A numerical study of internal wave propagation through ocean fine structure

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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Numerical study on the spatial and temporal characteristics of nonlinear internal wave energy in the Northern South China sea

Deep Sea Research Part I Oceanographic Research Papers ◽

10.1016/j.dsr.2021.103640 ◽

2021 ◽

pp. 103640

Author(s):

Guangzhen Jin ◽

Zhigang Lai ◽

Xiaodong Shang

Keyword(s):

South China Sea ◽

Internal Wave ◽

South China ◽

Wave Energy ◽

Numerical Study ◽

Northern South China Sea ◽

Nonlinear Internal Wave ◽

Temporal Characteristics ◽

China Sea ◽

Spatial And Temporal Characteristics

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Numerical Study of the Shock Wave Propagation in a Micron-Scale Contracting Channel

10.1063/1.3562741 ◽

2011 ◽

Cited By ~ 2

Author(s):

G. V. Shoev ◽

Ye. A. Bondar ◽

D. V. Khotyanovsky ◽

A. N. Kudryavtsev ◽

G. Mirshekari ◽

...

Keyword(s):

Shock Wave ◽

Wave Propagation ◽

Numerical Study ◽

Shock Wave Propagation

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Internal wave propagation in an inhomogeneous fluid of non-uniform depth

Journal of Fluid Mechanics ◽

10.1017/s002211206900022x ◽

1969 ◽

Vol 38 (2) ◽

pp. 365-374 ◽

Cited By ~ 27

Author(s):

Joseph B. Keller ◽

Van C. Mow

Keyword(s):

Wave Propagation ◽

Internal Wave ◽

Experimental Result ◽

Bottom Surface ◽

Radius Of Curvature ◽

Constant Density ◽

Trapped Waves ◽

Inhomogeneous Fluid ◽

Sloping Beach ◽

Scale Length

An asymptotic solution is obtained to the problem of internal wave propagation in a horizontally stratified inhomogeneous fluid of non-uniform depth. It also applies to fluids which are not stratified, but in which the constant density surfaces have small slopes. The solution is valid when the wavelength is small compared to all horizontal scale lengths, such as the radius of curvature of a wavefront, the scale length of the bottom surface variations and the scale length of the horizontal density variations. The theory underlying the solution involves rays, a phase function satisfying the eiconal equation, and amplitude functions satisfying transport equations. All these equations are solved in terms of the rays and of the solution of the internal wave problem for a horizontally stratified fluid of constant depth. The theory is thus very similar to geometrical optics and its extensions. It can be used to treat problems of propagation, reflexion from vertical cliffs or from shorelines, refraction, determination of the frequencies and wave patterns of trapped waves, etc. For fluid of constant density, it reduces to the theory of Keller (1958). The theory is applied to waves in a fluid with an exponential density distribution on a uniformly sloping beach. The predicted wavelength is shown to agree well with the experimental result of Wunsch (1969). It is also applied to determine edge waves near a shoreline and trapped waves in a channel.

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