A new numerical method of internal wave propagation base on SAR

2014 ◽  
Author(s):  
J. Wang ◽  
X.Y. Li ◽  
X.D. Zhang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Numerical Method

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.

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

1969 ◽  
Vol 38 (2) ◽  
pp. 365-374 ◽  
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.

scholarly journals QUASINORMAL MODES AND LATE-TIME TAILS OF CANONICAL ACOUSTIC BLACK HOLES

2007 ◽  
Vol 16 (07) ◽  
pp. 1211-1218 ◽  
Author(s):  
PING XI ◽  
XIN-ZHOU LI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Wave Propagation ◽  
Angular Momentum ◽  
Numerical Method ◽  
Time Scale ◽  
Quasinormal Modes ◽  
Late Time ◽  
Classical Wave ◽  
Acoustic Black Holes

In this paper, we investigate the evolution of classical wave propagation in the canonical acoustic black hole by a numerical method and discuss the details of the tail phenomenon. The oscillating frequency and damping time scale both increase with the angular momentum l. For lower l, numerical results show the lowest WKB approximation gives the most reliable result. We also find that the time scale of the interim region from ringing to tail is not affected obviously by changing l.

Exact Green’s functions using leaking modes for axisymmetric boreholes in solid elastic media

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 609-620 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Media ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

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