scholarly journals Embedded Eigenvalues for Water-Waves in a Three-Dimensional Channel with a Thin Screen

2018 ◽  
Vol 71 (2) ◽  
pp. 187-220
Author(s):  
Valeria Chiadó Piat ◽  
Sergey A Nazarov ◽  
Jari Taskinen
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Embedded Eigenvalues ◽  
Thin Screen

scholarly journals RESONANCES ON HEDGEHOG MANIFOLDS

2013 ◽  
Vol 53 (5) ◽  
pp. 416-426 ◽  
Author(s):  
Pavel Exner ◽  
Jiří Lipovský
Keyword(s):  
Real Axis ◽  
Quantum Particle ◽  
Single Point ◽  
Three Dimensional ◽  
High Energy ◽  
Quantum Graphs ◽  
The Real ◽  
Momentum Plane ◽  
Embedded Eigenvalues ◽  
Aharonov Bohm

We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads is attached. Resolvent and scattering resonances are shown to coincide in this situation. Next we consider the resonances together with embedded eigenvalues and ask about the high-energy asymptotics of such a family. For the case when all the halflines are attached at a single point we prove that all resonances are in the momentum plane confined to a strip parallel to the real axis, in contrast to the analogous asymptotics in some metric quantum graphs; we illustrate this on several simple examples. On the other hand, the resonance behaviour can be influenced by a magnetic field. We provide an example of such a ‘hedgehog’ manifold at which a suitable Aharonov-Bohm flux leads to absence of any true resonance, i.e. that corresponding to a pole outside the real axis.

Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves

1977 ◽  
Vol 21 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Hung-Tao Shen ◽  
Cesar Farell
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Integral Term ◽  
Linearized Theory ◽  
Single Integral ◽  
Numerical Computing ◽  
Complex Exponential ◽  
Derivatives Of

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

NUMERICAL SIMULATION OF THREE DIMENSIONAL TSUNAMIS WATER WAVES GENERATED BY LANDSLIDES: COMPARISON BETWEEN PHYSICAL MODEL RESULTS, VOF AND SPH

2007 ◽  
Author(s):  
Paolo De Girolamo ◽  
Tso-Ren Wu ◽  
Philip L.-F. Liu ◽  
Andrea Panizzo ◽  
Giorgio Bellotti ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Physical Model ◽  
Water Waves ◽  
Three Dimensional

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

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