scholarly journals Flow caused by a point sink in a fluid having a free surface

1990 ◽  
Vol 32 (2) ◽  
pp. 231-249 ◽  
Author(s):  
Lawrence K. Forbes ◽  
Graeme C. Hocking
Keyword(s):  
Free Surface ◽  
Numerical Solution ◽  
Froude Number ◽  
Stagnation Point ◽  
Nonlinear Problem ◽  
Stagnation Line ◽  
Fully Nonlinear ◽  
Maximum Value ◽  
Low Froude Number ◽  
Nonlinear Solutions

AbstractThe flow caused by a point sink immersed in an otherwise stationary fluid is investigated. Low Froude number solutions are sought, in which the flow is radially symmetric and possesses a stagnation point at the surface, directly above the sink. A small-Froude-number expansion is derived and compared with the results of a numerical solution to the fully nonlinear problem. It is found that solutions of this type exist for all Froude numbers less than some maximum value, at which a secondary circular stagnation line is formed at the surface. The nonlinear solutions are reasonably well predicted by the small-Froude-number expansion, except for Froude numbers close to this maximum.

scholarly journals A note on the flow induced by a line sink beneath a free surface

1991 ◽  
Vol 32 (3) ◽  
pp. 251-260 ◽  
Author(s):  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Ideal Fluid ◽  
Critical Value ◽  
Homogeneous Fluid ◽  
Substitution Method ◽  
A Value ◽  
Line Sink ◽  
Low Froude Number

AbstractThe problem of withdrawing water through a line sink from a region containing an homogeneous fluid beneath a free surface is considered. Assuming steady, irrotational flow of an ideal fluid, solutions with low Froude number containing a stagnation point on the free surface above the sink are sought using a series substitution method. The solutions are shown to exist for a value of the Froude number up to a critical value of about 1.4. No solutions of this type are found for Froude numbers greater than this value.

scholarly journals A model for the free-surface flow due to a submerged source in water of infinite depth

1998 ◽  
Vol 39 (4) ◽  
pp. 528-538 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Surface Condition ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Nonuniform Distribution ◽  
Infinite Depth ◽  
Collocation Points ◽  
Series Truncation Method

AbstractWe consider a free-surface flow due to a source submerged in a fluid of infinite depth. It is assumed that there is a stagnation point on the free surface just above the source. The free-surface condition is linearized around the rigid-lid solution, and the resulting equations are solved numerically by a series truncation method with a nonuniform distribution of collocation points. Solutions are presented for various values of the Froude number. It is shown that for sufficiently large values of the Froude number, there is a train of waves on the free surface. The wavelength of these waves decreases as the distance from the source increases.

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 The effect of disturbances on the flows under a sluice gate and past an inclined plate

2007 ◽  
Vol 576 ◽  
pp. 475-490 ◽  
Author(s):  
B. J. BINDER ◽  
J.-M. VANDEN-BROECK
Keyword(s):  
Free Surface ◽  
Boundary Integral ◽  
Sluice Gate ◽  
Inclined Plate ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Potential Flows ◽  
Integral Equation Methods ◽  
Different Types ◽  
Nonlinear Solutions

Free surface potential flows past disturbances in a channel are considered. Three different types of disturbance are studied: (i) a submerged obstacle on the bottom of a channel; (ii) a pressure distribution on the free surface; and (iii) an obstruction in the free surface (e.g. a sluice gate or a flat plate). Surface tension is neglected, but gravity is included in the dynamic boundary condition. Fully nonlinear solutions are computed by boundary integral equation methods. In addition, weakly nonlinear solutions are derived. New solutions are found when several disturbances are present simultaneously. They are discovered through the weakly nonlinear analysis and confirmed by numerical computations for the fully nonlinear problem.

