Further improvement of weakly nonlinear theory of hydrodynamic stability

1998 ◽  
Vol 41 (1) ◽  
pp. 84-92 ◽  
Author(s):  
Zhou Heng ◽  
K. Fujimura
Keyword(s):  
Nonlinear Theory ◽  
Hydrodynamic Stability ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

scholarly journals Weakly nonlinear theory and sea state bias estimations

1999 ◽  
Vol 104 (C4) ◽  
pp. 7641-7647 ◽  
Author(s):  
Tanos Elfouhaily ◽  
Donald Thompson ◽  
Douglas Vandemark ◽  
Bertrand Chapron
Keyword(s):  
Nonlinear Theory ◽  
Sea State ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Sea State Bias

scholarly journals “Extraordinary” modulation instability in optics and hydrodynamics

2021 ◽  
Vol 118 (14) ◽  
pp. e2019348118
Author(s):  
Guillaume Vanderhaegen ◽  
Corentin Naveau ◽  
Pascal Szriftgiser ◽  
Alexandre Kudlinski ◽  
Matteo Conforti ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Stability Analysis ◽  
Linear Stability ◽  
Nonlinear Theory ◽  
Linear Stability Analysis ◽  
Water Waves ◽  
Modulation Instability ◽  
Nonlinear Effects ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

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