scholarly journals A numerical model for simulation of near-shore waves and wave induced currents using the depth-averaged non-hydrostatic shallow water equations with an improvement of wave energy dissipation

2020 ◽  
Vol 20 (2) ◽  
pp. 155-172
Author(s):  
Phung Dang Hieu ◽  
Phan Ngoc Vinh
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Wave Height ◽  
Shallow Water Equations ◽  
Wave Breaking ◽  
Water Model ◽  
Height Distribution ◽  
Time Duration ◽  
Wave Energy Dissipation ◽  
Near Shore

This study proposes a numerical model based on the depth-integrated non-hydrostatic shallow water equations with an improvement of wave breaking dissipation. Firstly, studies of parameter sensitivity were carried out using the proposed numerical model for simulation of wave breaking to understand the effects of the parameters of the breaking model on wave height distribution. The simulated results of wave height near the breaking point were very sensitive to the time duration parameter of wave breaking. The best value of the onset breaking parameter is around 0.3 for the non-hydrostatic shallow water model in the simulation of wave breaking. The numerical results agreed well with the published experimental data, which confirmed the applicability of the present model to the simulation of waves in near-shore areas.

scholarly journals WAVE HEIGHT DISTRIBUTION IN CONSTANT AND FINITE DEPTHS

2012 ◽  
Vol 1 (33) ◽  
pp. 15 ◽  
Author(s):  
Sofia Caires ◽  
Marcel R.A. Van Gent
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Wave Breaking ◽  
Rayleigh Distribution ◽  
Height Distribution ◽  
High Wave ◽  
Wave Height Distribution ◽  
Individual Wave ◽  
Wave Heights

Several alternatives to the Rayleigh distribution have been proposed for describing individual wave heights in regions where depth-induced wave breaking occurs. The most widely used of these is the so-called Battjes and Groenendijk distribution. This distribution has been derived and validated in a context of a shallow water foreshore waves propagating over a gently sloping shallow region towards the shore. Its validity for waves propagating in regions with shallow flat bottoms is investigated here. It is concluded that the distribution on average underestimates (outside its range of validity) high wave height measurements in shallow flat bottoms by as much as 15%.

A Model for Long-Term Distribution of Wave Induced Loads in Steep and Breaking Shallow Water Waves

2012 ◽  
Author(s):  
Hans Fabricius Hansen ◽  
Iris Pernille Lohmann ◽  
Jacob Tornfeldt Sørensen ◽  
Flemming Schlütter
Keyword(s):  
Transfer Function ◽  
Shallow Water ◽  
Wave Height ◽  
Wave Breaking ◽  
Extreme Value Analysis ◽  
Offshore Wind Turbine ◽  
Height Distribution ◽  
Wave Load ◽  
Wave Induced

A new approach to determine the design wave load on bottom-fixed structures in shallow water breaking waves is presented here. The method takes into account the effects that wave breaking has on both the wave height distribution and the wave induced loads on the structure. The loads on offshore wind turbine foundations in irregular seas with a significant amount of wave breaking are modeled in a physical wave tank. The loads are related to wave characteristics as steepness and Ursell number, and a non-linear transfer function between wave height/period and wave load is established. Characteristic historical load events are now established by combining the transfer function with a record of the wave climate at the site. The latter is taken from a hindcast database, but could also come from site measurements. The long-term distribution of the load is estimated by adopting traditional extreme value analysis techniques to the historical characteristic loads.

Wave-driven currents and vortex dynamics on barred beaches

2001 ◽  
Vol 449 ◽  
pp. 313-339 ◽  
Author(s):  
OLIVER BÜHLER ◽  
TIVON E. JACOBSON
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Wave Breaking ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Vortex Structures ◽  
Water Model ◽  
Mean Flow ◽  
The Mean