Nonlinear Ship Waves at Low Froude Number

1989 ◽  
Vol 33 (03) ◽  
pp. 176-193
Author(s):  
A. J. Hermans ◽  
F. J. Brandsma
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Continuous Dependence ◽  
Wave Pattern ◽  
Ray Method ◽  
Ship Waves ◽  
Asymptotic Evaluation ◽  
Low Froude Number ◽  
Field Wave

The wave pattern of a thick ship-like object with finite bow and stern angles 0 <β<π/2 is studied. The completely blunt form p = π/2 is excluded. It turns out that the wave pattern is strongly influenced by the nonlinear terms at the free surface. The wave pattern is determined by means of the ray method. The rays are generated mainly at the bow and the stern. A crucial step is the determination of the so-called excitation coefficients. They are constructed by means of an asymptotic evaluation of a distribution of "local"sources at the free surface. It is shown that for small angles β<< 1 the excitation coefficients are the same as the ones obtained by means of an asymptotic expansion for small values of the Froude number of the results of Michell's thin-ship theory. For increasing values of β, the excitation coefficients change asymptotically. The theory herein shows a continuous dependence, nevertheless. Similar changes are observed in the far-field wave pattern.

Unsteady flow over a submerged source with low Froude number

2014 ◽  
Vol 25 (5) ◽  
pp. 655-680 ◽  
Author(s):  
CHRISTOPHER J. LUSTRI ◽  
S. JONATHAN CHAPMAN
Keyword(s):  
Free Surface ◽  
Unsteady Flow ◽  
Froude Number ◽  
Gravity Waves ◽  
Surface Gravity ◽  
Infinite Depth ◽  
Surface Gravity Waves ◽  
Flow Past ◽  
Low Froude Number ◽  
Exponential Asymptotics

In the low-Froude number limit, free-surface gravity waves caused by flow past a submerged obstacle have amplitude that is exponentially small. Consequently, these cannot be represented using an asymptotic series expansion. Previous studies have considered linearized steady flow past a submerged source in infinite-depth fluids, in which exponential asymptotics were used to determine the behaviour of downstream longitudinal and transverse free-surface gravity waves. Here, unsteady flow past a submerged source in an infinite-depth fluid is investigated, with the free surface taken to be initially waveless. The source is taken to be weak, and the flow is linearized about the undisturbed solution. Exponential asymptotics are applied to determine the wave behaviour on the free surface in terms of the two-dimensional plan-view, in order to show how the free surface waves evolve over time and eventually tend to the steady solution.

Divergent low-Froude-number series expansion of nonlinear free-surface flow problems

1978 ◽  
Vol 361 (1705) ◽  
pp. 207-224 ◽  
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Continuous Wave ◽  
Free Surface Flow ◽  
Formal Series ◽  
Surface Flow ◽  
Exponential Integral ◽  
Flow Problems ◽  
Low Froude Number ◽  
Nonlinear Free Surface

The low-Froude-number approximation in free-surface hydrodynamics is singular, and leads to formal series in powers of the Froude number with zero radius of convergence. The properties of these divergent series are discussed for several types of two-dimensional flows. It is shown that the divergence is of ‘n!' or exponential-integral character. A potential or actual lack of uniqueness is discovered and discussed. The series are summed by use of suitable nonlinear iterative transformations, giving good accuracy even for moderately large Froude number. Converged ' solutions ’ are obtained in this way, which possess jump discontinuities on the free surface. These jumps can be explained and, in principle, removed, by consideration of appropriate choices for the branch cut of the limiting exponential-integral solution. For example, we provide here a solution for a continuous wave-like flow, behind a semi-infinite moving body.

Nonlinear free-surface flow at a two-dimensional bow

1989 ◽  
Vol 209 ◽  
pp. 57-75 ◽  
Author(s):  
Mark A. Grosenbaugh ◽  
Ronald W. Yeung
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Free Surface Flow ◽  
Surface Flow ◽  
The Body ◽  
Two Dimensional ◽  
Bow Wave ◽  
Bulbous Bow ◽  
Nonlinear Free Surface

Unsteady free-surface flow at the bow of a steadily moving, two-dimensional body is solved using a modified Eulerian-Lagrangian technique. Lagrangian marker particles are distributed on both the free surface and the far-field boundary. The flow field corresponding to an inviscid, double-body solution is used for the initial condition. Solutions are obtained over a range of Froude numbers for bodies of three different shapes: a vertical step, a faired profile, and a bulbous bow. A transition Froude number exists at which the bow wave begins to overturn and break. The value of the transition Froude number depends on the bow shape. A stagnation point is observed to be present below the free surface during the initial stage of the wave formation. For flows occurring above the transition Froude number, the stagnation point remains trapped below the free surface as the wave overturns. Below the transition Froude number, the stagnation point rises to the surface as the crest of the transient bow wave moves upstream and away from the body.

Sign in / Sign up

Export Citation Format

Share Document