World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Effective Coastal Boundary Conditions for Tsunami Wave Run-up Over Sloping Bathymetry : Volume 1, Issue 1 (21/03/2014)

By Kristina, W.

Click here to view

Book Id: WPLBN0004020093
Format Type: PDF Article :
File Size: Pages 53
Reproduction Date: 2015

Title: Effective Coastal Boundary Conditions for Tsunami Wave Run-up Over Sloping Bathymetry : Volume 1, Issue 1 (21/03/2014)  
Author: Kristina, W.
Volume: Vol. 1, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Groesen, E. V., Bokhove, O., & Kristina, W. (2014). Effective Coastal Boundary Conditions for Tsunami Wave Run-up Over Sloping Bathymetry : Volume 1, Issue 1 (21/03/2014). Retrieved from

Description: Department of Applied Mathematics, University of Twente, Enschede, the Netherlands. An effective boundary condition (EBC) is introduced as a novel technique to predict tsunami wave run-up along the coast and offshore wave reflections. Numerical modeling of tsunami propagation at the coastal zone has been a daunting task since high accuracy is needed to capture aspects of wave propagation in the more shallow areas. For example, there are complicated interactions between incoming and reflected waves due to the bathymetry and intrinsically nonlinear phenomena of wave propagation. If a fixed wall boundary condition is used at a certain shallow depth contour, the reflection properties can be unrealistic. To alleviate this, we explore a so-called effective boundary condition, developed here in one spatial dimension. From the deep ocean to a seaward boundary, i.e., in the simulation area, we model wave propagation numerically over real bathymetry using either the linear dispersive variational Boussinesq or the shallow water equations. We measure the incoming wave at this seaward boundary, and model the wave dynamics towards the shoreline analytically, based on nonlinear shallow water theory over sloping bathymetry. We calculate the run-up heights at the shore and the reflection caused by the slope. The reflected wave is then influxed back into the simulation area using the EBC. The coupling between the numerical and analytic dynamics in the two areas is handled using variational principles, which leads to (approximate) conservation of the overall energy in both areas. We verify our approach in a series of numerical test cases of increasing complexity, including a case akin to tsunami propagation to the coastline at Aceh, Sumatra, Indonesia.

Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry

Antuono, M. and Brocchini, M.: The boundary value problem for the nonlinear shallow water equations, Stud. Appl. Math., 119, 73–93, 2007.; Antuono, M. and Brocchini, M.: Solving the nonlinear shallow-water equations in physical space, J. Fluid Mech., 643, 207–232, 2010.; Audusse, E., Bouchut, F., Bristeau, M. O., Klein, R., and Perthame, B.: A fast and stable well-balaced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comput., 25, 2050–2065, 2004.; Brocchini, M. and Peregrine, D. H.: Integral flow properties of the swash zone and averaging, J. Fluid Mech., 317, 241–273, 1996.; Bokhove, O.: Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension, J. Sci. Comput., 22, 47–82, 2005.; Carrier, G. F. and Greenspan, H. P.: Water waves of finite amplitude on a sloping beach, J. Fluid Mech., 4, 97–109, 1957.; Choi, B. H., Kaistrenko, V., Kim, K. O., Min, B. I., and Pelinovsky, E.: Rapid forecasting of tsunami runup heights from 2-D numerical simulations, Nat. Hazards Earth Syst. Sci., 11, 707–714, doi:10.5194/nhess-11-707-2011, 2011.; Choi, B. H., Pelinovsky, E., Kim, K. O., and Min, B. I.: Estimation of run-up Heights of the 2011 off the Pacific Coast of Tohoku Earthquake Tsunami Based on Numerical Simulations, The Open Oceanography Journal, 6, 5–13, 2012.; Cotter, C. J. and Bokhove, O.: Variational water-wave model with accurate dispersion and vertical vorticity, J. Eng. Math., 67, 33–54, 2010.; Didenkulova, I. and Pelinovsky, E.: Run-up of long waves on a beach: the influence of the incident wave form, Oceanology, 48, 1–6, 2008.; Gagarina, E., van der Vegt, J., and Bokhove, O.: Horizontal circulation and jumps in Hamiltonian wave models, Nonlin. Processes Geophys., 20, 483-500, doi:10.5194/npg-20-483-2013, 2013.; van Groesen, E.: Variational Boussinesq Model, part 1: Basic equations in Cartesian coordinates, Technical Report of LabMath-Indonesia, 2006.; Harten, A., Lax, P. D., and Van Leer, B.: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25, 35–61, 1983.; Horrillo, J., Kowalik, Z., and Shigihara, Y.: Wave Dispersion Study in the Indian Ocean-Tsunami of December 26, 2004, Mar. Geod., 29, 149–166, 2006.; Klaver, F.: Coupling of numerical models for deep and shallow water, M.Sc. thesis, University of Twente, the Netherlands, 2009.; Klopman, G., Van Groesen, E., and Dingemans, M.: A variational approach to Boussinesq modelling of fully non-linear water waves, J. Fluid Mech., 657, 36–63, 2010.; Kristina, W., Van Groesen, E., and Bokhove, O.: Effective Coastal Boundary Conditions for Dispersive Tsunami Propagation, Memorandum 1983, Department of Applied Mathematics, University of Twente, Enschede, the Netherlands, 2012.; Li, Y. and Raichlen, F.: Solitary wave run-up on plane slopes, J. Waterw. Port C. Div., 127, 33–44, 2001.; Liu, Y., Shi, Y., Yuen, D. A., Sevre, E. O. D., Yuan, X., and Xing, H. L.: Comparison of linear and nonlinear shallow wave water equations applied to tsunami waves over the China sea, Acta Geotechnica, 4, 129–137, 2009.; Luke, J. C.: A variational principle for fluids with a free surface, J. Fluid Mech., 27, 395–397, 1967.; Madsen, P. A. and Schaffer, H. A.: Analytical solutions for tsunami run-up on a plane beach: single waves, N-waves and transient waves, J. Fluid Mech., 645, 27–57, 2010.; Madsen, P. A., Murray, R., and Sorensen, O. R.: A new form of the Boussinesq equations with improved linear dispersion characteristics, Coastal Eng., 15, 371–388, 1991.; Mei, C. C.: The applied dynamics of ocean surface waves, World Scientific Publishing Singapore, 1989.; Miles, J. W.: On Hamilton's principle for surface waves, J. Fluid Mech., 83, 153–158, 1977.; Ryrie, S. C.: Longshore motion generated on beaches by obliquely incident bores, J. Fl


Click To View

Additional Books

  • Electromagnetic and Mechanical Control o... (by )
  • Comprehensive Analysis of Tornado Statis... (by )
  • Features of Criticality in Precursory Se... (by )
  • A Reexamination of Methods for Evaluatin... (by )
  • Mapping Soil Fractal Dimension in Agricu... (by )
  • Three-wave Coupling in a Stratified Mhd ... (by )
  • Contraction of Westward-travelling Nonlo... (by )
  • Nonlinear Analysis of Magnetospheric Dat... (by )
  • Quantitative Analysis of Randomness Exhi... (by )
  • Mirror Mode Structures and Elf Plasma Wa... (by )
  • Phase Space Structure and Fractal Trajec... (by )
  • Expanding the Validity of the Ensemble K... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.