On tsunami and the regularized solitary-wave theory
For ideal hydrodynamic modeling of earthquake-generated tsunamis, the principal features of tsunamis occuring in nature are abstracted to provide a fundamental case of a one-dimensional solitary wave of height a, propagating in a layer of water of uniform rest depth h for modeling the tsunami progressing in the open ocean over long range, with height down to a/h ≃ 10−4 as commonly known. The Euler model is adopted for evaluating the irrotational flow in an incompressible and inviscid fluid to attain exact solutions so that the effects of nonlinearity and wave dispersion can both be fully accounted for with maximum relative error of O(10−6) or less. Such high accuracy is needed to predict the wave-energy distribution as the wave magnifies to deliver any devastating attack on coastal destinations. The present UIFE method, successful in giving the maximum wave of height (a/h = 0.8331990) down to low ones (e.g. a/h = 0.01), becomes, however, impractical for similar evaluations of the dwarf waves (a/h < 0.01) due to the algebraic branch singularities rising too high to be accurately resolved. Here, these singularities are all removed by introducing regularized coordinates under conformal mapping to establish the regularized solitary-wave theory. This theory is ideal to differentiate between the nonlinear and dispersive effects in various premises for producing an optimal tsunami model, with new computations all regular uniformly down to such low tsunamis as that of height a/h = 10−4.
Keywords1-D tsunami wave Conformal mapping Dwarf solitary waves Optimal tsunami model Regularized coordinates Regularized solitary-wave theory Tsunami energy distribution
Unable to display preview. Download preview PDF.
- 1.Committee of the Great Earthquake Report: (1972) The Great Earthquake of 1964. Published by National Academy of Sciences. Academy Press, Washington, DCGoogle Scholar
- 2.Van Dorn WG (1964) Source mechanism of the tsunami of March 28, 1964 in Alaska. In: Proceedings of 9th conference on Coastal Engineer ASCE, pp 166–190Google Scholar
- 3.Van Dorn WG (1966) Theoretical and experimental study of wave enhancement and runup on uniformly sloping impermeable beach. University of California, Scripps Institution of Oceanography, SIO 66-11Google Scholar
- 4.Van Dorn WG (1970) A model experiment on the generation of the tsunami of 1964 in Alaska. In: Adams WM (eds) Tsunamis in the Pacific Ocean. East-West Center Press, Honolulu, pp 33–45Google Scholar
- 10.Wang XL (2008) Integral convergence of the higher-order theory for solitary waves for F = 1.0005. UnpublishedGoogle Scholar
- 11.Milne-Thomson LM (1968) Theoretical hydrodynamics, 5th edn, Sect. 14.75. Macmillan, LondonGoogle Scholar
- 12.Yamada H (1957) On the highest solitary wave. Rep Res Inst Appl Mech Kyushu Univ 5: 53–67Google Scholar
- 13.Murashige S, Wu TY (2010) Dwarf solitary waves and low tsunamis. In: Proceedings of 9th international conference on Hydrodynamics (ICHD-2010), China Ocean Press, pp 960–968Google Scholar