A fully dispersive weakly nonlinear model for water waves

1997 ◽  
Vol 453 (1957) ◽  
pp. 303-318 ◽  
Author(s):  
K. Nadaoka ◽  
S. Beji ◽  
Y. Nakagawa
Keyword(s):  
Nonlinear Model ◽  
Water Waves ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Model

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

2009 ◽  
Vol 26 (7) ◽  
pp. 074704 ◽  
Author(s):  
Wang Li-Feng ◽  
Ye Wen-Hua ◽  
Fan Zheng-Feng ◽  
Xue Chuang ◽  
Li Ying-Jun
Keyword(s):  
Nonlinear Model ◽  
Incompressible Fluids ◽  
Helmholtz Instability ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Model

scholarly journals Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth

1987 ◽  
Vol 184 ◽  
pp. 183-206 ◽  
Author(s):  
Juan A. Zufiria
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Hamiltonian Formulation ◽  
Finite Depth ◽  
Capillary Waves ◽  
Bifurcation Structure ◽  
Low Gravity ◽  
Bifurcation Tree ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Model

A weakly nonlinear model is developed from the Hamiltonian formulation of water waves, to study the bifurcation structure of gravity-capillary waves on water of finite depth. It is found that, besides a very rich structure of symmetric solutions, non-symmetric Wilton's ripples exist. They appear via a spontaneous symmetrybreaking bifurcation from symmetric solutions. The bifurcation tree is similar to that for gravity waves. The solitary wave with surface tension is studied with the same model close to a critical depth. It is found that the solution is not unique, and that further non-symmetric solitary waves are possible. The bifurcation tree has the same structure as for the case of periodic waves. The possibility of checking these results in low-gravity experiments is postulated.

Equilibration of baroclinic instability in westward flows

2021 ◽  
Author(s):  
Timour Radko ◽  
James C. McWilliams ◽  
Georgi G. Sutyrin
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Model ◽  
Baroclinic Instability ◽  
Bottom Friction ◽  
Dynamics Model ◽  
Unstable Systems ◽  
Weakly Nonlinear ◽  
Nonlinear Properties ◽  
Linear And Nonlinear ◽  
Weakly Nonlinear Model

AbstractWe explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasi-geostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.

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