Radiation and diffraction of water waves by a submerged sphere at forward speed

1988 ◽  
Vol 417 (1853) ◽  
pp. 433-461 ◽  
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Surface Condition ◽  
Wave Resistance ◽  
The Body ◽  
Legendre Functions ◽  
Forward Speed ◽  
Submerged Sphere ◽  
Exciting Forces ◽  
Similar Equation

A submerged sphere advancing in regular deep-water waves at constant forward speed is analysed by linearized potential theory. A distribution of sources over the surface of the sphere is expanded into a series of Legendre functions, by extension of the method used by Farell ( J . Ship Res . 17, 1 (1973)) in analysing the wave resistance on a submerged spheroid. The equations governing the velocity potential are satisfied by use of the appropriate Green function and by choosing the coefficients in the series of Legendre functions such that the body surface condition is satisfied. Numerical results are obtained for the wave resistance, hydrodynamic coefficients and exciting forces on the sphere. Some theoretical aspects of a body advancing in waves are also discussed. The far-field equation of Newman ( J . Ship Res . 5, 44 (1961)) for calculation of the damping coefficients is extended, and a similar equation for the exciting forces is derived.

The hydrodynamic forces on a submerged sphere moving in a circular path

1990 ◽  
Vol 428 (1874) ◽  
pp. 215-227 ◽  
Keyword(s):  
Green Function ◽  
Body Surface ◽  
Velocity Potential ◽  
Surface Condition ◽  
Hydrodynamic Forces ◽  
Constant Angular Velocity ◽  
The Body ◽  
Circular Path ◽  
Legendre Functions ◽  
Submerged Sphere

Analytical solutions for various hydrodynamic problems are briefly reviewed. The case of a submerged sphere moving in a circular path at constant angular velocity is then analysed based on the linearized velocity potential theory. The potential is expressed by means of a Green function and a distribution of sources over the body surface, written in terms of Legendre functions. The coefficients in the series of the Legendre functions are obtained by imposing the body surface condition. Figures are provided showing the hydrodynamic forces on the sphere.

scholarly journals Wave forces on three-dimensional floating bodies with small forward speed

1991 ◽  
Vol 227 ◽  
pp. 135-160 ◽  
Author(s):  
Jan Nossen ◽  
John Grue ◽  
Enok Palm
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Wave Forces ◽  
Forward Speed ◽  
Floating Bodies ◽  
Wave Drift ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Wave Drift Damping ◽  
The Mean

A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.

The Coupled Damping Coefficients of a Symmetric Ship

1963 ◽  
Vol 6 (01) ◽  
pp. 1-7
Author(s):  
R. Timman ◽  
J. N. Newman
Keyword(s):  
Velocity Potential ◽  
Surface Condition ◽  
The Body ◽  
Forward Speed ◽  
Small Oscillations ◽  
Damping Coefficients ◽  
Submerged Body ◽  
Symmetry Properties ◽  
Transverse Symmetry ◽  
Oscillatory Velocity

A study is made of a floating or submerged body with longitudinal and transverse symmetry, which is moving with constant forward speed and performing small oscillations. The analysis is quite general in the sense that the shape of the body and the nature of the oscillations are unspecified, but it is assumed that the linearized free-surface condition holds. With this assumption the oscillatory velocity potential is found in terms of an unknown Green's function, the existence of which is also assumed. This potential is then used to show the symmetry properties of the cross-coupling damping coefficients.

Radiation and diffraction by a submerged sphere advancing in water waves of finite depth

1995 ◽  
Vol 448 (1932) ◽  
pp. 29-54 ◽  
Keyword(s):  
Water Waves ◽  
Finite Depth ◽  
Multipole Expansion ◽  
The Body ◽  
Field Equations ◽  
Damping Coefficients ◽  
Submerged Sphere ◽  
Added Masses ◽  
Exciting Forces ◽  
Depth Water

A submerged sphere advancing in a regular finite depth water wave at constant forward speed is analysed by linearized velocity potential. The solution is ob­tained by the multipole expansion extended from that developed for zero speed. Numerical results are obtained for wave-making resistance and lift, added masses, damping coefficients and exciting forces. Far field equations are also derived for calculating damping coefficients and exciting forces. They are used to check the results obtained from integrating pressure over the body surface. Excellent agree­ment is found.

