scholarly journals Water waves as a spatial dynamical system; infinite depth case

2005 ◽  
Vol 15 (3) ◽  
pp. 037112 ◽  
Author(s):  
Matthieu Barrandon ◽  
Gérard Iooss
Keyword(s):  
Dynamical System ◽  
Water Waves ◽  
Infinite Depth

Reflexion of water waves by a permeable barrier

1979 ◽  
Vol 95 (1) ◽  
pp. 141-157 ◽  
Author(s):  
C. Macaskill
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Finite Depth ◽  
Infinite Depth ◽  
Permeable Barrier ◽  
Impermeable Barrier ◽  
Linearized Problem ◽  
Special Case ◽  
Thin Barrier ◽  
Standard Techniques

The linearized problem of water-wave reflexion by a thin barrier of arbitrary permeability is considered with the restriction that the flow be two-dimensional. The formulation includes the special case of transmission through one or more gaps in an otherwise impermeable barrier. The general problem is reduced to a set of integral equations using standard techniques. These equations are then solved using a special decomposition of the finite depth source potential which allows accurate solutions to be obtained economically. A representative range of solutions is obtained numerically for both finite and infinite depth problems.

An integrable normal form for water waves in infinite depth

1995 ◽  
Vol 84 (3-4) ◽  
pp. 513-531 ◽  
Author(s):  
Walter Craig ◽  
Patrick A. Worfolk
Keyword(s):  
Normal Form ◽  
Water Waves ◽  
Infinite Depth

scholarly journals Water waves over a channel of infinite depth

1953 ◽  
Vol 11 (2) ◽  
pp. 201-214 ◽  
Author(s):  
Thom R. Greene ◽  
Albert E. Heins
Keyword(s):  
Water Waves ◽  
Infinite Depth

Interaction of water waves with two closely spaced vertical obstacles

1974 ◽  
Vol 66 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Water Waves ◽  
Asymptotic Theory ◽  
Fluid Motion ◽  
Vertical Oscillation ◽  
Flat Plates ◽  
Local Flow ◽  
Infinite Depth ◽  
Transmission Coefficients ◽  
Rapid Changes ◽  
Critical Wavenumber

Two-dimensional waves are incident upon a pair of vertical flat plates intersecting the free surface in a fluid of infinite depth. An asymptotic theory is developed for the resulting wave reflexion and transmission, assuming that the separation between the plates is small. The fluid motion between the plates is a uniform vertical oscillation, matched to the outer wave field by a local flow at the opening beneath the plates. It is shown that the reflexion and transmission coefficients undergo rapid changes, ranging from complete reflexion to complete transmission, in the vicinity of a critical wavenumber where the fluid column between the obstacles is resonant.

scholarly journals Scattering of Oblique Water Waves by an Infinite Step

2018 ◽  
Vol 23 (2) ◽  
pp. 327-338
Author(s):  
P. Dolai ◽  
D.P. Dolai
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Water Wave ◽  
Wave Train ◽  
Reflection And Transmission Coefficients ◽  
Physical Parameters ◽  
Reflection And Transmission ◽  
Infinite Depth ◽  
Transmission Coefficients ◽  
Galerkin Approximations

AbstractThe present paper is concerned with the problem of scattering of obliquely incident surface water wave train passing over a step bottom between the regions of finite and infinite depth. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain very accurate numerical estimates for reflection and transmission coefficients. The numerical results are illustrated in tables.

Further developments in a nonlinear theory of water waves for finite and infinite depths

1987 ◽  
Vol 324 (1577) ◽  
pp. 47-72 ◽  
Keyword(s):  
General Theory ◽  
Nonlinear Theory ◽  
Water Waves ◽  
Finite Depth ◽  
Balance Laws ◽  
Jump Conditions ◽  
Infinite Depth ◽  
Inviscid Fluids ◽  
Special Cases ◽  
Special Case

This paper is a companion to an earlier one (Green & Naghdi 1986, Phil. Trans. R. Soc. Lond . A 320, 37-70 (1986)) and deals with certain aspects of a nonlinear waterwave theory and its applications to waters of infinite and finite depths. A new procedure is used to establish a 1-1 correspondence between the lagrangian and eulerian formulations of the integral balance laws of a general thermomechanical theory of directed fluid sheets, as well as their associated jump conditions in the presence of any number of directors. (Such a correspondence between lagrangian and eulerian formulations was previously possible in the special case of a single constrained director.) These results are valid for both compressible and incompressible (not necessarily inviscid) fluids. Applications are then made to special cases of the general theory (including the jump conditions) for incompressible inviscid fluids of infinite depth (with two directors) and of finite depth (with three directors) and the nature of the results are illustrated with particular reference to a wedge-like boat.

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