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.

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.

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 Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

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