Energy Transmission to Long Waves Generated by Instantaneous Ground Motion on a Beach

  • Arghya Bandyopadhyay Department of Mathematics, Khalisani College, Chandannagar, Hooghly, India – 712 138
  • Avijit Mandal Baidyapur Ramkrishna Vidyapith , Baidyapur, Burdwan, India – 713 122
DOI: http://dx.doi.org/10.36842/jomase.v6i1.500

Abstract

Historically speaking, all high frequency earth-quakes do not produce tsunami which is evident from several earthquakes that took place in Indian Ocean between 2004 and 2006. The works of Geist et.al [’06] and Ammon et.al [’05] are good examples of such study through which they have also pointed out the miserable failures of the existing warning system. The reasons of no-generation of tsunami due to large quakes may be several but in this article we have tried to throw some light on this puzzle and tried to analyze energy transmission to a tsunami motion at steady state and have shown that no energy transmits for certain frequencies of the forcing parameter. We discuss here tsunami waves which are generated instantaneous bottom dislocation where the ocean floor is taken to be of variable slope and analytical solutions are provided correct to all time t.

##Keywords:## Tsunami Waves; Shallow Water Equations; Hankel Transform; Hankel Functions; Asymptotic Expansion.
Published
Apr 20, 2014
How to Cite
BANDYOPADHYAY, Arghya; MANDAL, Avijit. Energy Transmission to Long Waves Generated by Instantaneous Ground Motion on a Beach. Journal of Ocean, Mechanical and Aerospace -science and engineering-, [S.l.], v. 6, n. 1, p. 17-23, apr. 2014. ISSN 2527-6085. Available at: <https://isomase.org/Journals/index.php/jomase/article/view/500>. Date accessed: 09 june 2026. doi: http://dx.doi.org/10.36842/jomase.v6i1.500.
Citation Formats
Issue
Vol 6 No 1 (2014): Journal of Ocean, Mechanical and Aerospace -science and engineering- (JOMAse)
Section
Articles

References

1. Geist et. al. (2006), Differences in Tsunami generation between the December 26, and March 28, 2005 Sumatra
Earthquakes. Earth Planets Space 58, 2006, 185 – 193.
2. Ammon C. J. et. al. (2005), The 17 July 2006 Java Tsunami Earthquake, Geo. Phy. Let. 33, L24308.
3. Stoker, J.J (1957). Water Waves, Interscience Pulishers, New York.
4. Tinti, S. and Tonini, R. (2005), Evolution of tsunamis induced by near-shore earthquakes on a constant slope
ocean, J. Fluid Mech. Vol 535, 33-64.
5. Weahausen, J. V. and Laitone, E. V. (1960), Surface waves, Handbuch der In Physik, Vol. 9, Part. 3, Springer
Berlin, 446–778.
6. Tuck, EO and Hwang, LS (1972)., Long wave generation on a sloping beach, J. Fluid Mech. Vol 51, pp 449–461.
7. Pelinovsky,E and Talipova, T. et. al.(2001), Nonlinear mechanism of tsunami wave generation by atmospheric
disturbances, Natural Hazards and Earth Sys. Sc. Vol 1, 243–250.
8. Erdléyi et. al. (1954), Tables of Integral Transforms, Vol II, pp 29, McGraw-Hill.
9. Erdléyi et. al. (1953), Higher Transcendental Functions, Vol II, pp 58, McGraw-Hill.
10. Liu, PL-F, Lynett, P and Synolakis, CE (2003), Analytical solution for forced long waves on a sloping
beach, J. Fluid Mech. Vol 478, 101–109
11. Oberhettinger, F (1970), Tables of Bessel Transforms, Springer
12. Edward Bryant (2003), Tsunami the underrated hazards: CUP
13. Synolakis, CE. (1991), Tsunami Runup on Steep Slopes: How Good Linear Theory Is, Natural Hazards, Vol 4, 221-234, Kluwer Academic Publishers.
14. Okada, Y. (1992), Internal deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., Vol 82, pp.1018-1040.
15. Dutykh, et. al. (2012), On the contribution of the horizontal sea-bed displacements into the tsunami
generation process, Ocean Modelling, 56, 43-56.