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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M. and Stegun, I. A.: 1972, Handbook of Mathematical Functions, Natl. Bur. Stands., Washington, D.C.
Carrier, G. F.: 1966, J. Fluid Mech. 24, 641–659.
Carrier, G. F.: 1971, Proc. 6th Summer Seminar on Applied Mathematics, RPI, Troy, NY, 1970, Amer Math. Soc.
Carrier, G. F. and Greenspan, H. P.: 1958, J. Fluid Mech. 17, 97–110.
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, Moide, Norway), Kluwer Academic Publishers, Dordrecht.
Guza, R. T. and Thornton, E. B.: 1982, J. Geophys. Res. 87, 483–491.
Hall, J. V. and Watts, J. W.: 1953, TM 33, BEB, US Army Corps Eng.
Heitner, K. L. and Housner, G. W.: 1970, Proc. ASCE, J. Wat. Harb. Coastal Engng., WW3, pp. 701–719.
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).
Keller, J. B. and Keller, H. B.: 1964, ONR Research Report Contract No. NONR-3828(00), Dept. of the Navy, Washington, D.C.
Kim, S. K., Liu, P. L-F. and Ligett, J. A.: 1983. Coastal Engng. 7, 299–317.
Lamb, H.: 1932, Hydrodynamics, 6th edn., Cambridge University Press.
Pedersen, G. and Gjevik, B.: 1983, J. Fluid Mech. 135, 283–299.
Pelinofsky, E. N.: 1989, Sci. Tsun. Hazards 7, 117–126.
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).
Ohyama, T.: 1987, Proc. JSCE 381, II-7, 189–198. (in Japanese.)
Shuto, N.: 1973, Coastal Engineering in Japan 16, 25–42.
Synolakis, C. E.: 1986, The runup of long waves, PhD Thesis, California Institute of Technology, Pasadena.
Synolakis, C. E.: 1987, J. Fluid Mech. 185, 523–545.
Synolakis, C. E., Deb M. K. and Skjelbreia, E. J.: 1988a, Phys. Fluids 31, 1–4.
Synolakis, C. E.: 1988b, Quart. Appl. Math. 46, 105–107.
Synolakis, C. E.: 1990, J. Water. Harb. Coast. Eng. 116, 252–266.
Svendsen, I. A.: 1974, Cnoidal waves over gently sloping bottom. Inst. Hydr. Eng., Techn. Univ. Denmark, Ser. Paper 6, Lyngby, Denmark.
Tuck, E. O. and Hwang, L.: 1972, J. Fluid Mech. 51, 449–461.
Yeh, H.: 1991, Tsunami bore run-up, Natural Hazards 4, 209–220 (this issue).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Kluwer Academic Publishers
About this chapter
Cite this chapter
Synolakis, C.E. (1991). Tsunami Runup on Steep Slopes: How Good Linear Theory Really Is. In: Bernard, E.N. (eds) Tsunami Hazard. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3362-3_8
Download citation
DOI: https://doi.org/10.1007/978-94-011-3362-3_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5486-7
Online ISBN: 978-94-011-3362-3
eBook Packages: Springer Book Archive