Dead-Water Effects of a Ship Moving in Stratified Seas

1993 ◽  
Vol 115 (2) ◽  
pp. 105-110 ◽  
Author(s):  
T. Miloh ◽  
M. P. Tulin ◽  
G. Zilman
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Finite Depth ◽  
Prolate Spheroid ◽  
Wave Resistance ◽  
Water Effects ◽  
Linearized Theory ◽  
Dead Water ◽  
Surface Disturbances

A linearized theory is presented for the dead-water phenomena. A two-layer fluid model of finite depth is assumed and the solutions for both the wave resistance, as well as the interface and free-surface disturbances, are obtained in terms of Green’s function. Numerical solutions are given for the case of a semi-submersible slender-body (prolate spheroid) moving steadily on the free-surface.

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.

The translation of two bodies under the free surface of a heavy fluid

1950 ◽  
Vol 46 (3) ◽  
pp. 453-468 ◽  
Author(s):  
A. Coombs
Keyword(s):  
Free Surface ◽  
Large Range ◽  
Three Dimensional ◽  
Finite Depth ◽  
Arbitrary Cross Section ◽  
Wave Resistance ◽  
Vertical Force ◽  
First Approximation ◽  
Special Case ◽  
Two Bodies

1. Many investigations have been made to determine the wave resistance acting on a body moving horizontally and uniformly in a heavy, perfect fluid. Lamb obtained a first approximation for the wave resistance on a long circular cylinder, and this was later confirmed to be quite sufficient over a large range. In 1926 and 1928, Havelock (4, 5) obtained a second approximation for the wave resistance and a first approximation for the vertical force or lift. Later, in 1936(6), he gave a complete analytical solution to this problem, in which the forces were expressed in the form of infinite series in powers of the ratio of the radius of the cylinder to the depth of the centre below the free surface of the fluid. General expressions for the wave resistance and lift of a cylinder of arbitrary cross-section were found by Kotchin (7) using integral equations, and the special case of a flat plate was evaluated. He continued with a discussion of the motion of a three-dimensional body. More recently, Haskind (3) has examined the same problem when the stream has a finite depth.

scholarly journals A note on withdrawal through a point sink in fluid of finite depth

1996 ◽  
Vol 37 (3) ◽  
pp. 406-416 ◽  
Author(s):  
Lawrence K. Forbes ◽  
Graeme C. Hocking ◽  
Graeme A. Chandler
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Flow Through

AbstractWithdrawal flow through a point sink on the bottom of a fluid of finite depth is considered. The fluid is at rest at infinity, and a stagnation point is present at the free surface, directly above the point sink. Numerical solutions are computed by means of the method of fundamental solutions, and it is observed that flows of this type are apparently possible for Froude number less than about 1.5. Relationships to previous work are discussed.

scholarly journals A note on the free surface induced by a submerged source at infinite Froude number

1988 ◽  
Vol 30 (2) ◽  
pp. 147-156 ◽  
Author(s):  
A. C. King ◽  
M. I. G. Bloor
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Conformal Transformation ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Closed Form Expression ◽  
Free Surface Elevation ◽  
Form Expression ◽  
Transformation Technique ◽  
Surface Angle

AbstractThe free surface due to a submerged source in a fluid of finite depth at infinite Froude number is reconsidered. A conformal transformation technique is used to formulate this problem as an integral equation for the free-surface angle. An elementary solution is found for the equation, which results in a closed form expression for the free-surface elevation. Comparison is made with previous numerical solutions.

Blockage with a Free Surface

1976 ◽  
Vol 20 (04) ◽  
pp. 199-203
Author(s):  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Finite Depth ◽  
Wave Resistance ◽  
Steady Flows ◽  
Two Dimensional ◽  
Present Context ◽  
Two Dimensional Flow ◽  
Field Radiation ◽  
Radiation Conditions

The occurrence of blockage, or a jump in the velocity potential between the upstream and downstream infinities, is well known for steady two-dimensional flow past a body in a rigid channel. This paper considers the analogous situation where there is a free surface, as in the wave resistance problem for submerged two-dimensional bodies in a fluid of finite depth. It is shown that blockage occurs in spite of the free surface, taking values which depend not only on the dipole moment but also upon the Froude number based on depth. The occurrence of blockage, in the present context, has a bearing primarily upon the correct formulation of far-field radiation conditions for steady flows with finite depth.

