Research Article
BibTex RIS Cite

Maximum run-up behavior of tsunamis under non-zero initial velocity condition

Year 2018, Volume: 19 Issue: 1, 122 - 131, 31.03.2018

Abstract

The tsunami run-up problem is solved non-linearly under the most general initial conditions, that is, for realistic initial waveforms such as N-waves, as well as standard initial waveforms such as solitary waves, in the presence of initial velocity. An initial-boundary value problem governed by the non-linear shallow-water wave equations is solved analytically utilizing the classical separation of variables technique, which proved to be not only fast but also accurate analytical approach for this type of problems. The results provide important information on maximum tsunami run-up qualitatively. We observed that, although the calculated maximum run-ups increase significantly, going as high as double that of the zero-velocity case, initial waves having non-zero fluid velocity exhibit the same run-up behavior as waves without initial velocity, for all wave types considered in this study.

References

  • Gusiakov VK. Tsunami History: Recorded. In: Bernard EN, Robinson AR, editors. The Sea, Volume 15: Tsunamis. Cambridge, MA, USA and London, England: Harvard University Press, 2009. pp. 23-53.
  • Intergovernmental Oceanographic Commission. Tsunami Glossary, 2008. Paris, UNESCO: IOC Technical Series, 85, 2008.
  • Carrier GF, Greenspan HP. Water waves of finite amplitude on a sloping beach. J Fluid Mech 1958; 4: 97-109.
  • Keller JB, Keller HB. Water wave run-up on a beach. ONR Research Report NONR-3828(00), Department of the Navy, Washington, DC, USA, 1964.
  • Peregrine DH. Long waves on a beach. J Fluid Mech 1967; 27: 815-827.
  • Synolakis CE. The runup of solitary waves. J Fluid Mech 1987; 185: 523-545.
  • Hibbert SD, Peregrine H. Surf and runup on a beach: a uniform bore. J Fluid Mech 1979; 95: 323-345.
  • Pedersen G, Gjevik B. Run-up of solitary waves. J Fluid Mech 1983; 135: 283-299.
  • Zelt JA. The run-up of nonbreaking and breaking solitary waves. Coast Eng 1991; 15: 205-246.
  • Li Y, Raichlen F. Non-breaking and breaking solitary wave run-up. J Fluid Mech 2002; 456: 295-318.
  • Kim SK, Liu PLF, Liggett JA. Boundary integral equation solutions for solitary wave generation, propagation and run-up. Coast Eng 1983; 7: 299-317.
  • Hall JV, Watts, JW. Laboratory investigation of the vertical rise of solitary waves on impermeable slopes. Tech. Memo. 33, Beach Erosion Board, USACE, 1953.
  • Street RL, Camfield FE. Observations and experiments on solitary wave deformation. In: Tenth International Conference on Coastal Engineering; September 1966; Tokyo, Japan: ASCE. pp. 284-301.
  • Hammack JL. A note on tsunamis: their generation and propagation in an ocean of uniform depth. J Fluid Mech 1973; 60: 769-799.
  • Synolakis CE, Bernard EN. Tsunami science before and beyond Boxing Day 2004. Phil Trans R Soc A 2006; 364: 2231-2265.
  • Tadepalli S, Synolakis CE. The run-up of N-waves on sloping beaches. Proc R Soc London A 1994; 445: 99-112.
  • Kânoğlu U, Synolakis CE. Initial value problem solution of nonlinear shallow water-wave equations. Phys Rev Lett 2006; 148501.
  • Stoker JJ. Water Waves: The Mathematical Theory with Applications. Wiley Classics Library ed. New York, NY, USA: John Wiley & Sons, Inc., 1992.
  • Aydın B. Analytical solutions of shallow-water wave equations. PhD, Middle East Technical University, Ankara, Turkey, 2011.
  • Aydın B, Kânoğlu U. New analytical solution for nonlinear shallow water-wave equations. Pure Appl Geophys 2017; 174: 3209-3218.
  • Carrier GF, Wu TT, Yeh H. Tsunami run-up and draw-down on a plane beach. J Fluid Mech 2003; 475: 79-99.
  • Prichard D, Dickinson L. The near-shore behaviour of shallow-water waves with localized initial conditions. J Fluid Mech 2007, 591: 413-436.
  • Kânoğlu U. Nonlinear evolution and runup-rundown of long waves over a sloping beach. J Fluid Mech 2004; 513: 363-372.
Year 2018, Volume: 19 Issue: 1, 122 - 131, 31.03.2018

