General linear theory of damped, beam-driven oscillations of a single wave

1998 ◽  
Author(s):  
P.H. Stoltz ◽  
J.R. Cary
Keyword(s):  
Linear Theory ◽  
General Linear ◽  
Single Wave

General linear theory of damped, beam-driven oscillations of a single mode

1998 ◽  
Vol 5 (11) ◽  
pp. 4084-4093 ◽  
Author(s):  
Peter H. Stoltz ◽  
John R. Cary
Keyword(s):  
Linear Theory ◽  
Single Mode ◽  
General Linear

Higher order approximations in the theory of longitudinal plasma oscillations

1967 ◽  
Vol 1 (4) ◽  
pp. 483-497 ◽  
Author(s):  
F. Einaudi ◽  
W. I. Axford
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
Linear Theory ◽  
Asymptotic Series ◽  
Finite Amplitude ◽  
Single Wave ◽  
Background Distribution ◽  
Damping Rate ◽  
Linear Behaviour ◽  
Longitudinal Plasma

The non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma is considered for the case in which a single wave of small, but finite amplitude is excited initially. The Vlasov–Poisson equations are solved using the method of strained co-ordinates in which the independent variable t, the electric field and the distribution function are expanded in the form of asymptotic series, the terms of which are founded by an iterative procedure. An ordering parameter e is introduced, which is proportional to the initial amplitude of the electric field given by linear theory. Differential equations are derived which can be solved sequentially to obtain uniformly valid solutions to all orders in ε. Solutions are given to second order and applied to the case in which the background distribution function is Maxwellian. It is found that the changes in the real and imaginary part of the frequency are small in comparison to the values obtained in the linear theory; that the free-streaming terms decay exponentially in time with a damping rate proportional to ε2, in contrast with the linear theory where they are Un- damped; and that the analysis allows us to calculate the changes in the background distribution function for large time, resulting from particle-wave interactions.

scholarly journals On the most general linear theory of gravitation

1969 ◽  
Vol 13 (3) ◽  
pp. 254-256 ◽  
Author(s):  
Otto Nachtmann ◽  
Harald Schmidle ◽  
Roman U. Sexl
Keyword(s):  
Linear Theory ◽  
General Linear ◽  
Theory Of Gravitation

Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution

2013 ◽  
Vol 720 ◽  
pp. 357-392 ◽  
Author(s):  
Wenting Xiao ◽  
Yuming Liu ◽  
Guangyu Wu ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Linear Theory ◽  
Nonlinear Wave ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Single Wave ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Nonlinear Wave Field

AbstractWe study the occurrence and dynamics of rogue waves in three-dimensional deep water using phase-resolved numerical simulations based on a high-order spectral (HOS) method. We obtain a large ensemble of nonlinear wave-field simulations ($M= 3$ in HOS method), initialized by spectral parameters over a broad range, from which nonlinear wave statistics and rogue wave occurrence are investigated. The HOS results are compared to those from the broad-band modified nonlinear Schrödinger (BMNLS) equations. Our results show that for (initially) narrow-band and narrow directional spreading wave fields, modulational instability develops, resulting in non-Gaussian statistics and a probability of rogue wave occurrence that is an order of magnitude higher than linear theory prediction. For longer times, the evolution becomes quasi-stationary with non-Gaussian statistics, a result not predicted by the BMNLS equations (without consideration of dissipation). When waves spread broadly in frequency and direction, the modulational instability effect is reduced, and the statistics and rogue wave probability are qualitatively similar to those from linear theory. To account for the effects of directional spreading on modulational instability, we propose a new modified Benjamin–Feir index for effectively predicting rogue wave occurrence in directional seas. For short-crested seas, the probability of rogue waves based on number frequency is imprecise and problematic. We introduce an area-based probability, which is well defined and convergent for all directional spreading. Based on a large catalogue of simulated rogue wave events, we analyse their geometry using proper orthogonal decomposition (POD). We find that rogue wave profiles containing a single wave can generally be described by a small number of POD modes.

The General Linear Theory of Shells

2001 ◽  
pp. 325-348
Author(s):  
Eduard Ventsel ◽  
Theodor Krauthammer
Keyword(s):  
Linear Theory ◽  
General Linear ◽  
Theory Of Shells
Sign in / Sign up

Export Citation Format

Share Document