On the Motion of a Slender Body Submerged Beneath Surface Waves

1988 ◽  
Vol 32 (03) ◽  
pp. 208-219 ◽  
Author(s):  
P. Wilmott
Keyword(s):  
Velocity Potential ◽  
Axisymmetric Body ◽  
The Body ◽  
Body Motion ◽  
Vertical Force ◽  
Forward Speed ◽  
Body Velocity ◽  
Exciting Forces ◽  
Deep Fluid ◽  
The Mean

A slender axisymmetric body is submerged beneath a regular train of waves on an inviscid, incompressible, infinitely deep fluid. Using the method of matched asymptotic expansions, the velocity potential in the neighborhood of the body is calculated, thus determining the mean second-order vertical force when the body is permitted to respond to the exciting forces and moment but is otherwise moving with constant forward speed and depth beneath a head sea. To stablilize the body motion, the effects of a hydrofoil placed on the body axis are included. Several examples are computed showing the dependence of mean vertical force on body velocity.

On the Radiation and Diffraction of Surface Waves by Submerged Spheroids

1989 ◽  
Vol 33 (02) ◽  
pp. 84-92
Author(s):  
G. X. Wu ◽  
R. Eatock Taylor
Keyword(s):  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Added Mass ◽  
Wave Radiation ◽  
Legendre Functions ◽  
Incoming Wave ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients ◽  
Exciting Forces

The problem of wave radiation and diffraction by submerged spheroids is analyzed using linearized three-dimensional potential-flow theory. The solution is obtained by expanding the velocity potential into a series of Legendre functions in a spheroidal coordinate system. Tabulated and graphical results are provided for added mass and damping coefficients of various spheroids undergoing motions in six degrees of freedom. Graphs are also provided for exciting forces and moments corresponding to a range of incoming wave angles.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

Forward-Speed Vertical Wave Exciting Forces on Ships

1985 ◽  
Vol 29 (02) ◽  
pp. 105-111
Author(s):  
P. D. Sclavounos
Keyword(s):  
Velocity Potential ◽  
Reverse Flow ◽  
Diffraction Problem ◽  
Three Dimensional ◽  
Forward Speed ◽  
Direct Solution ◽  
Radiation Problem ◽  
Strip Theory ◽  
Exciting Forces ◽  
Wave Exciting Forces

Expressions are derived for the heave and pitch exciting force and moment on a ship advancing in waves. They are obtained in the form of an integral over the ship axis of the outer source strength of the reverse-flow radiation problem multiplied by the value of the incident-wave velocity potential. Their performance is tested for two slender spheroids. Comparisons are made with predictions obtained from a three-dimensional numerical solution at zero speed—the expression common to strip-theory programs which uses the ship hull as the integration surface—and the direct solution of the diffraction problem.

Radiation and diffraction of second-order surface waves by floating bodies

1988 ◽  
Vol 196 ◽  
pp. 65-91 ◽  
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Linear Problem ◽  
Velocity Potential ◽  
Surface Condition ◽  
Second Order ◽  
The Body ◽  
Green Functions ◽  
Floating Bodies ◽  
Free Surface Condition ◽  
Body Boundary

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

Hydrodynamic forces on submerged oscillating cylinders at forward speed

1987 ◽  
Vol 414 (1846) ◽  
pp. 149-170 ◽  
Keyword(s):  
Surface Condition ◽  
Outer Region ◽  
Finite Element Approximation ◽  
Boundary Integral ◽  
The Body ◽  
Element Approximation ◽  
Test Cases ◽  
Forward Speed ◽  
Derivatives Of ◽  
Unbounded Fluid

The hydrodynamic problem of submerged oscillating cylinders at forward speed is analysed by linearized potential theory. The numerical method used combines a finite-element approximation of the velocity potential in a region surrounding the cylinder with a boundary integral equation representation of the outer region. This method avoids the calculation of the second-order derivatives of the steady potential due to forward speed, which appear in the body surface condition for the unsteady potential due to the oscillation of the cylinder. Numerical results from the present method for test cases of a circular cylinder in an unbounded fluid and below a free surface are in excellent agreement with the analytical solutions. Further results for elliptic cylinders are provided and the influence of forward speed on the hydrodynamic force on a submerged cylinder is investigated.

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