Water waves generated by moving atmospheric pressure: theoretical analyses with applications to the 2022 Tonga event

Abstract

Both one-dimensional in the horizontal direction (1DH, dispersive and non-dispersive) and two-dimensional in the horizontal direction (2DH) axisymmetric (approximate, non-dispersive) analytical solutions are derived for water waves generated by moving atmospheric pressures. For 1DH, three wave components can be identified: the locked wave propagating with the speed of the atmospheric pressure, $C_p$ , and two free wave components propagating in opposite directions with the respective wave celerity, according to the linear frequency dispersion relationship. Under the supercritical condition ( $C_p > C$ , which is the fastest celerity of the water wave), the leading water wave is the locked wave and has the same sign (i.e. phase) as the atmospheric pressure, while the trailing free wave has the opposite sign. Under the subcritical condition ( $C >C_p$ ) the fastest moving free wave component leads, and its free surface elevation has the same sign as the atmospheric pressure. For a long atmospheric pressure disturbance, the induced free surface profile mimics that of the atmospheric pressure. The 2DH problem involves an axisymmetric atmospheric pressure decaying in the radial direction as $O(r^{-1/2})$ . Due to symmetry, only two wave components, locked and free, appear. The tsunami DART data captured during Tonga's volcanic eruption event are analysed. Corrections are necessary to isolate the free surface elevation data. Comparisons between the corrected DART data and the analytical solutions, including the arrival times of the leading locked waves and the trailing free waves, and the amplitude ratios, are in agreement in order of magnitude.