초록

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Abstract ▼ AI-Helper

Time evolution of linear water waves on a constant depth generated by a disturbance is analyzed by asymptotic methods; stationary phase, steepest descents and leading wave approximation. In order to verify the derived formulae of surface displacements for 1-D and 2-D waves. surface displacements are...

Time evolution of linear water waves on a constant depth generated by a disturbance is analyzed by asymptotic methods; stationary phase, steepest descents and leading wave approximation. In order to verify the derived formulae of surface displacements for 1-D and 2-D waves. surface displacements are calculated and plotted from both the formulae and a numerical integration. The existing results for surface displacements are verified in which the leading amplitude of 1-D waves during the evolution decays as f- T/B, the rest of the wavetrain as t$^{-1}$ 2/ and the rest of the wavetrain of 2-D waves as t-1. But it is shown that the leading amplitude of 2-D waves decays as t 5/6 which is different from Kajiura's result t$^{-4}$ 3/.