Advertisement

Natural Hazards

, Volume 4, Issue 2–3, pp 221–234 | Cite as

Tsunami runup on steep slopes: How good linear theory really is

  • Costas Emmanuel Synolakis
Article

Abstract

This is a study of the application of linear theory for the estimation of the maximum runup height of long waves on plane beaches. The linear theory is reviewed and a method is presented for calculating the maximum runup. This method involves the calculation of the maximum value of an integral, now known as the runup integral. Laboratory and numerical results are presented to support this method. The implications of the theory are used to reevaluate many existing empirical runup correlations. It is shown that linear theory predicts the maximum runup satisfactorily. This study demonstrates that it is now possible to match complex offshore wave-evolution algorithms with linear theory runup solutions for the purpose of obtaining realistic tsunami inundation estimates.

Key words

Tsunami runup longwave runup linear shallow water theory swash runup solitary waves cnoidal waves Green's law 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz, M. and Stegun, I. A.: 1972, Handbook of Mathematical Functions, Natl. Bur. Stands., Washington, D.C.Google Scholar
  2. Carrier, G. F.: 1966, J. Fluid Mech. 24, 641–659.Google Scholar
  3. Carrier, G. F.: 1971, Proc. 6th Summer Seminar on Applied Mathematics, RPI, Troy, NY, 1970, Amer Math. Soc.Google Scholar
  4. Carrier, G. F. and Greenspan, H. P.: 1958, J. Fluid Mech. 17, 97–110.Google Scholar
  5. Grilli, S. and Svendsen, I. A.: 1989, Computations of nonlinear wave kinematics during propagation and runup on a slope, in Water Wave Kinematics (Proc. NATO-ARW, Molde, Norway), Kluwer Academic Publishers, Dordrecht.Google Scholar
  6. Guza, R. T. and Thornton, E. B.: 1982, J. Geophys. Res. 87, 483–491.Google Scholar
  7. Hall, J. V. and Watts, J. W.: 1953, TM 33, BEB, US Army Corps Eng.Google Scholar
  8. Heitner, K. L. and Housner, G. W.: 1970, Proc. ASCE, J. Wat. Harb. Coastal Engng., WW3, pp. 701–719.Google Scholar
  9. Kaistrenko, V. M., Mazova, R. K., Pelinofsky, E. N. and Simonov, K. V.: 1985, Tsunami Runup on Shore, Inst. Appl. Phys., U.S.S.R. Academy of Sciences, Gorky (in Russian).Google Scholar
  10. Keller, J. B. and Keller, H. B.: 1964, ONR Research Report Contract No. NONR-3828(00), Dept. of the Navy, Washington, D.C.Google Scholar
  11. Kim, S. K., Liu, P. L-F. and Ligett, J. A.: 1983. Coastal Engng. 7, 299–317.Google Scholar
  12. Lamb, H.: 1932, Hydrodynamics, 6th edn., Cambridge University Press.Google Scholar
  13. Pedersen, G. and Gjevik, B.: 1983, J. Fluid Mech. 135, 283–299.Google Scholar
  14. Pelinofsky, E. N.: 1989, Sci. Tsun. Hazards 7, 117–126.Google Scholar
  15. Pelinofsky, E. N., Golinko, V. I. and Mazova, R. K.: 1989, Tsunami wave runup on a beach; Exact analytical results, preprint No. 232, Inst. Appl. Phys., U.S.S.R. Academy of Sciences, Gorky (in English).Google Scholar
  16. Ohyama, T.: 1987, Proc. JSCE 381, II-7, 189–198. (in Japanese.)Google Scholar
  17. Shuto, N.: 1973, Coastal Engineering in Japan 16, 25–42.Google Scholar
  18. Synolakis, C. E.: 1986, The runup of long waves, PhD Thesis, California Institute of Technology, Pasadena.Google Scholar
  19. Synolakis, C. E.: 1987, J. Fluid Mech. 185, 523–545.Google Scholar
  20. Synolakis, C. E., Deb M. K. and Skjelbreia, E. J.: 1988a, Phys. Fluids 31, 1–4.Google Scholar
  21. Synolakis, C. E.: 1988b, Quart. Appl. Math. 46, 105–107.Google Scholar
  22. Synolakis, C. E.: 1990, J. Water. Harb. Coast. Eng. 116, 252–266.Google Scholar
  23. Svendsen, I. A.: 1974, Cnoidal waves over gently sloping bottom. Inst. Hydr. Eng., Techn. Univ. Denmark, Ser. Paper 6, Lyngby, Denmark.Google Scholar
  24. Tuck, E. O. and Hwang, L.: 1972, J. Fluid Mech. 51, 449–461.Google Scholar
  25. Yeh, H.: 1991, Tsunami bore run-up, Natural Hazards 4, 209–220 (this issue).Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Costas Emmanuel Synolakis
    • 1
  1. 1.School of EngineeringUniversity of Southern CaliforniaLos AngelesU.S.A.

Personalised recommendations