scholarly journals Third-order theory for bichromatic bidirectional water waves partially reflected from vertical breakwaters

2010 ◽  
Vol 59 (7) ◽  
pp. 4442
Author(s):  
Yang Li ◽  
Huang Hu
Keyword(s):  
Water Waves ◽  
Order Theory ◽  
Third Order

scholarly journals Third-order theory for multi-directional irregular waves

2012 ◽  
Vol 698 ◽  
pp. 304-334 ◽  
Author(s):  
Per A. Madsen ◽  
David R. Fuhrman
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Transfer Functions ◽  
Order Theory ◽  
Irregular Waves ◽  
Third Order ◽  
Finite Water Depth ◽  
Wave Trains ◽  
Harmonic Resonance

AbstractA new third-order solution for multi-directional irregular water waves in finite water depth is presented. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential. Expressions for the velocity potential at the free surface are also provided, and the formulation incorporates the effect of an ambient current with the option of specifying zero net volume flux. Harmonic resonance may occur at third order for certain combinations of frequencies and wavenumber vectors, and in this situation the perturbation theory breaks down due to singularities in the transfer functions. We analyse harmonic resonance for the case of a monochromatic short-crested wave interacting with a plane wave having a different frequency, and make long-term simulations with a high-order Boussinesq formulation in order to study the evolution of wave trains exposed to harmonic resonance.

Third-order theory for bichromatic bi-directional water waves

2006 ◽  
Vol 557 ◽  
pp. 369 ◽  
Author(s):  
PER A. MADSEN ◽  
DAVID R. FUHRMAN
Keyword(s):  
Water Waves ◽  
Order Theory ◽  
Third Order

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

Dynamic Analysis of a Functionally Greded Sandwich Beam Traversed by a Moving Mass Based on a Refined Third-Order Theory

2021 ◽  
pp. 301-315
Author(s):  
Le Thi Ngoc Anh ◽  
Tran Van Lang ◽  
Vu Thi An Ninh ◽  
Nguyen Dinh Kien
Keyword(s):  
Dynamic Analysis ◽  
Sandwich Beam ◽  
Order Theory ◽  
Moving Mass ◽  
Third Order

Asymptotic theory for third-order differential equations with extension to higher odd-order equations

1991 ◽  
Vol 117 (3-4) ◽  
pp. 215-223 ◽  
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Order Theory ◽  
Linear Differential Equations ◽  
Asymptotic Solutions ◽  
Third Order ◽  
Odd Order ◽  
Linear Differential ◽  
General Conditions

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. Theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.

Periodicity Conditions for Third-Order Nonlinear With Application to Wave Propagation in Relaxing Media

2007 ◽  
Author(s):  
G. Nakhaie Jazar ◽  
M. Mahinfalah ◽  
J. Christopherson ◽  
A. Khazaei ◽  
G. Nazari
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Propagation ◽  
Acoustic Waves ◽  
Water Waves ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Rapid Convergence ◽  
Third Order ◽  
Specific Equation

It is known that wave propagation in nonlinear continues media, such as acoustic waves in solids, water waves, and solitary waves in arteries, can be reduced to a third order ordinary differential equations. They can be cast in a general third order ODE as x‴‴‴+f(t,x,x′,x″)=0. However, having an ODE as a reduced model for a phenomenon expressible by a partial differential equation lacks a proof to grantee for having a periodic solution. A third-order existence theorem has been proven to establish the sufficient conditions of periodicity for the above general third-order ODE. However, the equation is too general. In this paper we examine the following more specific equation x‴‴‴+g1(x′)x″+g2(x)x′+g(x,x′,t)=e(t). and prove a new theorem to establish the sufficient condition for its periodicity. To obtain the periodicity conditions, the Schauder’s fixed-point theorem is implemented. A numerical method is also developed for rapid convergence.

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