Run-up of solitary waves of different bell-like shapes (solitary-like and Lorentz-like waves and sine-like pulses) is studied in a linearly inclined bay of parabolic cross-section. Their maximum run-up heights, maximum water flow velocities, and parameters of wave breaking on the beach are calculated, compared, and discussed. It is shown that these parameters for different pulses of the same height and characteristic wavelength coincide with an acceptable accuracy, hence allowing parameterization of the corresponding formulas for run-up characteristics.
Antuono, M. and Brocchini, M. 2007. The boundary value problem for the nonlinear shallow water equation. Stud. Appl. Math., 119, 71–91.
http://dx.doi.org/10.1111/j.1365-2966.2007.00378.x
Antuono, M. and Brocchini, M. 2008. Maximum run-up, breaking conditions and dynamical forces in the swash zone: a boundary value approach. Coast. Eng., 55, 732–740.
http://dx.doi.org/10.1016/j.coastaleng.2008.02.002
Antuono, M. and Brocchini, M. 2010. Solving the nonlinear shallow-water equations in physical space. J. Fluid Mech., 643, 207–232.
http://dx.doi.org/10.1017/S0022112009992096
Brocchini, M. and Gentile, R. 2001. Modelling the run-up of significant wave groups. Cont. Shelf Res., 21, 1533–1550.
http://dx.doi.org/10.1016/S0278-4343(01)00015-2
Carrier, G. and Greenspan, H. 1958. Water waves of finite amplitude on a sloping beach. J. Fluid Mech., 4, 97–109.
http://dx.doi.org/10.1017/S0022112058000331
Carrier, G., Wu, T., and Yeh, H. 2003. Tsunami run-up and draw-down on a plane beach. J. Fluid Mech., 475, 79–99.
http://dx.doi.org/10.1017/S0022112002002653
Didenkulova, I. 2009. New trends in the analytical theory of long sea wave runup. In Applied Wave Mathematics: Selected Topics in Solids, Fluids, and Mathematical Methods (Quak, E. and Soomere, T., eds). Springer, 265–296.
http://dx.doi.org/10.1007/978-3-642-00585-5_14
Didenkulova, I. 2013. Tsunami runup in narrow bays: the case of Samoa 2009 tsunami. Nat. Hazards, 65, 1629–1636.
http://dx.doi.org/10.1007/s11069-012-0435-7
Didenkulova, I. and Pelinovsky, E. 2008. Run-up of long waves on a beach: the influence of the incident wave form. Oceanology, 48, 1–6.
http://dx.doi.org/10.1134/S0001437008010013
Didenkulova, I. and Pelinovsky, E. 2011a. Nonlinear wave evolution and runup in an inclined channel of a parabolic cross-section. Phys. Fluids, 23, 086602.
http://dx.doi.org/10.1063/1.3623467
Didenkulova, I. and Pelinovsky, E. 2011b. Runup of tsunami waves in U-shaped bays. Pure Appl. Geophys., 168, 1239–1249.
http://dx.doi.org/10.1007/s00024-010-0232-8
Didenkulova, I., Zahibo, N., Kurkin, A., and Pelinovsky, E. 2006. Steepness and spectrum of a nonlinearly deformed wave on shallow waters. Izv., Atm. Ocean. Phys., 42, 773–776.
http://dx.doi.org/10.1134/S0001433806060119
Didenkulova, I., Kurkin, A., and Pelinovsky, E. 2007a. Run-up of solitary waves on slopes with different profiles. Izv., Atm. Ocean. Phys., 43, 384–390.
http://dx.doi.org/10.1134/S0001433807030139
Didenkulova, I., Pelinovsky, E., Soomere, T., and Zahibo, N. 2007b. Runup of nonlinear asymmetric waves on a plane beach. In Tsunami & Nonlinear Waves (Kundu, A., ed.). Springer, 175–190.
http://dx.doi.org/10.1007/978-3-540-71256-5_8
Didenkulova, I., Pelinovsky, E., and Zahibo, N. 2008. Reflection of long waves from a “non-reflecting” bottom profile. Fluid Dynamics, 43, 101–107.
http://dx.doi.org/10.1134/S001546280804011X
Kânoğlu, U. 2004. Nonlinear evolution and runup-drawdown of long waves over a sloping beach. J. Fluid Mech., 513, 363–372.
http://dx.doi.org/10.1017/S002211200400970X
Kânoğlu, U. and Synolakis, C. 2006. Initial value problem solution of nonlinear shallow water-wave equations. Phys. Rev. Lett., 97, 148501.
http://dx.doi.org/10.1103/PhysRevLett.97.148501
Madsen, P. and Fuhrman, D. 2008. Run-up of tsunamis and periodic long waves in terms of surf-similarity. Coast. Eng., 55, 209–223.
http://dx.doi.org/10.1016/j.coastaleng.2007.09.007
Okal, E., Fritz, H., Synolakis, C., Borrero, J., Weiss, R., Lynett, P., et al. 2010. Field survey of the Samoa tsunami of 29 September 2009. Seismol. Res. Lett., 81, 577–591.
http://dx.doi.org/10.1785/gssrl.81.4.577
Pedersen, G. and Gjevik, B. 1983. Runup of solitary waves. J. Fluid Mech., 142, 283–299.
http://dx.doi.org/10.1017/S0022112083003080
Pelinovsky, E. 1982. Nonlinear Dynamics of Tsunami Waves. IPF RAN, Akad. Nauk SSSR, Gorky [in Russian].
Pelinovsky, E. and Mazova, R. 1992. Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles. Natur. Hazards, 6, 227–249.
http://dx.doi.org/10.1007/BF00129510
Spielvogel, L. 1975. Runup of single waves on a sloping beach. J. Fluid Mech., 74, 685–694.
http://dx.doi.org/10.1017/S0022112076002000
Synolakis, C. 1987. The runup of solitary waves. J. Fluid Mech., 185, 523–545.
http://dx.doi.org/10.1017/S002211208700329X
Tadepalli, S. and Synolakis, C. 1994. The runup of N-waves on sloping beaches. P. Roy. Soc. Lond., A, 445, 99–112.
Tinti, S. and Tonini, R. 2005. Analytical evolution of tsunamis induced by near-shore earthquakes on a constant-slope ocean. J. Fluid Mech., 535, 33–64.http://dx.doi.org/10.1017/S0022112005004532
