the depth is large. It is shown that the corrections to be added to the infinite depth results of these coefficients can be expressed as algebraic series in powers ofa/hstarting with(a/h)2where “a” is the radius of the circular cylinder. It is also shown that the coefficients of(a/h)2in these corrections do not vanish identically.

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