scholarly journals Weakly Nonlinear Dynamics of Near-CJ Detonation Waves

1994 ◽  
pp. 513-540 ◽  
Author(s):  
John B. Bdzil ◽  
Rupert Klein
Keyword(s):  
Nonlinear Dynamics ◽  
Detonation Waves ◽  
Weakly Nonlinear

Nonlinear dynamics of the elliptic instability

2010 ◽  
Vol 646 ◽  
pp. 471-480 ◽  
Author(s):  
NATHANAËL SCHAEFFER ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulations ◽  
Shear Layer ◽  
Rapid Growth ◽  
Vortex Core ◽  
Nonlinear Evolution ◽  
Core Size ◽  
Layer Formation ◽  
Vortex Loop ◽  
Weakly Nonlinear

In this paper, we analyse by numerical simulations the nonlinear dynamics of the elliptic instability in the configurations of a single strained vortex and a system of two counter-rotating vortices. We show that although a weakly nonlinear regime associated with a limit cycle is possible, the nonlinear evolution far from the instability threshold is, in general, much more catastrophic for the vortex. In both configurations, we put forward some evidence of a universal nonlinear transition involving shear layer formation and vortex loop ejection, leading to a strong alteration and attenuation of the vortex, and a rapid growth of the vortex core size.

scholarly journals An Analytical Study of Weakly Nonlinear Dynamics of a Walters’ Liquid B around a Flexible Sheet Undergoing Super Linear Stretching

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
P. G. Siddheshwar ◽  
A. Chan ◽  
U. S. Mahabaleswar
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equation ◽  
Boundary Layer ◽  
Analytical Study ◽  
Stretching Sheet ◽  
Quadratic Function ◽  
Weakly Nonlinear ◽  
Governing Differential Equation ◽  
Layer Flow ◽  
Analytical Expressions

The paper discusses the boundary layer flow of Walters’ liquid B over a stretching sheet. The stretching is assumed to be a quadratic function of the coordinate along the direction of stretching. The study encompasses within its realm both Walters’ liquid B and second order liquid. The velocity distribution is obtained by solving the nonlinear governing differential equation. Analytical expressions are obtained for stream function and velocity components as functions of the viscoelastic and stretching related parameters. It is shown that the viscoelasticity goes hand in hand with quadratic stretching in enhancing the lifting of the liquid as we go along the sheet.

Nonlinear Dynamics and Internal Resonances of a Ship With a Rectangular Cross-Section in Head Seas

2008 ◽  
Author(s):  
A. Kleiman ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Cross Section ◽  
Nonlinear Response ◽  
Rectangular Cross Section ◽  
Orbital Stability ◽  
Internal Resonances ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Evolution Dynamics ◽  
Ship Roll

We investigate the nonlinear dynamics and internal resonances of a ship with a rectangular cross-section in head seas. We employ an asymptotic averaging method to obtain the slowly varying system evolution dynamics for the weakly nonlinear response, complemented by numerical integration in the strongly nonlinear regime. This combined approach resolves both parametric instabilities and internal resonances induced for both weak and finite nonlinear interactions, and culminates with criteria for orbital stability thresholds describing the onset of quasiperiodic response and magnification of energy transfer between coupled pitch-heave and ship roll that can lead to capsize.

Weakly nonlinear dynamics of electrostatic perturbations in marginally stable plasmas

1998 ◽  
Vol 5 (11) ◽  
pp. 3886-3900 ◽  
Author(s):  
D. del-Castillo-Negrete
Keyword(s):  
Nonlinear Dynamics ◽  
Weakly Nonlinear

scholarly journals Weakly nonlinear dynamics and the σ8parameter

2010 ◽  
Vol 2010 (02) ◽  
pp. 021-021 ◽  
Author(s):  
Roman Juszkiewicz ◽  
Hume A Feldman ◽  
J.N Fry ◽  
Andrew H Jaffe
Keyword(s):  
Nonlinear Dynamics ◽  
Weakly Nonlinear

The nonlinear dynamics of baroclinic wave ensembles

1981 ◽  
Vol 102 ◽  
pp. 169-209 ◽  
Author(s):  
Joseph Pedlosky
Keyword(s):  
Nonlinear Dynamics ◽  
Multiple Equilibria ◽  
Finite Amplitude ◽  
Unstable Wave ◽  
Hysteresis Phenomenon ◽  
List Type ◽  
Final State ◽  
Weakly Nonlinear ◽  
Wave Forcing

A theory is developed to describe the weakly nonlinear dynamics which applies in the simultaneous presence of several, long, baroclinic waves. The geometry is flat (i.e. β = 0) and dissipation is modelled by Ekman friction in the context of the quasi-geostrophic two-layer model. Three main problems are discussed. For free, unstable waves it is shown that the wave which is realized in finite amplitude is not the linearly most unstable wave. Rather a longer wave, capable of achieving the single largest steady amplitude, is favoured in the competition for the potential energy of the basic state. This result is shown necessary if the end state is steady and numerous numerical calculations indicate the pre-eminence of the same wave if the final state is vacillatory. The notion of conjugate waves, capable of identical final amplitude, is also discussed.If the free waves are subject to time-varying supercriticality so that intervals of stability ensue, the response is asymmetric over the period of the forcing. Sufficiently rapid ‘seasonal’ forcing leads to long-term aperiodic response.If each wave in the spectrum is directly forced a wave hysteresis phenomenon occurs. Sudden jumps in the wave amplitude at critical values of the forcing are intrinsic to the wave response. Again, sufficiently rapid wave forcing produces an aperiodic response.The forced wave problem exhibits multiple equilibria. Each solution branch corresponds to a different dominant wave. The determination of the realized branch depends on the relative stability criteria developed for the free waves.

Weakly Nonlinear Detonation Waves

1983 ◽  
Vol 43 (5) ◽  
pp. 1086-1118 ◽  
Author(s):  
Rodolfo R. Rosales ◽  
Andrew Majda
Keyword(s):  
Detonation Waves ◽  
Weakly Nonlinear
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