scholarly journals A Lagrangian approach to the weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow

2015 ◽  
Vol 47 (1) ◽  
pp. 015509
Author(s):  
Yasuhide Fukumoto ◽  
Youichi Mie
Keyword(s):  
Symmetry Breaking ◽  
Nonlinear Interaction ◽  
Kelvin Waves ◽  
Lagrangian Approach ◽  
Rotating Flow ◽  
Weakly Nonlinear ◽  
Symmetry Breaking Bifurcation

Three-dimensional tidal sand waves

2009 ◽  
Vol 618 ◽  
pp. 1-11 ◽  
Author(s):  
PAOLO BLONDEAUX ◽  
GIOVANNA VITTORI
Keyword(s):  
Stability Analysis ◽  
Nonlinear Interaction ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Time Development ◽  
Resonance Mechanism ◽  
Weakly Nonlinear ◽  
Sand Waves ◽  
Tidal Sand ◽  
Harmonic Components

The process which leads to the formation of three-dimensional sand waves is investigated by means of a stability analysis which considers the time development of a small-amplitude bottom perturbation of a shallow tidal sea. The weakly nonlinear interaction of a triad of resonant harmonic components of the bottom perturbation is considered. The results show that the investigated resonance mechanism can trigger the formation of a three-dimensional bottom pattern similar to that observed in the field.

Amplitude Modulation and Symmetry Breaking Bifurcation in Micro Devices

2012 ◽  
Author(s):  
Z. C. Feng ◽  
Mahmoud Almasri
Keyword(s):  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Amplitude Modulation ◽  
Dynamic Responses ◽  
Symmetric Structure ◽  
Different Types ◽  
Asymmetric Responses ◽  
Symmetric Response ◽  
Symmetry Breaking Bifurcation

Designs of many micro devices take advantage of the symmetry for better performance, immunity to noise, and for simpler analysis. When a symmetric structure is subjected to symmetric forcing, the symmetric response can become unstable leading to asymmetric responses. The occurrence of symmetry breaking bifurcation leads to complicated dynamic responses which often result in less desirable performances. In this paper, we obtain analytical criteria for the onset of symmetry breaking bifurcations. We also conduct numerical simulations to demonstrate different types of asymmetric dynamic responses resulting from the symmetry breaking bifurcation. In particular, we show the occurrence of amplitude modulated motions in such systems.

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