The Wave and Induced Drag of a Hydrofoil of Finite Span in Water of Limited Depth

1961 ◽  
Vol 5 (03) ◽  
pp. 15-21
Author(s):  
J. P. Breslin
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Finite Depth ◽  
Wave Resistance ◽  
Finite Span ◽  
Induced Drag ◽  
Special Cases ◽  
The Waves ◽  
Limited Depth ◽  
Good Agreement

The wave resistance and the induced drag of a simple hydrofoil of finite span moving at a fixed submergence in water of finite depth are derived from a knowledge of the shallow water potential of a source. From this the waves produced by the semi-infinite doublet sheet which represents the undisturbed mathematical model of the hydrofoil are computed and the wave resistance is then inferred from the formula for the waves. Special cases which have been published previously are recaptured from the formulas. The induced drag is computed from a knowledge of the nature of the potential functions needed to satisfy the boundary conditions on the bottom and free surface. A comparison with one set of experimental data shows the theory to underestimate the experimentally determined lift-dependent drag curve at low Froude numbers F and to agree very well as high F. It is conjectured that the lack of good agreement at low F is due to the neglect of the influence of the free surface on the lift which has been omitted in this analysis.

scholarly journals Smoothly attaching bow flows with constant vorticity

2001 ◽  
Vol 42 (3) ◽  
pp. 354-371
Author(s):  
S. W. McCue ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Surface Flow ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Front Face ◽  
Infinite Body ◽  
Constant Vorticity

AbstractThe free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a comer is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

Flow Due to a Moving Pressure Distribution on Free-Surface With Finite-Depth Bottom

2002 ◽  
Author(s):  
Iskender Sahin ◽  
Noriaki Okita
Keyword(s):  
Free Surface ◽  
Pressure Distribution ◽  
Current Method ◽  
Finite Depth ◽  
Steady State Solution ◽  
Wave Resistance ◽  
Surface Elevation ◽  
Bottom Pressure ◽  
Approximation Techniques ◽  
Pressure Profiles

Surface elevation and dynamic bottom pressure profiles caused by a moving pressure distribution over the free-surface are obtained. A direct numerical integration approach for the linear, two-dimensional, and steady-state solution has been developed. The behavior of the surface elevation and bottom pressure profiles along with wave resistance for increasing Froude number or depth are presented. The agreement of the wave resistance calculations using the profiles obtained by the current method and the expression given by Newman and Poole (1962) indicates that the current method can be used as a reliable tool for prediction as well as validation for other numerical approximation techniques.

THREE-DIMENSIONAL WAVE-FREE POTENTIALS IN THE THEORY OF WATER WAVES

2013 ◽  
Vol 55 (2) ◽  
pp. 175-195 ◽  
Author(s):  
HARPREET DHILLON ◽  
B. N. MANDAL
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Surface Condition ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Finite Depth ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Thin Elastic Plate ◽  
Linearized Theory

AbstractProblems of wave interaction with a body with arbitrary shape floating or submerged in water are of immense importance in the literature on the linearized theory of water waves. Wave-free potentials are used to construct solutions to these problems involving bodies with circular geometry, such as a submerged or half-immersed long horizontal circular cylinder (in two dimensions) or sphere (in three dimensions). These are singular solutions of Laplace’s equation satisfying the free surface condition and decaying rapidly away from the point of singularity. Wave-free potentials in two and three dimensions for infinitely deep water as well as water of uniform finite depth with a free surface are known in the literature. The method of constructing wave-free potentials in three dimensions is presented here in a systematic manner, neglecting or taking into account the effect of surface tension at the free surface or for water with an ice cover modelled as a thin elastic plate floating on the water. The forms of the wave motion at the upper surface (free surface or ice-covered surface) related to these wave-free potentials are depicted graphically in a number of figures for all the cases considered.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

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