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.

Solvability of a supercritical free surface flow problem under gravity-capillarity

2017 ◽  
Vol 97 (10) ◽  
pp. 1701-1716
Author(s):  
N. Foukroun ◽  
R. Ait-Yahia-Djouadi ◽  
D. Hernane-Boukari
Keyword(s):  
Free Surface ◽  
Flow Problem ◽  
Free Surface Flow ◽  
Surface Flow

Nonlinear free-surface flow due to an impulsively started submerged point sink

1998 ◽  
Vol 364 ◽  
pp. 325-347 ◽  
Author(s):  
MING XUE ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Numerical Study ◽  
Free Surface Flow ◽  
Small Time ◽  
Surface Flow ◽  
Boundary Integral ◽  
Critical Regime ◽  
Gravitational Acceleration ◽  
Nonlinear Free Surface

The unsteady fully nonlinear free-surface flow due to an impulsively started submerged point sink is studied in the context of incompressible potential flow. For a fixed (initial) submergence h of the point sink in otherwise unbounded fluid, the problem is governed by a single non-dimensional physical parameter, the Froude number, [Fscr ]≡Q/4π(gh5)1/2, where Q is the (constant) volume flux rate and g the gravitational acceleration. We assume axisymmetry and perform a numerical study using a mixed-Eulerian–Lagrangian boundary-integral-equation scheme. We conduct systematic simulations varying the parameter [Fscr ] to obtain a complete quantification of the solution of the problem. Depending on [Fscr ], there are three distinct flow regimes: (i) [Fscr ]<[Fscr ]1≈0.1924 – a ‘sub-critical’ regime marked by a damped wave-like behaviour of the free surface which reaches an asymptotic steady state; (ii) [Fscr ]1<[Fscr ]<[Fscr ]2≈0.1930 – the ‘trans-critical’ regime characterized by a reversal of the downward motion of the free surface above the sink, eventually developing into a sharp upward jet; (iii) [Fscr ]>[Fscr ]2 – a ‘super-critical’ regime marked by the cusp-like collapse of the free surface towards the sink. Mechanisms behind such flow behaviour are discussed and hydrodynamic quantities such as pressure, power and force are obtained in each case. This investigation resolves the question of validity of a steady-state assumption for this problem and also shows that a small-time expansion may be inadequate for predicting the eventual behaviour of the flow.

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.

scholarly journals Fully implicit time discretization for a free surface flow problem

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 619-620 ◽  
Author(s):  
Eberhard Bänsch ◽  
Stephan Weller
Keyword(s):  
Free Surface ◽  
Flow Problem ◽  
Free Surface Flow ◽  
Time Discretization ◽  
Surface Flow ◽  
Implicit Time ◽  
Fully Implicit
Sign in / Sign up

Export Citation Format

Share Document