scholarly journals Wave-making experiments and theoretical models for internal solitary waves in a two-layer fluid of finite depth

2013 ◽  
Vol 62 (8) ◽  
pp. 084705
Author(s):  
Huang Wen-Hao ◽  
You Yun-Xiang ◽  
Wang Xu ◽  
Hu Tian-Qun
Keyword(s):  
Solitary Waves ◽  
Theoretical Models ◽  
Finite Depth ◽  
Internal Solitary Waves

Strongly dispersive internal solitary waves transformation over slope-shelf topography

2020 ◽  
pp. 2150031
Author(s):  
Changhong Zhi ◽  
Ke Chen ◽  
Yun-Xiang You
Keyword(s):  
Solitary Waves ◽  
Kdv Equation ◽  
Bottom Topography ◽  
Finite Depth ◽  
Variable Coefficients ◽  
Internal Solitary Waves ◽  
Initial Amplitude ◽  
Layer System ◽  
Amplitude Variation ◽  
Coupling Terms

The evolution of strongly dispersive internal solitary waves (ISWs) over slope-shelf topography is studied in a two-layer system of finite depth. We consider the high-order vmeKdV model extending the Korteweg-de Vries (KdV) equation with coupling terms of [Formula: see text] order to treat the strong dispersion in the problem which has variable coefficients to adapt the varying bottom topography. The strongly dispersive initial ISW is characterized by the meKdV equation according to the comparison with experiments and can be propagated by the vmeKdV equation according to the comparison between vmeKdV and vKdV theories. The vmeKdV equation is numerically implemented adopting the finite difference scheme. Three dimensionless ISW amplitudes [Formula: see text], 1.136, 1.41 and two slope inclinations [Formula: see text], 1/10 are considered. The deformation of the ISW is observed when a wave propagates past over the slope. The balancing of shoaling effect and energy dispersion determine the amplitude variation. In the cases of mild or steeper slopes, the terminal wave has a stable profile and amplitude, commonly consistent to the meKdV profile with smaller amplitude. In a particular case of mild slope with very small initial amplitude, the terminal wave amplitude grows larger than the original value.

Comparison principles for free-surface flows with gravity

1991 ◽  
Vol 230 ◽  
pp. 231-243 ◽  
Author(s):  
Walter Craig ◽  
Peter Sternberg
Keyword(s):  
Solitary Waves ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Immiscible Fluids ◽  
Steady Flows ◽  
Two Dimensional ◽  
Surface Flows ◽  
Ship Hulls ◽  
Geometrical Information ◽  
Supercritical Flows

This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids.

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