An example of non–uniqueness in the two–dimensional linear water–wave problem involving a submerged body

1998 ◽  
Vol 454 (1980) ◽  
pp. 3145-3165 ◽  
Author(s):  
D. V. Evans ◽  
R. Porter
Keyword(s):  
Water Wave ◽  
Two Dimensional ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Submerged Body

scholarly journals An example of non-uniqueness in the two-dimensional linear water wave problem

1996 ◽  
Vol 315 ◽  
pp. 257-266 ◽  
Author(s):  
M. McIver
Keyword(s):  
Free Surface ◽  
Numerical Calculation ◽  
Water Wave ◽  
Two Dimensional ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Source Point ◽  
The Waves

An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.

A note on uniqueness in the linearized water-wave problem

1999 ◽  
Vol 386 ◽  
pp. 5-14 ◽  
Author(s):  
N. G. KUZNETSOV ◽  
M. J. SIMON
Keyword(s):  
Free Surface ◽  
Finite Number ◽  
Water Wave ◽  
Axisymmetric Problem ◽  
Two Dimensional ◽  
Plane Region ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Infinite Depth ◽  
The Uniqueness Theorem

The uniqueness theorem of Simon & Ursell (1984), concerning the linearized two-dimensional water-wave problem in a fluid of infinite depth, is extended in two directions. First, we consider a two-dimensional geometry involving two submerged symmetric bodies placed sufficiently far apart that they are not confined in the vertical right angle having its vertex on the free surface as the theorem of Simon & Ursell requires. A condition is obtained guaranteeing the uniqueness outside a finite number of bounded frequency intervals. Secondly, the method of Simon & Ursell is generalized to prove uniqueness in the axisymmetric problem for bodies violating John's condition provided the free surface is a connected plane region.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

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