scholarly journals Nonlinear internal wave penetration via parametric subharmonic instability

2016 ◽  
Vol 28 (1) ◽  
pp. 011703 ◽  
Author(s):  
S. J. Ghaemsaidi ◽  
S. Joubaud ◽  
T. Dauxois ◽  
P. Odier ◽  
T. Peacock
Keyword(s):  
Internal Wave ◽  
Nonlinear Internal Wave ◽  
Parametric Subharmonic Instability

A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

Effect of background mean flow on PSI of internal wave beams

2019 ◽  
Vol 869 ◽  
Author(s):  
Boyu Fan ◽  
T. R. Akylas
Keyword(s):  
Internal Wave ◽  
Evolution Equations ◽  
Internal Gravity Wave ◽  
Necessary Condition ◽  
Finite Width ◽  
Asymptotic Model ◽  
Mean Flow ◽  
Short Scale ◽  
The Mean ◽  
Parametric Subharmonic Instability

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

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