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.

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.

Stability of water waves

1986 ◽  
Vol 406 (1830) ◽  
pp. 115-125 ◽  
Keyword(s):  
Hamiltonian Systems ◽  
Water Waves ◽  
Water Wave ◽  
Loss Of Stability ◽  
Imaginary Eigenvalue ◽  
Linearized Problem ◽  
Stability Of Water ◽  
Permanent Form

We apply some general results for Hamiltonian systems, depending on the notion of signature of eigenvalues, to determine the circumstances under which collisions of imaginary eigenvalue for the linearized problem about a travelling water wave of permanent form are avoided or lead to loss of stability, up to non-degeneracy assumptions. A new superharmonic instability is predicted and verified.

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.

scholarly journals Reflection from a water waves from a vertical vortex sheet in water of finite depth

1987 ◽  
Vol 29 (2) ◽  
pp. 127-141 ◽  
Author(s):  
W. D. McKee ◽  
F. Tesoriero
Keyword(s):  
Integral Equation ◽  
Variational Method ◽  
Water Waves ◽  
Water Wave ◽  
Finite Depth ◽  
Vortex Sheet ◽  
Transmission Properties ◽  
Obliquely Incident ◽  
Galerkin Solution ◽  
Wave Problems

AbstractThe reflection-transmission properties of water waves obliquely incident upon a vortex sheet in water of finite depth are studied. The problem is reduced to that of solving two integral equation. An accurate Galerkin solution is obtained which supports the use of the “variational method” in water wave problems that has recently been questioned by Kirby and Dalyrmple.

scholarly journals Existence and amplitude bounds for irrotational water waves in finite depth

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170094 ◽  
Author(s):  
Florian Kogelbauer
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Wave Speed ◽  
Finite Depth ◽  
Relative Mass ◽  
Wave Problem ◽  
Nonlinear Water Waves ◽  
Water Wave Problem ◽  
Pseudo Differential Equation ◽  
Nonlinear Solutions

We prove the existence of solutions to the irrotational water-wave problem in finite depth and derive an explicit upper bound on the amplitude of the nonlinear solutions in terms of the wavenumber, the total hydraulic head, the wave speed and the relative mass flux. Our approach relies upon a reformulation of the water-wave problem as a one-dimensional pseudo-differential equation and the Newton–Kantorovich iteration for Banach spaces. This article is part of the theme issue ‘Nonlinear water waves’.

Application and Verification of Deepwater Green Function for Water Waves

2001 ◽  
Vol 45 (03) ◽  
pp. 187-196
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Green Function ◽  
Water Waves ◽  
Near Field ◽  
Finite Depth ◽  
Offshore Structures ◽  
Accurate Analysis ◽  
Mathematical Functions ◽  
Infinite Depth ◽  
Analysis And Design ◽  
The Green Function

An efficient method for the numerical evaluation of the free-surface Green function for deep-water application was presented by Telste & Noblesse (1986) and again by Ponizy et al (1994). A FORTRAN code was include in their 1986 paper. The numerical method makes use of known mathematical functions. Numerical values of some of these mathematical functions were depicted, but no verification on the accuracy of the Green function routine in an application was given. The purpose of this paper is to compare their numerical values in the near-field and far-field regions with other similar computation for the infinite-depth Green function. The results of the infinite-depth Green function are also compared with the results from the finite-depth Green function that is more time consuming. Based on the accuracy of the various methods, the regions of application of the efficient deepwater Green function formulation and the effect of the water depth on the Green function are discussed. Any regions of inaccurate results are noted. Forces on submerged offshore structures and motions of the floating structures are determined using the lower-order panel method and these different Green function routines. The results on the motions of a semisubmersible in various water depths are compared and the accuracy of these routines in various regions is shown. The presented results will help the hydrodynamicist and designer to evaluate the suitable formulation and its regions of application for the accurate analysis and design of offshore structures.

scholarly journals Regularity of rotational travelling water waves

2012 ◽  
Vol 370 (1964) ◽  
pp. 1602-1615 ◽  
Author(s):  
Joachim Escher
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Travelling Wave ◽  
Capillary Waves ◽  
Wave Profile ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Common Assumption ◽  
Infinite Depth ◽  
Stagnation Points

Several recent results on the regularity of streamlines beneath a rotational travelling wave, along with the wave profile itself, will be discussed. The survey includes the classical water wave problem in both finite and infinite depth, capillary waves and solitary waves as well. A common assumption in all models to be discussed is the absence of stagnation points.

Korteweg–de Vries type equations for waves propagating along the interface between air–water

2008 ◽  
Vol 86 (12) ◽  
pp. 1427-1435 ◽  
Author(s):  
A M Abourabia ◽  
M A Mahmoud ◽  
G M Khedr
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Fluid Layer ◽  
Wave Packets ◽  
Multiple Scale ◽  
Finite Depth ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Kdv Equations ◽  
De Vries

We present solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity and surface tension. The method of multiple scale expansion is employed to obtain the Korteweg–de Vries (KdV) equations for solitons, which describes the behavior of the system for the free surface between air and water in a nonlinear approach. The solutions of the water wave problem split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as the solutions of the KdV equations. The solutions of the KdV equations are obtained analytically by using the tanh-function method. The dispersion relations of the model KdV equations are studied. Finally, we observe that the elevation of the water waves are in the form of traveling solitary waves. The horizontal and vertical velocities, and the phase diagrams of the velocity components have a nonlinear characters.PACS No.: 47.11.St

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.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

Sign in / Sign up

Export Citation Format

Share Document