4 edition of **Transition bifurcation branches in non-linear water waves** found in the catalog.

Transition bifurcation branches in non-linear water waves

E. F. Toro

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Published
**1984**
by College of Aeronautics, Cranfield Institute of Technology in Cranfield, Bedford, UK
.

Written in English

- Gravity waves.,
- Water waves.,
- Bifurcation theory.

**Edition Notes**

Statement | by E.F. Toro. |

Series | College of Aeronautics report ;, no. 8418 |

Classifications | |
---|---|

LC Classifications | QA927 .T67 1984 |

The Physical Object | |

Pagination | 14, [5] leaves of plates : |

Number of Pages | 14 |

ID Numbers | |

Open Library | OL2980489M |

ISBN 10 | 0947767150 |

LC Control Number | 84230681 |

OCLC/WorldCa | 12315186 |

In that case, to switch to a different branch than the one that follows the direction vi (as defined above) the continuation must be perturbed. The algebraic bifurcation equation gives the necessary direction. One can often also perturb the system and then try to converge parallel to the original branch; typically the second branch is then found. Dynamical systems can undergo critical transitions where the system suddenly shifts from one stable state to another at a critical threshold called the tipping point. The decrease in recovery rate Cited by:

The system parameter induces twice a saddle-node bifurcation. The amplitude of the high-frequency force and the fractional-order induce only once a saddle-node bifurcation in the subcritical and the supercritical case, respectively. The system presents a nonlinear response to the low-frequency by: waves on the ocean, sound waves in the air or other media, and electromagnetic waves, of which visible light is a special case. A common feature of these examples is that they all can be described by partial differential equations (PDE). The purpose of these lecture notes is to give an introduction to various kinds of PDE describing Size: 1MB.

Transitional Waves • Characteristics of both deep- and shallow-water waves • Celerity depends on both water depth and wavelength Wind-Generated Wave Development • Capillary waves – Wind generates stress on sea surface • Gravity waves – Increasing wave energy • Trochoidal waveforms – Increased energy, pointed crests & rounded. @article{osti_, title = {Studies in nonlinear problems of energy. Final report}, author = {Matkowsky, B J}, abstractNote = {The author completed a successful research program on Nonlinear Problems of Energy, with emphasis on combustion and flame propagation. A total of papers associated with the grant has appeared in the literature, and the efforts have twice been recognized .

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The numerical computation of progressive free surface gravity waves on a horizontal bed is addressed. They are regarded as families of bifurcation branches (lambda, A) sub Q of constant discharge Q. Two transition values Q sub 1 and Q sub 2 were numerically determined with corresponding transition bifurcation branches that classify waves into three disjoint branch sets B sub 1, B sub 2 and B sub 3.

Transition bifurcation branches in non‐linear water waves They are regarded as families of bifurcation branches (λ,A)Q of constant discharge Q. Numerically we determine two transition values Q1 and Q2 with corresponding transition bifurcation branches that. Transition Bifurcation Transition bifurcation branches in non-linear water waves book in Non- Linear Water Waves.

Author. Toro, E.F. Institution. Cranfield Institute of Technology, College of Aeronautics. Date. Abstract. Starting in as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in Author: E.F.

Toro. Liu, R. [] “ Coexistence of multifarious exact nonlinear wave solutions for generalized b-equation,” Int. Bifurcation and Ch – Link, ISI, Google Scholar Liu, Z. & Tang, H. [ ] “ Explicit periodic wave solutions and their bifurcations for generalized Camassa–Holm equation,” Int.

Bifurcation and Author: Zongguang Li, Rui Liu. Nonlinear traveling wave type secondary bifurcation branches are computed for plane Poiseuille flow in the search for a physically more relevant transition criterion. These solutions are approximated by truncated Fourier series in streamwise and spanwise direction together with Chebyshev collocation across the channel.

Using the local results near bifurcation points, the global solution is Cited by: 5. The bifurcation scenario in a practically interesting nonlinear wave system is investigated by using a new scheme that is performed in a purely nonlinear wave framework with the Doppler effect.

Antman S.S. () Bifurcation problems associated with nonlinear wave propagation. In: Sleeman B.D., Jarvis R.J. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol Cited by: 1.

