A STUDY ON APPLICABILITY OF HYDROSTATIC APPROXIMATION BASED ON NUMERICAL SIMULATIONS AND WAVE THEORIES

Abstract

 The applicability of hydrostatic approximation was studied by numerical simulations and theoretical speculations. By numerical simulations on tsunami propagation with soliton fission, it was found that the reproducibility of dispersive wave shape may be affected by horizontal grid size and non-hydrostatic pressure behind wave crest. Referring these results of numerical simulations, theoretical considerations were made based on theories about non-linier long-wave and finite amplitude wave. As a result, the conditions which can be applied hydrostatic approximation have been derived as δε<0.0087 and ε²<0.03 (here δ=Δz/Δx, ε=|w/u|) for numerical simulations on shallow water.