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.

On the free-surface flow of very steep forced solitary waves

2013 ◽  
Vol 739 ◽  
pp. 1-21 ◽  
Author(s):  
Stephen L. Wade ◽  
Benjamin J. Binder ◽  
Trent W. Mattner ◽  
James P. Denier
Keyword(s):  
Free Surface ◽  
Solitary Waves ◽  
Flow Problem ◽  
Nonlinear Approximation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Boundary Integral ◽  
Weakly Nonlinear ◽  
Nonlinear Solutions

AbstractThe free-surface flow of very steep forced and unforced solitary waves is considered. The forcing is due to a distribution of pressure on the free surface. Four types of forced solution are identified which all approach the Stokes-limiting configuration of an included angle of $12{0}^{\circ } $ and a stagnation point at the wave crests. For each type of forced solution the almost-highest wave does not contain the most energy, nor is it the fastest, similar to what has been observed previously in the unforced case. Nonlinear solutions are obtained by deriving and solving numerically a boundary integral equation. A weakly nonlinear approximation to the flow problem helps with the identification and classification of the forced types of solution, and their stability.

Nonlinear three-dimensional interfacial flows with a free surface

2007 ◽  
Vol 591 ◽  
pp. 481-494 ◽  
Author(s):  
E. I. PĂRĂU ◽  
J.-M. VANDEN-BROECK ◽  
M. J. COOKER
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Solitary Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Interfacial Flows ◽  
Fully Nonlinear Equations ◽  
Weakly Nonlinear ◽  
Integral Equation Methods ◽  
Superposed Fluids

A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity–capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.

Nonlinear interactions between a free-surface flow with surface tension and a submerged cylinder

2010 ◽  
Vol 648 ◽  
pp. 485-507 ◽  
Author(s):  
R. M. MOREIRA ◽  
D. H. PEREGRINE
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Gravity Waves ◽  
Classical Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Steady Solution ◽  
Small Scale ◽  
Fully Nonlinear ◽  
Submerged Cylinder

A submerged cylinder in a uniform stream flow is approximated by a horizontal doublet, following Lamb's classical method. A linear steady solution including surface tension effects is derived, showing that under certain conditions small-scale ripples are formed ahead of the cylinder, while a train of ‘gravity-like’ waves appear downstream. Surface tension effects and a dipole are included in the fully nonlinear unsteady non-periodic boundary-integral solver described by Tanaka et al. (J. Fluid Mech., vol. 185, 1987, pp. 235–248). Nonlinear effects are modelled by considering a flat free surface or the linear stationary solution as an initial condition for the fully nonlinear irrotational flow programme. Long-run computations show that these unsteady flows approach a steady solution for some parameters after waves have radiated away. In other cases the flow does not approach a steady solution. Interesting features at the free surface such as the appearance of ‘parasitic capillaries’ near the crest of gravity waves and the formation of capillary–gravity waves upstream of the cylinder are found.

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.

Nonlinear long waves generated by a moving pressure disturbance

1996 ◽  
Vol 325 ◽  
pp. 399-418 ◽  
Author(s):  
C. M. Casciola ◽  
M. Landrini
Keyword(s):  
Free Surface ◽  
Finite Depth ◽  
Boundary Integral ◽  
Long Waves ◽  
Integral Approach ◽  
Wave System ◽  
Boussinesq Model ◽  
Fully Nonlinear ◽  
Pressure Disturbance ◽  
De Vries

The evolution of long waves generated by a pressure disturbance acting on an initially unperturbed free surface in a channel of finite depth is analysed. Both off-critical and transcritical conditions are considered in the context of the fully nonlinear inviscid problem. The solution is achieved by using an accurate boundary integral approach and a time-stepping procedure for the free-surface dynamics.The discussion emphasizes the comparison between the present results and those provided by both the Boussinesq and the related Korteweg–de Vries model. For small amplitudes of the forcing, the predictions of the asymptotic theories are essentially confirmed. However, for finite intensities of the disturbance, several new features significantly affect the physical results. In particular, the interaction among different wave components, neglected in the Korteweg–de Vries approximation, is crucial in determining the evolution of the wave system. A substantial difference is indeed observed between the solutions of the Korteweg–de Vries equation and those of both the fully nonlinear and the Boussinesq model. For increasing dispersion and fixed nonlinearity the agreement between the Boussinesq and fully nonlinear description is lost, indicating a regime where dispersion becomes dominant.Consistently with the long-wave modelling, the transcritical regime is characterized by an unsteady flow and a periodic emission of forward-running waves. However, also in this case, quantitative differences are observed between the three models. For larger amplitudes, wave steepening is almost invariably observed as a precursor of the localized breaking commonly detected in the experiments. The process occurs at the crests of either the trailing or the upstream-emitted wave system for Froude numbers slightly sub- and super-critical respectively.

Numerical calculations of the free-surface flow under a sluice gate

1997 ◽  
Vol 330 ◽  
pp. 339-347 ◽  
Author(s):  
J.-M. VANDEN-BROECK
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Large Amplitude ◽  
Numerical Solutions ◽  
Free Surface Flow ◽  
Radiation Condition ◽  
Surface Flow ◽  
Boundary Integral ◽  
Sluice Gate ◽  
The Waves

The free-surface flow under a sluice gate is considered. The fluid is assumed to be inviscid and incompressible. The problem is solved numerically by using a boundary integral equation technique. Accurate numerical solutions are obtained when the intersection of the upstream free surface with the gate is a stagnation point. It is shown that the radiation condition is not satisfied far upstream and that there is a train of waves on the upstream free surface. For large values of the downstream Froude number F, the amplitude of the waves is so small that the upstream free surface is essentially flat. However for small values of F, the waves are of large amplitude. They ultimately approach the Stokes' limiting configuration with an angle of 120° at their crest as F is decreased.

scholarly journals Two-dimensional generalized solitary waves and periodic waves under an ice sheet

2011 ◽  
Vol 369 (1947) ◽  
pp. 2957-2972 ◽  
Author(s):  
Jean-Marc Vanden-Broeck ◽  
Emilian I. Părău
Keyword(s):  
Solitary Waves ◽  
Gravity Waves ◽  
Ice Sheet ◽  
Periodic Waves ◽  
Two Dimensional ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Dimensional Gravity ◽  
Nonlinear Solutions

Two-dimensional gravity waves travelling under an ice sheet are studied. The flow is assumed to be potential. Weakly nonlinear solutions are derived and fully nonlinear solutions are calculated numerically. Periodic waves and generalized solitary waves are studied.

scholarly journals On satisfying the radiation condition in free-surface flows

2009 ◽  
Vol 624 ◽  
pp. 179-189 ◽  
Author(s):  
B. J. BINDER ◽  
J.-M. VANDEN-BROECK ◽  
F. DIAS
Keyword(s):  
Radiation Condition ◽  
Integral Equation Method ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Steady Flows ◽  
Surface Flows ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
Critical Solutions ◽  
Nonlinear Solutions

Binder & Vanden-Broeck (2005) showed there are no subcritical or critical solutions satisfying the radiation condition for steady flows past a flat plate. By using a weakly nonlinear analysis, it is shown that such flows exist for a curved plate. Fully nonlinear solutions are computed by a boundary integral equation method, and new nonlinear solutions for supercritical and generalized critical flows past a curved plate are presented.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

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