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

Conditions for the applicability of the dispersionless theory of long waves for reproducing dispersive tsunami waves are analyzed. As a quantitative criterion, the dispersive destruction distance is proposed for use, which is 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 the correction factor \(\alpha .\) The physical meaning of the \(\alpha \) value 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 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 quantity \(\alpha .\) Using the “\(\alpha \) coefficient scale”, the ranking of the criteria that were previously proposed by other authors was performed.