Development of a three-dimensional numerical model to solve shallow-water equations in compound channels

2008 ◽  
Vol 35 (9) ◽  
pp. 963-974 ◽  
Author(s):  
F. Jazizadeh ◽  
A. R. Zarrati
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Free Surface Elevation ◽  
Compound Channels ◽  
Secondary Currents ◽  
Flood Plains ◽  
Rough Beds

Velocity gradient between main channel and flood plains in compound channels leads to the formation of a large shear layer and secondary currents between these two subsections. These phenomena in the interaction region bring about a complex three-dimensional nature of the flow in compound channels. To cope with these flows, many numerical investigations have utilized three-dimensional formulations with advanced turbulence models. However, the free surface in many of these models is fixed and rigid-lid assumption has been used. In the present research, three-dimensional shallow water equations were used to calculate the flow field in compound channels. Three-dimensional equations were integrated in layers and were combined with the continuity equation. In this formulation, free-surface elevation was calculated without the need to solve any additional equations. Velocity and bed shear stress distribution and the stage–discharge relationship in compound channels with smooth and rough beds and with different relative depths were analyzed to verify this model, and satisfactory results were obtained.

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

A domain decomposition method for the three-dimensional shallow water equations

1995 ◽  
Vol 3 (4-5) ◽  
pp. 307-325 ◽  
Author(s):  
E.D. de Goede ◽  
J. Groeneweg ◽  
K.H. Tan ◽  
M.J.A. Borsboom ◽  
G.S. Stelling
Keyword(s):  
Domain Decomposition ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Three Dimensional

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

scholarly journals Port-Hamiltonian model of two-dimensional shallow water equations in moving containers

2020 ◽  
Vol 37 (4) ◽  
pp. 1348-1366 ◽  
Author(s):  
Flávio Luiz Cardoso-Ribeiro ◽  
Denis Matignon ◽  
Valérie Pommier-Budinger
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Physical Phenomenon ◽  
Hamiltonian Formulation ◽  
Two Dimensional ◽  
Surface Motion ◽  
Infinite Dimensional ◽  
Hamiltonian Model ◽  
Rigid Body Motions

Abstract The free surface motion in moving containers is an important physical phenomenon for many engineering applications. One way to model the free surface motion is by employing shallow water equations (SWEs). The port-Hamiltonian systems formulation is a powerful tool that can be used for modeling complex systems in a modular way. In this work, we extend previous work on SWEs using the port-Hamiltonian formulation, by considering the two-dimensional equations under rigid body motions. The resulting equations consist of a mixed-port-Hamiltonian system, with finite and infinite-dimensional energy variables and ports. 2000 Math Subject Classification: 34K30, 35K57, 35Q80, 92D25

On the necessity of non-hydrostatic pressure models for free surface flow over complex topography

2020 ◽  
Author(s):  
Isabel Echeverribar ◽  
Pilar Brufau ◽  
Pilar García-Navarro
Keyword(s):  
Free Surface ◽  
Hydrostatic Pressure ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Complex Topography ◽  
Source Terms ◽  
Pressure Correction ◽  
Wide Range

<p><span><strong>There is a wide range of geophysical flows, such as flow in open channels and rivers, tsunami and flood modeling, that can be mathematically represented by the non-linear shallow water 1D equations involving hydrostatic pressure assumptions as an approximation of the Navier Stokes equations. In this context, special attention must be paid to bottom source terms integration and numerical corrections when dealing with wet/dry fronts or strong slopes in order to obtain physically-based solutions (Murillo and García-Navarro, 2010) in complex and realistic cases with irregular topography. However, although these numerical corrections have been developed in recent years achieving not only more robust models but also more accurate results, they still might find a limit when dealing with specific scenarios where vertical information or disspersive effects become crucial. This work presents a 1D shallow water model that introduces vertical information by means of a non-hydrostatic pressure correction when necessary. In particular, the pressure correction method (Hirsch, 2007) is applied to a 1D finite volume scheme for a rectification of the velocity field in free surface scenarios. It is solved by means of an implicit scheme, whereas the depth-integrated shallow water equations are solved using an explicit scheme. It is worth highlighting that it preserves all the advantages and numerical fixes aforementioned for the pure shallow water system. Computations with and without non-hydrostatic corrections are compared for the same cases to test the validity of the conventional hydrostatic pressure assumption at some scenarios involving complex topography.</strong></span></p><p><span>[1] J. Murillo and P. Garcia-Navarro, Weak solutions for partial differential equations with source terms: application to the shallow water equations, Journal of Computational Physics, vol. 229, iss. 11, pp. 4327-4368, 2010.</span></p><p><span>[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.</span></p>

Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear

2013 ◽  
Vol 723 ◽  
pp. 289-317 ◽  
Author(s):  
Andrew L. Stewart ◽  
Paul J. Dellar
Keyword(s):  
Shallow Water ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Shear Instability ◽  
Vertical Shear ◽  
Vortex Sheets ◽  
Multilayer Shallow Water Equations ◽  
Complete Coriolis Force

