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 Free-surface flow due to a source submerged in a fluid of infinite depth with two stagnant regions

1993 ◽  
Vol 34 (3) ◽  
pp. 368-376 ◽  
Author(s):  
Hocine Mekias ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Surface Profile ◽  
Free Surface Flow ◽  
Shear Layers ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Infinite Depth ◽  
Free Surface Profile ◽  
Series Truncation Method

AbstractTwo-dimensional free-surface flows produced by a submerged source in a fluid of infinite depth are considered. It is assumed that the point on the free surface just above the source is a stagnation point and that the fluid outside two shear layers is at rest. The free-surface profile and the shape of the shear layers are determined numerically by using a series-truncation method. It is shown that there is a solution for each value of the Froude number F > 0. When F tends to infinity, the flow also describes a thin jet impinging in a fluid at rest.

The time-dependent free surface flow induced by a submerged line source or sink

1995 ◽  
Vol 284 ◽  
pp. 225-237 ◽  
Author(s):  
E. M. Sozer ◽  
M. D. Greenberg
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Stagnation Point ◽  
Line Source ◽  
Flow Direction ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Time Dependent ◽  
Infinite Depth ◽  
Source And Sink

The unsteady nonlinear potential flow induced by a submerged line source or sink is studied by a vortex sheet method, both to trace the free surface evolution and to explore the possible existence of steady-state solutions. Only steady-state flows have been considered by other investigators, and these flows have been insensitive to whether they are generated by a source or sink, except with respect to the flow direction along the streamlines. The time-dependent solution permits an assessment of the stability of previously found steady solutions, and also reveals differences between source and sink flows: for the infinite-depth case, steady stagnation-point-type solutions are found both for source flows and sink flows, above the critical value reported by other investigators; finally, it is shown that streamline patterns of steady stagnation-point flows are identical for source and sink flows only in the limiting case of infinite depth.

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.

scholarly journals Two infinite-Froude-number cusped free-surface flows due to a submerged line source or sink

1986 ◽  
Vol 28 (2) ◽  
pp. 260-270 ◽  
Author(s):  
I. L. Collings
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Ideal Fluid ◽  
Line Source ◽  
Steady Motion ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Flow Problems

AbstractSolutions are found to two cusp-like free-surface flow problems involving the steady motion of an ideal fluid under the infinite-Froude-number approximation. The flow in each case is due to a submerged line source or sink, in the presence of a solid horizontal base.

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 Flow over Obstacles at Subcritical Froude Numbers

1978 ◽  
Vol 5 (2) ◽  
pp. 89-94
Author(s):  
J.S.C. Tong ◽  
I.G. Currie
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Finite Length ◽  
Theoretical Approach ◽  
Wave Train ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Horizontal Surface ◽  
Lee Waves ◽  
The Mean

Experiments were carried out on free-surface flow over obstacles of finite length. The obstacles were located on the otherwise horizontal surface which contained the free-surface flow. The Froude number in each case was subcritical and resulted in a train of lee waves on the surface, downstream of the obstacles. The results confirm the predicted phenomenon of ‘upstream influence’ – that the mean upstream depth and the mean downstream depth should differ. Serious discrepancies between the observed results and the results from existing theories are noted, however. Not only is the amplitude of the lee waves at variance with the theory, but the phasing of the wave train, relative to the obstacle, is different. An alternative theoretical approach is proposed, the results from which are in much better agreement with the observed results.

scholarly journals The Effects of the Upstream Froude Number on the Free Surface Flow over the Side Weirs

2012 ◽  
Vol 28 ◽  
pp. 644-647 ◽  
Author(s):  
Sharareh Mahmodinia ◽  
Mitra Javan ◽  
Afshin Eghbalzadeh
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Side Weirs

A Finite Element Method for a Nonlinear Sloshing Problem

2003 ◽  
Author(s):  
J. H. Kyoung ◽  
J. W. Kim ◽  
K. J. Bai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Impact Load ◽  
Surface Condition ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Time Step ◽  
Nonlinear Sloshing ◽  
Element Method

A nonlinear sloshing problem in LNG tanker is numerically simulated. During excessive sloshing, the sloshing-induced impact load can cause a critical damage on the tank structure. Recently, this problem became one of important issues in FPSO design. A three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory. The exact nonlinear free surface condition is satisfied numerically. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The computations are made through an iterative method at each time step. The hydrodynamic loading on the pillar in the tank is computed and compared with other results.

Non-uniqueness of steady free-surface flow at critical Froude number

2014 ◽  
Vol 105 (4) ◽  
pp. 44003 ◽  
Author(s):  
Benjamin J. Binder ◽  
Mark G. Blyth ◽  
Sanjeeva Balasuriya
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Free Surface Flow ◽  
Surface Flow

Spilling breakers in shallow water: applications to Favre waves and to the shoaling and breaking of solitary waves

2016 ◽  
Vol 808 ◽  
pp. 441-468 ◽  
Author(s):  
S. L. Gavrilyuk ◽  
V. Yu. Liapidevskii ◽  
A. A. Chesnokov
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Shallow Water ◽  
Froude Number ◽  
Fluid Velocity ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Undular Bore ◽  
Characteristic Wavelength ◽  
Good Agreement

A two-layer long-wave approximation of the homogeneous Euler equations for a free-surface flow evolving over mild slopes is derived. The upper layer is turbulent and is described by depth-averaged equations for the layer thickness, average fluid velocity and fluid turbulent energy. The lower layer is almost potential and can be described by Serre–Su–Gardner–Green–Naghdi equations (a second-order shallow water approximation with respect to the parameter $H/L$, where $H$ is a characteristic water depth and $L$ is a characteristic wavelength). A simple model for vertical turbulent mixing is proposed governing the interaction between these layers. Stationary supercritical solutions to this model are first constructed, containing, in particular, a local turbulent subcritical zone at the forward slope of the wave. The non-stationary model was then numerically solved and compared with experimental data for the following two problems. The first one is the study of surface waves resulting from the interaction of a uniform free-surface flow with an immobile wall (the water hammer problem with a free surface). These waves are sometimes called ‘Favre waves’ in homage to Henry Favre and his contribution to the study of this phenomenon. When the Froude number is between 1 and approximately 1.3, an undular bore appears. The characteristics of the leading wave in an undular bore are in good agreement with experimental data by Favre (Ondes de Translation dans les Canaux Découverts, 1935, Dunod) and Treske (J. Hydraul Res., vol. 32 (3), 1994, pp. 355–370). When the Froude number is between 1.3 and 1.4, the transition from an undular bore to a breaking (monotone) bore occurs. The shoaling and breaking of a solitary wave propagating in a long channel (300 m) of mild slope (1/60) was then studied. Good agreement with experimental data by Hsiao et al. (Coast. Engng, vol. 55, 2008, pp. 975–988) for the wave profile evolution was found.

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