Abstract

References

  • Gusiakov VK. Tsunami History: Recorded. In: Bernard EN, Robinson AR, editors. The Sea, Volume 15: Tsunamis. Cambridge, MA, USA and London, England: Harvard University Press, 2009. pp. 23-53.
  • Intergovernmental Oceanographic Commission. Tsunami Glossary, 2008. Paris, UNESCO: IOC Technical Series, 85, 2008.
  • Carrier GF, Greenspan HP. Water waves of finite amplitude on a sloping beach. J Fluid Mech 1958; 4: 97-109.
  • Keller JB, Keller HB. Water wave run-up on a beach. ONR Research Report NONR-3828(00), Department of the Navy, Washington, DC, USA, 1964.
  • Peregrine DH. Long waves on a beach. J Fluid Mech 1967; 27: 815-827.
  • Synolakis CE. The runup of solitary waves. J Fluid Mech 1987; 185: 523-545.
  • Hibbert SD, Peregrine H. Surf and runup on a beach: a uniform bore. J Fluid Mech 1979; 95: 323-345.
  • Pedersen G, Gjevik B. Run-up of solitary waves. J Fluid Mech 1983; 135: 283-299.
  • Zelt JA. The run-up of nonbreaking and breaking solitary waves. Coast Eng 1991; 15: 205-246.
  • Li Y, Raichlen F. Non-breaking and breaking solitary wave run-up. J Fluid Mech 2002; 456: 295-318.
  • Kim SK, Liu PLF, Liggett JA. Boundary integral equation solutions for solitary wave generation, propagation and run-up. Coast Eng 1983; 7: 299-317.
  • Hall JV, Watts, JW. Laboratory investigation of the vertical rise of solitary waves on impermeable slopes. Tech. Memo. 33, Beach Erosion Board, USACE, 1953.
  • Street RL, Camfield FE. Observations and experiments on solitary wave deformation. In: Tenth International Conference on Coastal Engineering; September 1966; Tokyo, Japan: ASCE. pp. 284-301.
  • Hammack JL. A note on tsunamis: their generation and propagation in an ocean of uniform depth. J Fluid Mech 1973; 60: 769-799.
  • Synolakis CE, Bernard EN. Tsunami science before and beyond Boxing Day 2004. Phil Trans R Soc A 2006; 364: 2231-2265.
  • Tadepalli S, Synolakis CE. The run-up of N-waves on sloping beaches. Proc R Soc London A 1994; 445: 99-112.
  • Kânoğlu U, Synolakis CE. Initial value problem solution of nonlinear shallow water-wave equations. Phys Rev Lett 2006; 148501.
  • Stoker JJ. Water Waves: The Mathematical Theory with Applications. Wiley Classics Library ed. New York, NY, USA: John Wiley & Sons, Inc., 1992.
  • Aydın B. Analytical solutions of shallow-water wave equations. PhD, Middle East Technical University, Ankara, Turkey, 2011.
  • Aydın B, Kânoğlu U. New analytical solution for nonlinear shallow water-wave equations. Pure Appl Geophys 2017; 174: 3209-3218.
  • Carrier GF, Wu TT, Yeh H. Tsunami run-up and draw-down on a plane beach. J Fluid Mech 2003; 475: 79-99.
  • Prichard D, Dickinson L. The near-shore behaviour of shallow-water waves with localized initial conditions. J Fluid Mech 2007, 591: 413-436.
  • Kânoğlu U. Nonlinear evolution and runup-rundown of long waves over a sloping beach. J Fluid Mech 2004; 513: 363-372.
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Baran Aydın 0000-0001-7838-3708

Publication Date March 31, 2018
Published in Issue Year 2018 Volume: 19 Issue: 1

Cite

APA Aydın, B. (2018). Maximum run-up behavior of tsunamis under non-zero initial velocity condition. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 19(1), 122-131. https://doi.org/10.18038/aubtda.340255
AMA Aydın B. Maximum run-up behavior of tsunamis under non-zero initial velocity condition. AUJST-A. March 2018;19(1):122-131. doi:10.18038/aubtda.340255
Chicago Aydın, Baran. “Maximum Run-up Behavior of Tsunamis under Non-Zero Initial Velocity Condition”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19, no. 1 (March 2018): 122-31. https://doi.org/10.18038/aubtda.340255.
EndNote Aydın B (March 1, 2018) Maximum run-up behavior of tsunamis under non-zero initial velocity condition. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19 1 122–131.
IEEE B. Aydın, “Maximum run-up behavior of tsunamis under non-zero initial velocity condition”, AUJST-A, vol. 19, no. 1, pp. 122–131, 2018, doi: 10.18038/aubtda.340255.
ISNAD Aydın, Baran. “Maximum Run-up Behavior of Tsunamis under Non-Zero Initial Velocity Condition”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19/1 (March 2018), 122-131. https://doi.org/10.18038/aubtda.340255.
JAMA Aydın B. Maximum run-up behavior of tsunamis under non-zero initial velocity condition. AUJST-A. 2018;19:122–131.
MLA Aydın, Baran. “Maximum Run-up Behavior of Tsunamis under Non-Zero Initial Velocity Condition”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 19, no. 1, 2018, pp. 122-31, doi:10.18038/aubtda.340255.
Vancouver Aydın B. Maximum run-up behavior of tsunamis under non-zero initial velocity condition. AUJST-A. 2018;19(1):122-31.