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.

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.

Experimental Studies of Hydrodynamic Interaction of Two Bodies in Waves

2015 ◽  
Author(s):  
Quan Zhou ◽  
Ming Liu ◽  
Heather Peng ◽  
Wei Qiu
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Potential Flow ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Low Frequency ◽  
Surface Elevation ◽  
Linear Potential ◽  
Free Surface Elevation ◽  
Two Bodies

There are challenges in the prediction of low-frequency load and especially the resonant free surface elevation between two bodies in close proximity. Most of the linear potential-flow based seakeeping programs currently used by the industry over-predict the free surface elevation between the vessels/bodies and hence the low-frequency loadings on the hulls. Various methods, such as the lid technique, have been developed to suppress the unrealistic values of low-frequency forces by introducing artificial damping coefficients. However, without the experimental data, it is challenging to specify the coefficients. This paper presents the experimental studies of motions of two bodies with various gaps and the wave elevations between bodies. Model tests were performed at the towing tank of Memorial University. The objective was to provide benchmark data for further numerical studies of the viscous effect on the free surface predictions. The experimental data were compared with numerical solutions based on potential flow methods. The effect of tank walls were examined. Preliminary uncertainty analysis was also carried out.

scholarly journals Free surface flow past topography: A beyond-all-orders approach

2012 ◽  
Vol 23 (4) ◽  
pp. 441-467 ◽  
Author(s):  
CHRISTOPHER J. LUSTRI ◽  
SCOTT W. MCCUE ◽  
BENJAMIN J. BINDER
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Numerical Solutions ◽  
Power Series Expansion ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Asymptotic Results ◽  
Stagnation Points ◽  
Flow Past ◽  
Stokes Lines

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck, (2006) Exponential asymptotics and gravity waves. J. Fluid Mech.567, 299–326, the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of inclination. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

Free-surface flows past a surface-piercing object of finite length

1994 ◽  
Vol 273 ◽  
pp. 109-124 ◽  
Author(s):  
J. Asavanant ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Three Solutions ◽  
Surface Flows ◽  
Sharp Crest ◽  
Supercritical Flows

Steady two-dimensional flows past a parabolic obstacle lying on the free surface in water of finite depth are considered. The fluid is treated as inviscid and incompressible and the flow is assumed to be irrotational. Gravity is included in the free-surface condition. The problem is solved numerically by using boundary integral equation techniques. It is shown that there are solutions for which the flow is supercritical both upstream and downstream and others for which the flow is subcritical both upstream and downstream. These flows have continuous tangents at both ends of the obstacle at which separation occurs. For supercritical flows, there are up to three solutions corresponding to the same value of the Froude number when the obstacle is concave and up to two solutions when the obstacle is convex. For subcritical flows, there are solutions with waves behind the obstacle. As the Froude number decreases, these waves become steeper and the numerical calculations suggest that they, ultimately, reach limiting configurations with a sharp crest forming a 120° angle.

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

2002 ◽  
Vol 44 (2) ◽  
pp. 181-191 ◽  
Author(s):  
G. C. Hocking ◽  
J.-M. Vanden-Broeck ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Finite Depth ◽  
Experimental Results ◽  
Problem Comparison

The problem of withdrawal through a point sink of water from a fluid of finite depth with a free surface is considered. Assuming the flow to be axisymmetric, it is found that there is a maximum Froude number at which such flows can exist. This maximum corresponds to the formation of a secondary stagnation ring on the free surface. This result extends earlier work on this problem. Comparison is made with a small Froude number solution and past experimental results.

scholarly journals Steady free surface flows induced by a submerged ring source or sink

2012 ◽  
Vol 694 ◽  
pp. 352-370 ◽  
Author(s):  
T. E. Stokes ◽  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Numerical Solutions ◽  
Surface Deformation ◽  
Axisymmetric Flow ◽  
Free Surface Flows ◽  
Inviscid Fluid ◽  
Physical Reason ◽  
Small Surface ◽  
Source Radius

AbstractThe steady axisymmetric flow induced by a ring sink (or source) submerged in an unbounded inviscid fluid is computed and the resulting deformation of the free surface is obtained. Solutions are obtained analytically in the limit of small Froude number (and hence small surface deformation) and numerically for the full nonlinear problem. The small Froude number solutions are found to have the property that if the non-dimensional radius of the ring sink is less than $\rho = \sqrt{2} $, there is a central stagnation point on the surface surrounded by a dip which rises to the stagnation level in the far distance. However, as the radius of the ring sink increases beyond $\rho = \sqrt{2} $, a surface stagnation ring forms and moves outward as the ring sink radius increases. It is also shown that as the radius of the sink increases, the solutions in the vicinity of the ring sink/source change continuously from those due to a point sink/source ($\rho = 0$) to those due to a line sink/source ($\rho \ensuremath{\rightarrow} \infty $). These properties are confirmed by the numerical solutions to the full nonlinear equations for finite Froude numbers. At small values of the Froude number and sink or source radius, the nonlinear solutions look like the approximate solutions, but as the flow rate increases a limiting maximum Froude number solution with a secondary stagnation ring is obtained. At large values of sink or source radius, however, this ring does not form and there is no obvious physical reason for the limit on solutions. The maximum Froude numbers at which steady solutions exist for each radius are computed.

Bow and stern flows with constant vorticity

1999 ◽  
Vol 399 ◽  
pp. 277-300 ◽  
Author(s):  
SCOTT W. McCUE ◽  
LAWRENCE K. FORBES
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Radiation Condition ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Infinite Body ◽  
Constant Vorticity

Free surface flows of a rotational fluid past a two-dimensional semi-infinite body are considered. The fluid is assumed to be inviscid, incompressible, and of finite depth. A boundary integral method is used to solve the problem for the case where the free surface meets the body at a stagnation point. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterized by a train of waves upstream. It is shown numerically that the amplitude of these waves increases as each of the Froude number, vorticity and height of the body above the bottom increases.

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.

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.

scholarly journals Similarity and Froude Number Similitude in Kinematic and Hydrodynamic Features of Solitary Waves over Horizontal Bed

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1420
Author(s):  
Chang Lin ◽  
Ming-Jer Kao ◽  
James Yang ◽  
Rajkumar Venkatesh Raikar ◽  
Juan-Ming Yuan ◽  
...  
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Solitary Waves ◽  
High Speed ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Wave Kinematics ◽  
Wave Celerity ◽  
Image Velocimetry ◽  
Wave Heights

This study presents, experimentally, similarity and Froude number similitude (FNS) in the dimensionless features of two solitary waves propagating over a horizontal bed, using two wave gauges and a high-speed particle image velocimetry (HSPIV). The two waves have distinct wave heights H0 (2.9 and 5.8 cm) and still water depths h0 (8.0 and 16.0 cm) but identical H0/h0 (0.363). Together with the geometric features of free surface elevation and wavelength, the kinematic characteristics of horizontal and vertical velocities, as well as wave celerity, are elucidated. Illustration of the hydrodynamic features of local and convective accelerations are also made in this study. Both similarity and FNS hold true for the dimensionless free surface elevation (FSE), wavelength and celerity, horizontal and vertical velocities, and local and convective accelerations in the horizontal and vertical directions. The similarities and FNSs indicate that gravity dominates and governs the wave kinematics and hydrodynamics.

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