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Hamiltonian Approach to the Derivation of Evolution Equations for Wave Trains in Weakly Unstable Media : Volume 5, Issue 4 (30/11/-0001)

By Romanova, N. N.

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Book Id: WPLBN0004019914
Format Type: PDF Article :
File Size: Pages 13
Reproduction Date: 2015

Title: Hamiltonian Approach to the Derivation of Evolution Equations for Wave Trains in Weakly Unstable Media : Volume 5, Issue 4 (30/11/-0001)  
Author: Romanova, N. N.
Volume: Vol. 5, Issue 4
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
-0001
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Romanova, N. N. (-0001). Hamiltonian Approach to the Derivation of Evolution Equations for Wave Trains in Weakly Unstable Media : Volume 5, Issue 4 (30/11/-0001). Retrieved from http://hawaiilibrary.net/


Description
Description: Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevsky 3, 109017, Moscow, Russia. The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.

Summary
Hamiltonian approach to the derivation of evolution equations for wave trains in weakly unstable media

 

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