Run-up of tsunamis and long waves in terms of surf-similarity

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3-6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.
Original languageEnglish
JournalCoastal Engineering
Volume55
Issue number3
Pages (from-to)209-223
ISSN0378-3839
DOIs
Publication statusPublished - 2008

Keywords

  • tsunamis
  • surf-similarity
  • run-up
  • long waves

Cite this

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title = "Run-up of tsunamis and long waves in terms of surf-similarity",
abstract = "In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3-6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.",
keywords = "tsunamis, surf-similarity, run-up, long waves",
author = "Madsen, {Per A.} and Fuhrman, {David R.}",
year = "2008",
doi = "10.1016/j.coastaleng.2007.09.007",
language = "English",
volume = "55",
pages = "209--223",
journal = "Coastal Engineering",
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}

Run-up of tsunamis and long waves in terms of surf-similarity. / Madsen, Per A.; Fuhrman, David R.

In: Coastal Engineering, Vol. 55, No. 3, 2008, p. 209-223.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Run-up of tsunamis and long waves in terms of surf-similarity

AU - Madsen, Per A.

AU - Fuhrman, David R.

PY - 2008

Y1 - 2008

N2 - In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3-6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.

AB - In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3-6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.

KW - tsunamis

KW - surf-similarity

KW - run-up

KW - long waves

U2 - 10.1016/j.coastaleng.2007.09.007

DO - 10.1016/j.coastaleng.2007.09.007

M3 - Journal article

VL - 55

SP - 209

EP - 223

JO - Coastal Engineering

JF - Coastal Engineering

SN - 0378-3839

IS - 3

ER -