A Weakly Nonlinear Wave Model of Practical Use

2002 ◽  
Author(s):  
Jung Lyul Lee ◽  
Chan Sung Park
Keyword(s):  
Nonlinear Wave ◽  
Wave Model ◽  
Weakly Nonlinear

scholarly journals A Boussinesq-Type Model for Nonlinear Wave-Heaving Cylinder Interaction

Energies ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 469
Author(s):  
Theofanis Karambas ◽  
Eva Loukogeorgaki
Keyword(s):  
Numerical Model ◽  
Nonlinear Wave ◽  
Wave Model ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Floating Body ◽  
Type Model ◽  
Weakly Nonlinear ◽  
Exciting Forces ◽  
Heave Motion

In the present work, a Boussinesq-type numerical model is developed for the simulation of nonlinear wave-heaving cylinder interaction. The wave model is able to describe the propagation of fully dispersive and weakly nonlinear waves over any finite water depth. The wave-cylinder interaction is taken into account by solving simultaneously an elliptic equation that determines the pressure exerted by the fluid on the floating body. The heave motion for the partially immersed floating cylinder under the action of waves is obtained by solving numerically the body’s equation of motion in the z direction based on Newton’s law. The developed model is applied for the case of a fixed and a free-floating circular cylinder under the action of regular waves, as well as for a free-floating cylinder undergoing a forced motion in heave. Results (heave and surge exciting forces, heave motions, and wave elevation) are compared with those obtained using a frequency domain numerical model, which is based on the boundary integral equation method.

scholarly journals Null modes effect in Rossby wave model

2004 ◽  
Vol 11 (3) ◽  
pp. 281-293
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Nonlinear Wave ◽  
Rossby Wave ◽  
Wave Model ◽  
Wave Fields

Abstract. The problem of the null-modes existence and some particularities of their interaction with nonlinear vortex-wave-like structures is discussed. We show that the null-modes are fundamental elements of nonlinear wave fields. The conditions under which null-modes can manifest themselves are elucidated. The Rossby-Hasegawa-Mima (RHM) model is used for the illustration of features of null-modes-waves interactions.

scholarly journals Wave Directions in a Narrow Bay

2010 ◽  
Vol 40 (1) ◽  
pp. 155-169 ◽  
Author(s):  
Heidi Pettersson ◽  
Kimmo K. Kahma ◽  
Laura Tuomi
Keyword(s):  
Wave Model ◽  
Wave Climate ◽  
Spectral Peak ◽  
Step Size ◽  
Weakly Nonlinear ◽  
Spectral Wave Model ◽  
Directional Coupling ◽  
Directional Wave ◽  
The Baltic ◽  
The Waves

Abstract In slanting fetch conditions the direction of actively growing waves is strongly controlled by the fetch geometry. The effect was found to be pronounced in the long and narrow Gulf of Finland in the Baltic Sea, where it significantly modifies the directional wave climate. Three models with different assumptions on the directional coupling between the wave components were used to analyze the physics responsible for the directional behavior of the waves in the gulf. The directionally decoupled model produced the direction at the spectral peak correctly when the slanting fetch geometry was narrow but gave a weaker steering than observed when the fetch geometry was broader. The method of Donelan estimated well the direction at the spectral peak in well-defined slanting fetch conditions, but overestimated the longer fetch components during wave growth from a more complex shoreline. Neither the decoupled nor the Donelan model reproduced the observed shifting of direction with the frequency. The performance of the third-generation spectral wave model (WAM) in estimating the wave directions was strongly dependent on the grid resolution of the model. The dominant wave directions were estimated satisfactorily when the grid-step size was dropped to 5 km in the gulf, which is 70 km in its narrowest part. A mechanism based on the weakly nonlinear interactions is proposed to explain the strong steering effect in slanting fetch conditions.

Chaos in positive ion–negative ion magnetized plasmas

2020 ◽  
Vol 86 (6) ◽  
Author(s):  
Samiran Ghosh ◽  
Biplab Maity ◽  
Swarup Poria
Keyword(s):  
Nonlinear Wave ◽  
Low Frequency ◽  
Negative Ions ◽  
Dynamical Behaviour ◽  
Negative Ion ◽  
Sound Waves ◽  
Weakly Nonlinear ◽  
Positive Ions ◽  
Experimental Parameters ◽  
Map Analysis

The dynamical behaviour of weakly nonlinear, low-frequency sound waves are investigated in a plasma composed of only positive and negative ions incorporating the effects of a weak external uniform magnetic field. In the plasma model the mass (temperature) of the positive ions is smaller (larger) than that of the negative ions. The dynamics of the nonlinear wave is shown to be governed by a novel nonlinear equation. The stationary plane wave (analytical and numerical) nonlinear analysis on the basis of experimental parameters reveals that the nonlinear wave does have quasi-periodic and chaotic solutions. The Poincarè return map analysis confirms these observed complex structures.

scholarly journals Hamiltonian description of wave dynamics in nonequilibrium media

1994 ◽  
Vol 1 (4) ◽  
pp. 234-248 ◽  
Author(s):  
N. N. Romanova
Keyword(s):  
Nonlinear Wave ◽  
Evolution Equations ◽  
Normal Modes ◽  
Weak Nonlinearity ◽  
Hamiltonian Description ◽  
Weakly Nonlinear ◽  
Wave Dynamics ◽  
Canonical Variables ◽  
Stable Points ◽  
Stable Area

Abstract. We consider Hamiltonian description of weakly nonlinear wave dynamics in unstable and nonequilibrium media. We construct the appropriate canonical variables in the whole wavenumber space. The essentially new element is the construction of canonical variables in a vicinity of marginally stable points where two normal modes coalesce. The commonly used normal variables are not appropriate in this domain. The mater is that the approximation of weak nonlinearity breaks down when the dynamical system is written in terms of these variables. In this case we introduce the canonical variables based on the linear combination of modes belonging to the two different branches of dispersion curve. As an example of one of the possible applications of presented results the evolution equations for weakly nonlinear wave packets in the marginally stable area are derived. These equations cannot be derived if we deal with the commonly used normal variables.

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