International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 3, Pages 373-390

On generation and propagation of tsunamis in a shallow running ocean

Lokenath Debnath1 and Uma Basu2

1Mathematics & Physics Departments, East Carolina University, Greenville 27834, North Carolina, USA
2Centre of Advanced Study in Applied Mathematics, University of Calcutta, Calcutta, India

Received 3 January 1977; Revised 2 May 1977

Copyright © 1978 Lokenath Debnath and Uma Basu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically as t12 for the two dimensional case and as t1 for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.