The Equations for Water Waves. Variational Formulation. The Linearized Formulation. Linear Waves in Water of Constant Depth. Initial Value Problem. Behavior Near the Front of the Wavetrain. Waves on an Interface Between Two Fluids. Surface Tension. Waves on a Steady Stream. Shallow Water Theory: Long Waves.

The Korteweg‐deVries and Boussinesq. Bifurcation is a change in the equilibrium points or periodic orbits, or in their stability properties, as a parameter is varied Example x˙1 = µ − x2 1 x˙2 = −x2 Find the File Size: KB.

The strong nonlinear interactions between the two independent frequencies (f t,f s) leading to spectra broadening to form the couplingmf s +nf t are predicted and analyzed numerically, and the characteristics of the transition are described.

Longitudinal variations of the transition wave Author: Guocan Ling, Allen T. Chwang, Jiayu Niu, Dongjiao Wang. Nonlinearity 28 () D Noja et al of standing waves, or higher branches, can be ordered according to the increasing number of nodes and each family bifurcates from one of the standing waves which are identically zero outside the ring (−L,L).

For small ωbranch is composed by orbitally stable standing File Size: KB. A saddle–node bifurcation is a local bifurcation in which two fixed points (or equilibrium) of a dynamical system collide and annihilate each other. If the phase space is one dimensional, one of the fixed points is unstable (the saddle), while the other is stable (the node).

A Kelvin mode is interpreted as a modification of a Kelvin wave or a boundary wave along a closed boundary, and a mixed Rossby-gravity mode as a modification of an inertial oscillation or a boundary wave along an open boundary. Transition modes appearing in edge and continental-shelf waves, equatorial waves and free oscillations over a sphere are systematically understood by Cited by: 8.

The bifurcation patterns are analysed in some detail from the computed bifurcation diagram, which shows that in B1 bifurcation is to the left and the amplitude A increases as the wavelength λ.

For piecewise-linear maps, the phenomenon that a branch of a one-dimensional unstable manifold of a periodic solution is completely contained in its stable manifold is codimension-two. Unlike codimension-one homoclinic corners, such “subsumed” homoclinic connections can be associated with stable periodic solutions.

() Wilton Ripples in Weakly Nonlinear Dispersive Models of Water Waves: Existence and Analyticity of Solution Branches. Water Waves () Solvability of a three-dimensional free surface flow problem over an obstacle.

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field. Advances in Cited by: advection amplitude analysis aqueous assumed bands bifurcation theory calcite cementation Chadam Chapter chemical compaction complex concentration crystal deformation denoted dependence descriptive variables diagenesis diagenetic dissolution front domain dynamics equations equilibrium constant evolution example feedback finger flow fluid pressure formula units fraction fracture free energy gradient grain growth growing hence inlet instability interface kerogen kinetics layering linear.

This book also deals with nonlinear wave motion, hydrodynamic systems, ocean wave spectra, and Helmholtz concept. The remaining chapters look into the issues of steady water bifurcation, concept of anisotropic soils, and flow visualization. to break down. Then, we investigate these limits and discuss basic nonlinear water wave equations.

Linear water waves A one-dimensional linear wave can be represented by Fourier components u = ℜ{Aexp(ikx −iωt)}, (1) where k is the wavenumber, ω is the frequency, and A is the amplitude. Both ω and A may be functions of k. The linear. The nonlinear two-dimensional problem, describing periodic steady waves on water method that allows us to produce convincing results concerning global bifurcation branches, In his book Author: Nikolay Kuznetsov, Evgueni Dinvay.

Steady, planar combustion waves propagating through solids and high-density fluids can lose stability to a time-periodic mode of burning via Hopf bifurcation as an activation-energy parameter incre Cited by: 8.Classiﬁcation of water waves.

Water waves are classiﬁed into three main categories: Shallow water or long waves, if h. 0 water waves, if h. 0 > 1 2 Intermediate water waves, if 1 For the nonlinear Schrödinger (NLS) equation with fourth-order dispersion and dual power law nonlinearity, by using the method of dynamical systems, we investigate the bifurcations and exact traveling wave solutions.

Because obtained traveling wave system is an integrable singular traveling wave system having a singular straight line and the origin in the phase plane is a high-order Author: Jibin Li, Yan Zhou.