Shallow water hydrodynamics Comparing solutions of the coupled Boussinesq equations in shallow water

2014 ◽  
pp. 961-968 ◽  
Keyword(s):  
Shallow Water ◽  
Boussinesq Equations

scholarly journals Boussinesq modeling of surface waves due to underwater landslides

2013 ◽  
Vol 20 (3) ◽  
pp. 267-285 ◽  
Author(s):  
D. Dutykh ◽  
H. Kalisch
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Bottom Topography ◽  
Equations Of Motion ◽  
Boussinesq Equations ◽  
Time Dependent ◽  
Viscous Drag ◽  
Underwater Landslide ◽  
Landslide Mass ◽  
Run Up

Abstract. Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion that govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced that is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are solved simultaneously. The numerical solver for the Boussinesq equations can also be restricted to implement a shallow-water solver, and the shallow-water and Boussinesq configurations are compared. A particular bathymetry is chosen to illustrate the general method, and it is found that the Boussinesq system predicts larger wave run-up than the shallow-water theory in the example treated in this paper. It is also found that the finite fluid domain has a significant impact on the behavior of the wave run-up.

scholarly journals On a Coupled System of Shallow Water Equations Admitting Travelling Wave Solutions

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
D. Burini ◽  
S. De Lillo ◽  
D. Skouteris
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Boussinesq Equations ◽  
Coupled System ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Characteristic Parameters ◽  
Wave Solutions ◽  
Free Interfaces ◽  
Rigid Walls

We consider three inviscid, incompressible, irrotational fluids that are contained between the rigid wallsy=−h1andy=h+Hand that are separated by two free interfacesη1andη2. A generalized nonlocal spectral (NSP) formulation is developed, from which asymptotic reductions of stratified fluids are obtained, including coupled nonlinear generalized Boussinesq equations and(1+1)-dimensional shallow water equations. A numerical investigation of the(1+1)-dimensional case shows the existence of solitary wave solutions which have been investigated for different values of the characteristic parameters.

The Dynamic Response of a Moored Vessel in Shallow Water Using Boussinesq Equations

2009 ◽  
Author(s):  
Byeong W. Park ◽  
Rae H. Yuck ◽  
Seok K. Cho ◽  
Hang S. Choi
Keyword(s):  
Shallow Water ◽  
Bottom Topography ◽  
Boussinesq Equations ◽  
Linear Wave ◽  
Linear Potential ◽  
Wave Excitation ◽  
Wave Interactions ◽  
Water Effects ◽  
Excitation Force ◽  
Wave Excitation Force

In this study, firstly nonlinear waves in shallow water were simulated by using the Boussinesq equations. The simulated waves represented well the wave deformations such as shoaling and refraction as well as non-linear wave interactions among wave components as they approach coastal region from far field. The velocity components of the simulated waves at an arbitrary location in the fluid domain can be computed most effectively by introducing the so-called utility velocity. By taking the deformed wave field into account, the motion response of a moored floating barge was analyzed. The wave excitation and radiation force were estimated by the Constant Panel Method (CPM) based on linear potential theory. In order to estimate the wave excitation force including shallow water effects, the wave height and the wave velocity components obtained from the Boussinesq simulation were used. This approach used to estimate the wave excitation force including shallow water effects is herein referred to as Hybrid Boussinesq-CPM. An example calculation was made for the Pinkster barge, which is supposed to be located in a specific bottom topography and moored by the Tower Yoke Mooring System. The results were compared with those obtained for the equivalent constant water depth condition. The comparison showed that the motion responses obtained by the Hybrid model were larger than those for the even bottom case. In particular, the horizontal surge motion was significantly enlarged because of two facts: the wave deformation due to the bottom topography and the low frequency waves caused by nonlinear wave-wave interactions. The enlarged horizontal surge motion is important for mooring design in shallow water.

scholarly journals BOUSSINESQ MODELLING OF SOLITARY WAVE PROPAGATION, BREAKING, RUNUP AND OVERTOPPING

2011 ◽  
Vol 1 (32) ◽  
pp. 15
Author(s):  
Jana Orszaghova ◽  
Alistair G. L. Borthwick ◽  
Paul H. Taylor
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Wave Breaking ◽  
Laboratory Experiments ◽  
Boussinesq Equations ◽  
Breaking Waves ◽  
One Dimensional ◽  
Nonlinear Shallow Water Equations ◽  
Breaking Parameter ◽  
Surface Profiles

A one-dimensional hybrid numerical model is presented of a shallow-water flume with an incorporated piston paddle. The hybrid model is based on the improved Boussinesq equations by Madsen and Sorensen (1992) and the nonlinear shallow water equations. It is suitable for breaking and non-breaking waves and requires only two adjustable parameters: a friction coefficient and a wave breaking parameter. The applicability of the model is demonstrated by simulating laboratory experiments of solitary waves involving runup at a plane beach and overtopping of a laboratory seawall. The predicted free surface profiles, maximum runup and overtopping volumes agree very well with the measured values.

scholarly journals INTER-COUPLED TSUNAMI MODELLING THROUGH AN ABSORBING-GENERATING BOUNDARY

2020 ◽  
pp. 38
Author(s):  
Sangyoung Son ◽  
Patrick Lynett
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Boussinesq Equations ◽  
Equation Model ◽  
Water Model ◽  
Navier Stokes ◽  
Characteristic Form ◽  
Computationally Efficient ◽  
Boussinesq Model ◽  
Tsunami Modelling

For many practical and theoretical purposes, various types of tsunami wave models have been developed and utilized so far. Some distinction among them can be drawn based on governing equations used by the model. Shallow water equations and Boussinesq equations are probably most typical ones among others since those are computationally efficient and relatively accurate compared to 3D Navier-Stokes models. From this idea, some coupling effort between Boussinesq model and shallow water equation model have been made (e.g., Son et al. (2011)). In the present study, we couple two different types of tsunami models, i.e., nondispersive shallow water model of characteristic form(MOST ver.4) and dispersive Boussinesq model of non-characteristic form(Son and Lynett (2014)) in an attempt to improve modelling accuracy and efficiency.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/cTXybDEnfsQ

scholarly journals COMBINED REFRACTION-DIFFRACTION OF NONLINEAR WAVES IN SHALLOW WATER

1984 ◽  
Vol 1 (19) ◽  
pp. 68
Author(s):  
James T. Kirby ◽  
Philip L.F. Liu ◽  
Sung B. Yoon ◽  
Robert A. Dalrymple
Keyword(s):  
Shallow Water ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Evolution Equations ◽  
Boussinesq Equations ◽  
Two Dimensions ◽  
Parabolic Approximation ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Dimensional Domain

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow water waves. Two methods of approach are taken. In the first method Boussinesq equations are used to derive evolution equations for spectral wave components in a slowly varying two-dimensional domain. The second method modifies the equation of Kadomtsev s Petviashvili to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data and previous numerical calculations.

scholarly journals Expansion shock waves in regularized shallow-water theory

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160141 ◽  
Author(s):  
Gennady A. El ◽  
Mark A. Hoefer ◽  
Michael Shearer
Keyword(s):  
Shallow Water ◽  
Initial Conditions ◽  
Simple Wave ◽  
Boussinesq Equations ◽  
Shallow Water Theory ◽  
Initial Value ◽  
Algebraic Decay ◽  
New Type ◽  
Non Local ◽  
Shock Solution

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

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