Lagrangian approach to non-linear wave interactions in a warm plasma

1971 ◽  
Vol 6 (1) ◽  
pp. 53-72 ◽  
Author(s):  
J. J. Galloway ◽  
H. Kim
Keyword(s):  
Linear Equations ◽  
Wave Interaction ◽  
Lagrangian Approach ◽  
Linear Wave ◽  
Coupling Coefficients ◽  
Direct Expansion ◽  
Wave Interactions ◽  
Electrostatic Waves ◽  
Non Linear ◽  
Warm Plasma

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.

scholarly journals Non-linear wave interaction in a plasma column

1979 ◽  
Vol 46 (6) ◽  
pp. 577-594 ◽  
Author(s):  
J.-M. LARSEN† ◽  
F. W. CRAWFORD
Keyword(s):  
Plasma Column ◽  
Wave Interaction ◽  
Linear Wave ◽  
Non Linear

scholarly journals WATER-WAVE INTERACTION IN THE SURF ZONE

1974 ◽  
Vol 1 (14) ◽  
pp. 28
Author(s):  
D. Howell Peregrine
Keyword(s):  
Water Wave ◽  
Surf Zone ◽  
Linear Equations ◽  
Wave Interaction ◽  
Qualitative Description ◽  
Experimental Measurements ◽  
Wave Interactions

In the surf zone on beaches, there are strong effects which cannot be described by linear equations. This paper describes a number of wave interactions that can take place, using the simplest set of equations that give an adequate qualitative description. The results are of value for comparison with detailed experimental measurements and for gaining understanding of surf zone processes.

Non-Linear Wave Diffraction Around a Moored Ship

2004 ◽  
Author(s):  
J. Zang ◽  
R. Gibson ◽  
P. H. Taylor ◽  
R. Eatock Taylor ◽  
C. Swan
Keyword(s):  
Wave Diffraction ◽  
Scattering Problem ◽  
Wave Interaction ◽  
Wave Structure ◽  
Second Order ◽  
Linear Wave ◽  
Wave Impact ◽  
Non Linear ◽  
Focused Wave ◽  
Run Up

The objective of this research, part of the FP5 REBASDO Programme, is to examine the effects of directional wave spreading on the nonlinear hydrodynamic loads and the wave run-up around the bow of a floating vessel (FPSO) in random seas. In this work, the non-linear wave scattering problem is solved by employing a quadratic boundary element method. An existing scheme (DIFFRACT developed in Oxford) has been extended to deal with uni-directional and directional bi-chromatic input wave systems, calculating second-order wave diffraction under regular waves and focused wave groups. The second order wave interaction with a floating vessel in a unidirectional focused wave group is presented in this paper. Comparison of numerical results and the experimental measurements conducted at Imperial College shows excellent agreement. The second-order free surface components at the bow of the ship are very significant, and cannot be neglected if one requires accurate prediction of the wave-structure interaction; otherwise a major underestimation of the wave impact on the structure could occur.

Generation of surf beat by non-linear wave interactions

1971 ◽  
Vol 49 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Brent Gallagher
Keyword(s):  
Gravity Waves ◽  
Numerical Evaluation ◽  
Low Frequency ◽  
Linear Wave ◽  
Transfer Energy ◽  
Wave Interactions ◽  
Frequency Spectra ◽  
Non Linear ◽  
Linear Interactions ◽  
Low Frequency Waves

Non-linear interactions among wind-generated gravity waves transfer energy to low frequency waves in a coastal zone. A transfer function is derived for a straight coastline of constant bottom slope. This model is applied to three actual cases, and numerical evaluation of the energy transfer produces low frequency spectra which are compared with observations.

scholarly journals ASYMPTOTICAL ANALYSIS OF SOME COUPLED NONLINEAR WAVE EQUATIONS

2011 ◽  
Vol 16 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Rima Kriauzienė
Keyword(s):  
Wave Equations ◽  
Initial Conditions ◽  
Travelling Waves ◽  
Linear Equations ◽  
Travelling Wave ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Resonance Case ◽  
Non Linear ◽  
Asymptotical Analysis

We consider coupled nonlinear equations modelling a family of travelling wave solutions. The goal of our work is to show that the method of internal averaging along characteristics can be used for wide classes of coupled non-linear wave equations such as Korteweg-de Vries, Klein – Gordon, Hirota – Satsuma, etc. The asymptotical analysis reduces a system of coupled non-linear equations to a system of integro – differential averaged equations. The averaged system with the periodical initial conditions disintegrates into independent equations in non-resonance case. These equations describe simple weakly non-linear travelling waves in the non-resonance case. In the resonance case the integro – differential averaged systems describe interaction of waves and give a good asymptotical approximation for exact solutions.

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