AbstractWe analyse the hyperbolicity of our multilayer shallow water equations that include the complete Coriolis force due to the Earth’s rotation. Shallow water theory represents flows in which the vertical shear is concentrated into vortex sheets between layers of uniform velocity. Such configurations are subject to Kelvin–Helmholtz instabilities, with arbitrarily large growth rates for sufficiently short-wavelength disturbances. These instabilities manifest themselves through a loss of hyperbolicity in the shallow water equations, rendering them ill-posed for the solution of initial value problems. We show that, in the limit of vanishingly small density difference between the two layers, our two-layer shallow water equations remain hyperbolic when the velocity difference remains below the same threshold that also ensures the hyperbolicity of the standard shallow water equations. Direct calculation of the domain of hyperbolicity becomes much less tractable for three or more layers, so we demonstrate numerically that the threshold for the velocity differences, below which the three-layer equations remain hyperbolic, is also unchanged by the inclusion of the complete Coriolis force. In all cases, the shape of the domain of hyperbolicity, which extends outside the threshold, changes considerably. The standard shallow water equations only lose hyperbolicity due to shear parallel to the direction of wave propagation, but the complete Coriolis force introduces another mechanism for loss of hyperbolicity due to shear in the perpendicular direction. We demonstrate that this additional mechanism corresponds to the onset of a transverse shear instability driven by the non-traditional components of the Coriolis force in a three-dimensional continuously stratified fluid.

Numerical investigations of vortex flows and vortex suppression schemes in a large pumping-station sump

2011 ◽  
Vol 225 (6) ◽  
pp. 1459-1480 ◽  
Author(s):  
X L Tang ◽  
F J Wang ◽  
Y J Li ◽  
G H Cong ◽  
X Y Shi ◽  
...  
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Complex Nature ◽  
Stable Operation ◽  
Vortex Flows ◽  
Pumping Station ◽  
Pump Station ◽  
Pump Sump ◽  
Under Construction

This work uses a commercial computational fluid dynamics code to predict three-dimensional (3D) vortex flows in a large centrifugal-pump station under construction in China and proposes relevant vortex-eliminating schemes. Because of the complex nature of the vortex flows in sumps, different turbulence models, namely, standard k–ε, re-normalization group k–ε and realizable k–ε models, are first used to investigate their feasibility in predicting flows in a small physical model of an open pump sump, and various vortex streamlines and strength in the sump are predicted, analysed, and compared with the experimental data. The comparisons show that the realizable k–ε model predicts the position and strength of free-surface, sidewall-attached, and floor-attached vortices more accurately than the other two models. Then, the realizable k–ε model is used here to investigate 3D vortex flows in a large pumping-station sump. All the various vortices, such as free-surface, wall-attached vortices, are successfully predicted. Thus, based on the information of location, shape, size, and strength of the calculated vortices, three types of vortex-eliminating devices are proposed and their corresponding vortex suppression effects are analysed. These results will be used as reference for the safe and stable operation of the Hui–Nan–Zhuang pumping station in the future.

scholarly journals EXPERIMENTAL STUDY OF SOLITARY WAVE EVOLUTION OVER A 3D SHALLOW SHELF

2011 ◽  
Vol 1 (32) ◽  
pp. 1 ◽  
Author(s):  
Patrick J. Lynett ◽  
David Swigler ◽  
Sangyoung Son ◽  
Duncan Bryant ◽  
Scott Socolofsky
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Turbulent Energy ◽  
Shelf Break ◽  
Plan View ◽  
Fluid Velocities ◽  
Water Region ◽  
Side Walls

A laboratory experiment was performed to investigate the three-dimensional turbulence and kinematic properties that develop due to a breaking solitary propagating over an irregular shallow water bathymetry. The bathymetry consisted of a deep water region connected to a shallow shelf via a relatively steep slope. The offshore boundary of the shelf break varied in the longshore direction, such that the shelf had a triangular shape in plan view, with the widest part of the shelf along the basin centerline. Free surface elevations and fluid velocities were measured using wave gauges and three-dimensional acoustic-Doppler velocimeters (ADVs), respectively. From the free surface elevations the evolution and runup of the wave was revealed; while from the ADVs, the velocity and turbulent energy was determined and specific turbulent events and coherent structures were identified. It was found that significant shoaling was confined to areas with gentler sloping bathymetry near the basin side walls and the runup varied weakly in the alongshore direction. The runup was characterized by a refraction-generated jetting mechanism caused by the convergence of water mass near the basin centerline. The jetting mechanism caused the greatest cross-shore velocities to be located near the basin centerline. The greatest turbulent events were well correlated to borefronts, of which there were four, caused by the leading wave, beach reflections, and shelf-trapped oscillations. Along the shelf break, a large, shallow-water eddy developed which was found to have a peculiar three-dimensional flow field, where maximum velocity components were found at mid-depth.

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