Abstract
An analytical solution to shallow-water nonlinear equations determining the height of tsunami waves leaving the source is obtained. The initial water-level displacement in the source and the distribution of particle velocities are set. The numerical solution showed that analytical estimates fit well with source characteristics varying in a broad range, even if the waves produced by the source collapse.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. N. Pelinovsky, Hydrodynamics of Tsunami Waves (IPF RAN, Nizhni Novgorod, 1996) [in Russian].
B. V. Levin and M. A. Nosov, Physics of Tsunami and Related Phenomena in the Ocean (Yanus-K, Moscow, 2005) [in Russian].
Y. Okada, “Internal deformations due to shear and tensile faults in half-space,” Bull. Seism. Soc. Am. 82, 1018–1040 (1985).
Y. Tanioka and K. Satake, “Tsunami generation by horizontal displacement of ocean bottom,” Geophys. Res. Lett. 23, 861–864 (1996).
A. C. Yalciner, E. N. Pelinovsky, E. Okal, and C. E. Synolakis, Submarine Landslides and Tsunamis (Kluwer, 2003).
L. E. Novikova and L. A. Ostrovskii, “On the generation of tsunami waves by a running displacement of the ocean bottom,” in Methods for Calculating the Generation and Propagation of Tsunamis (Nauka, Moscow, 1978), pp. 88–99 [in Russian].
A. G. Marchuk, L. B. Chubarov, and Yu. I. Shokin, Numerical Simulation of Tsunamis (Nauka, Novosibirsk, 1983.
G. F. Carrier and H. P. Greenspan, “Water waves of finite amplitude on a sloping beach,” J. Fluid Mech. 4, 97–109 (1958).
S. Tinti and R. Tonini, “Analytical evolution of tsunamis induced by near-shore earthquakes on a constant-slope ocean,” J. Fluid Mech. 535, 33–64 (2005).
S. Yu. Dobrokhotov and B. Tirozzi, “Localized solutions of one-dimensional nonlinear shallow-water equations with velocity c 2 = x,” Usp. Mat. Nauk 65(1), 185–186 (2010).
I. Didenkulova and E. Pelinovsky, “Nonlinear wave evolution and runup in an inclined channel of a parabolic cross-section,” Phys. Fluids 23(8), 086602 (2011).
I. I. Didenkulova, N. Zahibo, A. A. Kurkin, and E. N. Pelinovsky, “Steepness and spectrum of a nonlinearly deformed wave on shallow waters,” 42(6), 773–776 (2006).
N. Zahibo, I. Didenkulova, A. Kurkin, and E. Pelinovsky, “Steepness and spectrum of nonlinear deformed shallow water wave,” Ocean Eng. 35(1), 47–52 (2008).
E. N. Pelinovsky and A. A. Rodin, “Nonlinear deformation of a large-amplitude wave on shallow water,” Dokl. Phys. 56(5), 305–308 (2011).
E. N. Pelinovsky and A. A. Rodin, “Transformation of a strongly nonlinear wave in a shallow-water basin,” 48(3), 343–349 (2012).
I. Didenkulova, E. Pelinovsky, and A. Rodin, “Nonlinear interaction of large-amplitude unidirectional waves in shallow waters,” Est. J. Eng. 17(4), 289–300 (2011).
R. J. LeVeque, Finite-Volume Methods for Hyperbolic Problems (Cambridge Univ. Press, Cambridge, 2004).
O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Nauka, Moscow, 1975) [In Russian].
K. I. Volyak, A. S. Gorshkov, and O. V. Rudenko, “On the generation of backward waves in homogenous non-linear media,” Vestn. Mosk. Univ., Ser. 3: Fiz., Astron., No. 1, 32–36 (1975).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.N. Pelinovsky, A.A. Rodin, 2013, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2013, Vol. 49, No. 5, pp. 595–600.
Rights and permissions
About this article
Cite this article
Pelinovsky, E.N., Rodin, A.A. Nonlinear effects at the initial stage of tsunami-wave development. Izv. Atmos. Ocean. Phys. 49, 548–553 (2013). https://doi.org/10.1134/S0001433813050083
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001433813050083