Nonlinear shoaling of shallow water waves: perspective in terms of the inverse scattering transform

1996 ◽  
Vol 19 (1) ◽  
pp. 151-176 ◽  
Author(s):  
A. R. Osborne ◽  
L. Bergamasco ◽  
M. Serio ◽  
L. Bianco ◽  
L. Cavaleri ◽  
...  
Keyword(s):  
Shallow Water ◽  
Inverse Scattering ◽  
Water Waves ◽  
Inverse Scattering Transform ◽  
Shallow Water Waves ◽  
Scattering Transform

scholarly journals Internal gravity waves: Analysis using the periodic, inverse scattering transform

1999 ◽  
Vol 6 (1) ◽  
pp. 11-26 ◽  
Author(s):  
W. B. Zimmerman ◽  
G. W. Haarlemmer
Keyword(s):  
Spectral Analysis ◽  
Inverse Scattering ◽  
Gravity Waves ◽  
Water Waves ◽  
Nonlinear Filtering ◽  
Kdv Equation ◽  
Internal Gravity Waves ◽  
Inverse Scattering Transform ◽  
Linear Superposition ◽  
Scattering Transform

Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s) * (ε/μ2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.

Time and Frequency Domain Analyses of Shallow Water Waves on a Slope

1991 ◽  
Author(s):  
D H Swart ◽  
J B Crowley
Keyword(s):  
Shallow Water ◽  
Frequency Domain ◽  
Water Waves ◽  
Shallow Water Waves

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach

scholarly journals New exact solitary wave solutions for the 3D-FWBBM model in arising shallow water waves by two analytical methods

2021 ◽  
Vol 25 ◽  
pp. 104230
Author(s):  
Shafqat-Ur-Rehman ◽  
Muhammad Bilal ◽  
Jamshad Ahmad
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Analytical Methods ◽  
Water Waves ◽  
Solitary Wave Solutions ◽  
Shallow Water Waves ◽  
Wave Solutions

scholarly journals Diverse novel analytical and semi-analytical wave solutions of the generalized (2+1)-dimensional shallow water waves model

AIP Advances ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 015223
Author(s):  
Yuming Chu ◽  
Mostafa M. A. Khater ◽  
Y. S. Hamed
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Wave Solutions

scholarly journals Active-subspace analysis of exceedance probability for shallow-water waves

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Kenan Šehić ◽  
Henrik Bredmose ◽  
John D. Sørensen ◽  
Mirza Karamehmedović
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Exceedance Probability ◽  
Subspace Analysis ◽  
Shallow Water Waves ◽  
Active Subspace
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