scholarly journals Emergence of dispersion in shallow water hydrodynamics via modulation of uniform flow

2014 ◽  
Vol 761 ◽  
Author(s):  
Thomas J. Bridges
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Open Channel ◽  
Mass Density ◽  
Uniform Flow ◽  
Shallow Water Models ◽  
Model Equations ◽  
New Perspective ◽  
Channel Hydraulics ◽  
Derivatives Of

AbstractA new theory for the emergence of dispersion in shallow water hydrodynamics in two horizontal space dimensions is presented. Starting with the key properties of uniform flow in open-channel hydraulics, it is shown that criticality is the key mechanism for generating dispersion. Modulation of the uniform flow then leads to model equations. The coefficients in the model equations are related precisely to the derivatives of the mass flux, momentum flux and mass density. The theory gives a new perspective – from the viewpoint of hydraulics – on how and why key shallow water models like the Korteweg–de Vries equation and Kadomtsev–Petviashvili equations arise in the theory of water waves.

A multiple exp-function method for the three model equations of shallow water waves

2017 ◽  
Vol 89 (3) ◽  
pp. 2291-2297 ◽  
Author(s):  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Abdullahi Rashid Adem
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Shallow Water Waves ◽  
Model Equations

Multi-Layer Modeling of Wave Groups From Deep to Shallow Water

2003 ◽  
Author(s):  
Patrick Lynett ◽  
Philip L.-F. Liu ◽  
Hwung-Hweng Hwung ◽  
Wen-Son Ching
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Water Waves ◽  
Water Wave ◽  
Linear Wave ◽  
Layer Model ◽  
Wave Groups ◽  
Good Linear ◽  
Model Equations ◽  
Linear Accuracy

A set of model equations for water wave propagation is derived by piecewise integration of the primitive equations of motion through N arbitrary layers. Within each layer, an independent velocity profile is determined. With N separate velocity profiles, matched at the interfaces of the layers, the resulting set of equations have N+1 free parameters, allowing for an optimization with known analytical properties of water waves. The optimized two-layer model equations show good linear wave characteristics up to kh ≈8, while the second-order nonlinear behavior is well captured to kh ≈6. The three-layer model shows good linear accuracy to kh ≈14, and the four layer to kh ≈20. A numerical algorithm for solving the model equations is developed and tested against nonlinear deep-water wave-group experiments, where the kh of the carrier wave in deep water is around 6. The experiments are set up such that the wave groups, initially in deep water, propagate up a constant slope until reaching shallow water. The overall comparison between the multi-layer model and the experiment is quite good, indicating that the multi-layer theory has good nonlinear, as well has linear, accuracy for deep-water waves.

scholarly journals Observation of broad-band water waveguiding in shallow water: a revival

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Fabián Sepúlveda-Soto ◽  
Diego Guzmán-Silva ◽  
Edgardo Rosas ◽  
Rodrigo A. Vicencio ◽  
Claudio Falcón
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Open Channel ◽  
Fluid Layer ◽  
Broad Band ◽  
Shallow Water Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Phenomena

Abstract We report on the observation and characterization of broad-band waveguiding of surface gravity waves in an open channel, in the shallow water limit. The waveguide is constructed by changing locally the depth of the fluid layer, which creates conditions for surface waves to propagate along the generated guide. We present experimental and numerical results of this shallow water waveguiding, which can be straightforwardly matched to the one-dimensional water wave equation of shallow water waves. Our work revitalizes water waveguiding research as a relevant and controllable experimental setup to study complex phenomena using waveguide geometries.

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