scholarly journals Global relationships between two-dimensional water wave potentials

1996 ◽  
Vol 312 ◽  
pp. 299-309 ◽  
Author(s):  
M. McIver
Keyword(s):  
Water Wave ◽  
Small Amplitude ◽  
Velocity Potential ◽  
Two Dimensional ◽  
Reciprocity Relations ◽  
Moving Body ◽  
Calm Water ◽  
Exciting Forces ◽  
Scattering Potential ◽  
Scattering And Radiation

When a body interacts with small-amplitude surface waves in an ideal fluid, the resulting velocity potential may be split into a part due to the scattering of waves by the fixed body and a part due to the radiation of waves by the moving body into otherwise calm water. A formula is derived which expresses the two-dimensional scattering potential in terms of the heave and sway radiation potentials at all points in the fluid. This result generalizes known reciprocity relations which express quantities such as the exciting forces in terms of the amplitudes of the radiated waves. To illustrate the use of this formula beyond the reciprocity relations, equations are derived which relate higher-order scattering and radiation forces. In addition, an expression for the scattering potential due to a wave incident from one infinity in terms of the scattering potential due to a wave from the other infinity is obtained.

scholarly journals The Exciting Forces on Fixed Bodies in Waves

1962 ◽  
Vol 6 (04) ◽  
pp. 10-17 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Wave Amplitude ◽  
Amplitude Ratio ◽  
Exciting Force ◽  
The Body ◽  
Forced Oscillations ◽  
Wave Number ◽  
Far Field ◽  
Two Dimensional ◽  
Calm Water ◽  
Exciting Forces

General expressions, originally given by Haskind, are derived for the exciting forces on an arbitrary fixed body in waves. These give the exciting forces and moments in terms of the far-field velocity potentials for forced oscillations in calm water and do not depend on the diffraction potential, or the disturbance of the incident wave by the body. These expressions are then used to compute the exciting forces on a submerged ellipsoid, and on floating two-dimensional ellipses. For the ellipsoid, the problem is solved using the far-field potentials, and detailed results and calculations are given for the roll moment. The other forces agree, for the special case of a spheroid, with earlier results obtained by Havelock. In the case of two-dimensional motion the exciting forces are related to the wave amplitude ratio A for forced oscillations in calm water, and this relation is used to compute the heave exciting force for several elliptic cylinders. Expressions are also given relating the damping coefficients and the exciting forces. A = wave amplitude A = wave-height ratio for forced oscillations(a1 a2 a3) = semi-axis of ellipsoidBij = damping coefficientsC4 = nondimensional roll exciting-force coefficientDj = virtual-mass coefficients, defined by equations (18) and (19)g = gravitational accelerationh = depth of submergencei = √ — 1j = index referring to direction of force or motionn(z) = spherical Bessel function, K = wave number, K = ω2/gPj = functions defined following equation (17)R = polar coordinateV, = velocity components (x, y, z) = Cartesian coordinatesαi = Green's integrals, defined by equation (20)β = angle of incidence of wave systemθ = polar coordinateρ= fluid densityφj = velocity potentialsω = circular frequency of encounter

Two-dimensional resonant piston-like sloshing in a moonpool

2007 ◽  
Vol 575 ◽  
pp. 359-397 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
OLAV F. ROGNEBAKKE ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Steady State ◽  
Velocity Potential ◽  
Experimental Studies ◽  
Vortex Method ◽  
Harmonic Excitation ◽  
Linear Potential ◽  
Two Dimensional ◽  
Discrete Vortex ◽  
Singular Behaviour ◽  
Calm Water

This paper presents combined theoretical and experimental studies of the two-dimensional piston-like steady-state motions of a fluid in a moonpool formed by two rectangular hulls (e.g. a dual pontoon or catamaran). Vertical harmonic excitation of the partly submerged structure in calm water is assumed. A high-precision analytically oriented linear-potential-flow method, which captures the singular behaviour of the velocity potential at the corner points of the rectangular structure, is developed. The linear steady-state results are compared with new experimental data and show generally satisfactory agreement. The influence of vortex shedding has been evaluated by using the local discrete-vortex method of Graham (1980). It was shown to be small. Thus, the discrepancy between the theory and experiment may be related to the free-surface nonlinearity.