We present a theoretical and numerical investigation of longshore currents driven by breaking waves on beaches, especially barred beaches. The novel feature considered here is that the wave envelope is allowed to vary in the alongshore direction, which leads to the generation of strong dipolar vortex structures where the waves are breaking. The nonlinear evolution of these vortex structures is studied in detail using a simple analytical theory to model the effect of a sloping beach. One of our findings is that the vortex evolution provides a robust mechanism through which the preferred location of the longshore current can move shorewards from the location of wave breaking. Such current dislocation is an often-observed (but ill-understood) phenomenon on real barred beaches.To underpin our results, we present a comprehensive theoretical description of the relevant wave–mean interaction theory in the context of a shallow-water model for the beach. Therein we link the radiation-stress theory of Longuet-Higgins & Stewart to recently established results concerning the mean vorticity generation due to breaking waves. This leads to detailed results for the entire life-cycle of the mean-flow vortex evolution, from its initial generation by wave breaking until its eventual dissipative decay due to bottom friction.In order to test and illustrate our theory we also present idealized nonlinear numerical simulations of both waves and vortices using the full shallow-water equations with bottom topography. In these simulations wave breaking occurs through shock formation of the shallow-water waves. We note that because the shallow-water equations also describe the two-dimensional flow of a homentropic perfect gas, our theoretical and numerical results can also be applied to nonlinear acoustics and sound–vortex interactions.

Dispersion Effects on Tsunami Propagation in South China Sea

2015 ◽  
Vol 09 (05) ◽  
pp. 1540001 ◽  
Author(s):  
Zhi-Yuan Ren ◽  
Xi Zhao ◽  
Hua Liu
Keyword(s):  
South China Sea ◽  
Shallow Water ◽  
Wave Height ◽  
South China ◽  
Shallow Water Equations ◽  
Height Distribution ◽  
Tsunami Propagation ◽  
China Sea ◽  
Dispersion Effects ◽  
Wave Height Distribution

As the Manila Trench is becoming the most tsunami-hazardous, it is necessary to ascertain the wave height and arrival time in the South China Sea region through numerical simulation of tsunamis generated from potential earthquake source along the Manila subduction zone. The Okada model is employed to generate tsunami. The surface elevation and depth-averaged horizontal velocity at first 5 min, coming from the simulation of shallow water equations, are then interpolated in the weakly dispersive model (FUNWAVE) to calculate tsunami propagation and far-field impact. The characteristics of tsunami wave height distribution in South China Sea are analyzed for the assessment of tsunami hazard near coasts around South China Sea due to the hypothetical earthquakes with magnitude of [Formula: see text] and the worst case scenario ([Formula: see text]). The maximum wave height distribution computed by the Boussinesq equations is compared with that by the shallow water equations to investigate the dispersion effects on propagation of tsunami in South China Sea. It is found that the dispersion effects of the tsunami waves propagating in South China Sea are not significant if the earthquake magnitude is large enough.

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

2018 ◽  
Vol 40 ◽  
pp. 05032
Author(s):  
Minh H. Le ◽  
Virgile Dubos ◽  
Marina Oukacine ◽  
Nicole Goutal
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Simple Wave ◽  
Water Model ◽  
Strong Interactions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Rigid Vegetation ◽  
Vertical Cylinders

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

scholarly journals A robust and well-balanced numerical model for solving the two-layer shallow water equations over uneven topography

2015 ◽  
Vol 343 (7-8) ◽  
pp. 429-442 ◽  
Author(s):  
Xinhua Lu ◽  
Bingjiang Dong ◽  
Bing Mao ◽  
Xiaofeng Zhang
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Shallow Water Equations

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>

TELEMAC: A new numerical model for solving shallow water equations

1991 ◽  
Vol 14 (3) ◽  
pp. 138-148 ◽  
Author(s):  
Jean-Charles Galland ◽  
Nicole Goutal ◽  
Jean-Michel Hervouet
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Shallow Water Equations

scholarly journals Symmetries and exact solutions of the rotating shallow-water equations

2009 ◽  
Vol 20 (5) ◽  
pp. 461-477 ◽  
Author(s):  
A. A. CHESNOKOV
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
New Class ◽  
New Exact Solutions ◽  
Time Periodic Solutions ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations ◽  
Time Periodic

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

Sign in / Sign up

Export Citation Format

Share Document