Criterion of Applicability of the Theory of Long Waves for Describing Dispersive Tsunami Waves

Conditions for the applicability of the dispersionless theory of long waves for reproducing dispersive tsunami waves are analyzed. The dispersive destruction distance is proposed for use as a quantitative criterion, a value that is uniquely determined by the wavelength that dominates in the spectrum of the initial elevation of the water surface in the tsunami source and by correction factor alpha. The physical meaning of value alpha is the fraction of the wavelength by which the dispersive wave packet lags behind the long-wave front when propagating over a distance equal to the dispersive destruction distance. Using the model residual displacement of the bottom surface, the geometrical parameters of which vary randomly, under the assumption of the instantaneous generation of waves and taking into account the smoothing effect of the water layer, the Monte Carlo method establishes a relationship between the accuracy of wave reproduction by the dispersionless model and the value alpha. Using the alpha coefficient scale, criteria previously proposed by other authors are ranked.