Nonlinear Internal Wave Equations: Spectral Properties and Long-Wave Asymptotics

2009 ◽  
Author(s):  
Nikolay Makarenko ◽  
Zhanna Maltseva ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Internal Wave ◽  
Spectral Properties ◽  
Wave Equations ◽  
Nonlinear Internal Wave ◽  
Long Wave

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

The Generalisation of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

1997 ◽  
Vol 66 (5) ◽  
pp. 1288-1290 ◽  
Author(s):  
Thangavel Alagesan ◽  
Ambigapathy Uthayakumar ◽  
Kuppusamy Porsezian
Keyword(s):  
Wave Equations ◽  
Long Wave

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.

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