scholarly journals Far-field representation for the vertical force on a floating structure

2012 ◽  
Vol 712 ◽  
pp. 661-670 ◽  
Author(s):  
M. McIver
Keyword(s):  
Velocity Potential ◽  
Three Dimensional ◽  
Low Frequency ◽  
Exciting Force ◽  
Far Field ◽  
Vertical Force ◽  
Floating Structure ◽  
Field Representation ◽  
Reciprocity Relations ◽  
Scattering Potential

AbstractEquations are derived that relate the vertical hydrodynamic force on two- and three-dimensional structures that are floating in a fluid of infinite depth to the far-field dipole coefficient in the velocity potential. By an application of Green’s theorem to the radiation or scattering potential and a suitable test potential, the heave added mass, the heave damping and the vertical exciting force are shown to be expressible in terms of the dipole coefficient in the relevant potential. The results add to the known reciprocity relations, which relate quantities such as the damping and the exciting force to the amplitude of the far-field radiated wave. The expressions are valid at all frequencies, and their high- and low-frequency asymptotics are investigated.

Estimating wave heights from pressure data at the bed

2014 ◽  
Vol 743 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Linear Theory ◽  
Wave Height ◽  
Water Wave ◽  
Small Amplitude ◽  
Wave Amplitude ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Pressure Data ◽  
Hydrostatic Approximation ◽  
Wave Heights

AbstractWe provide some estimates for the wave height of a two-dimensional travelling gravity water wave from pressure measurements at the flat bed. The approach is applicable without limitations on the wave amplitude. It improves the classical estimates available if one relies on the hydrostatic approximation or on the linear theory of waves of small amplitude.

The Exciting Forces on a Moving Body in Waves

1965 ◽  
Vol 9 (04) ◽  
pp. 190-199 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Asymptotic Form ◽  
Wave Length ◽  
Forward Speed ◽  
Regular Waves ◽  
Moving Body ◽  
Calm Water ◽  
Exciting Forces ◽  
Heading Angle ◽  
Analytical Relations ◽  
The Ideal

This paper generalizes the "Haskind relations" for the exciting forces in waves, to include the effects of constant forward speed. The analysis assumes the fluid to the ideal and incompressible, and the disturbance of the free surface to be small. The analytical relations are derived for the exciting forces in regular waves, in terms of the radiation potential associated with the forced harmonic oscillations of the same body in calm water. For this purpose it is sufficient to know the far-field asymptotic form of the radiation potential. The results are applied to the case of a submerged ellipsoid, to give the six exciting forces and moments as functions of the wave length, heading angle, and forward velocity.

A note on the uniqueness of small-amplitude water waves travelling in a region of varying depth

1979 ◽  
Vol 86 (3) ◽  
pp. 511-519 ◽  
Author(s):  
G. F. Fitz-Gerald ◽  
R. H. J. Grimshaw
Keyword(s):  
Linear Theory ◽  
Gravity Waves ◽  
Water Waves ◽  
Small Amplitude ◽  
Velocity Potential ◽  
Surface Gravity ◽  
Two Dimensional ◽  
Physical Interest ◽  
Surface Gravity Waves ◽  
Convexity Conditions

The two-dimensional, irrotational, linear theory used in the investigation of the propagation of monochromatic surface gravity waves in a region of varying depth is considered. Uniqueness of the velocity potential is established for bottom profiles satisfying certain convexity conditions. These include the majority of profiles of physical interest.

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

Internal waves in a viscous atmosphere

1975 ◽  
Vol 72 (4) ◽  
pp. 773-786 ◽  
Author(s):  
W. L. Chang ◽  
T. N. Stevenson
Keyword(s):  
Energy Source ◽  
Incompressible Fluid ◽  
Internal Waves ◽  
Infinite Number ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
The Waves ◽  
Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

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