Two-scale mathematical model for tsunami wave

Scale or dimension is critical for all physical laws, and different scales might result in distinct and sometimes contradicting laws for the same phenomenon. In this study, the idea of the two-scale fractal is utilized to model the time-fractional tsunami wave traveling on an unsmooth surface. Mass and momentum conservation equations are established in a fractal space. To covert the considered fractional model into a differential equation, the fractional complex transform is used, then He's variational iteration method is adopted to solve the resultant equation. The fractal model helps in studying the dynamic behavior of tsunami wave and their prevention through boundary control. The present study sheds new light on two-scale fluid mechanics.