Tsunami Intrusion and River Ice Movement

Abstract

A two-dimensional wave model coupled with ice dynamics is developed to evaluate ice effects on shallow water wave propagation on a beach and in a channel. The nonlinear Boussinesq equations with ice effects are derived and solved by the hybrid technique of the Godunov-type finite volume method and finite difference method with the third-order Runge-Kutta method for time integration. The shock capturing method enables the model to simulate complex flows over irregular topography. The model is capable of simulating wave propagations accurately, including non-hydrostatic water pressure and wave dispersions. The ice dynamic module utilizes a Lagrangian discrete parcel method, based on smoothed particle hydrodynamics. The Boussinesq wave model is validated with an analytical solution of water surface oscillation in a parabolic container, an analytical solitary wave propagation in a flat channel, and experimental data on tsunami wave propagations. The validated model is then applied to investigate the interaction between ice and tsunami wave propagation, in terms of ice attenuation on tsunami wave propagations over a beach, ice deposition on the beach driven by the tsunami wave, and ice jam formation and release in a coastal channel with the intrusion of the tsunami wave. The simulated results demonstrated the interactions between tsunami waves and surface ice, including the maximum run up, ice movement along the beach, and ice jamming in a channel.the Honshu earthquake that occurred on 11 March 2011 [17]. The Honshu tsunami wave produced wave run-up heights of 5 m and structure damages from the floating sea ice with thickness of about 0.3 m in the Kuril Islands were observed [18]. Although a tsunami accompanied by floating ice is destructive, the interaction between tsunami wave propagation and floating ice movement has not been quantitatively studied. However, significant progress has been made in ice dynamic studies, especially in terms of mathematical modeling. Shen et al. [19] developed a one-dimensional river ice model to examine the leading-edge propagation for ice jam and potential flooding risks. Later, the two-dimensional ice dynamic model was developed to explore the interactions between unsteady flows and ice movement [20][21][22][23]. Such techniques contributed to the understanding of ice jamming formation and release, and ice cover breakup [20][21][22][23].In the literature, the BE is rarely applied to investigate wave propagations with ice effects, while the ice dynamic models have not been coupled with the tsunami wave. The main objective of this study is to investigate the interaction between surface ice transport and tsunami wave propagation. This paper first proposes a two-dimensional Boussinesq wave model that is coupled with ice dynamics. Then, the model is validated with analytical solutions for oscillatory flows, theoretical solitary wave, and an experimental tsunami wave. The model is finally applied to simulate tsunami wave propagation with ice, including surface ice transport over a beach, i...

Numerical Modelling of Wave Fields and Currents in Coastal Area

“…The more recent works that feature BEs are Ref. [10][11][12][13][14]. In particular, in [10] broken waves characteristics in front of a vertical seawall are modelled and studied using a shock-capturing Boussinesq wave model.…”

“…[11] presents a shock-capturing numerical model based on extended BEs suitable for rapidly varying topography with respect to wave transformation, breaking, and runup. In [12], a two-dimensional wave model coupled with ice dynamics is developed to evaluate ice effects on shallow water propagation on a beach and in a channel. The study proposed by [13] utilizes a shock-capturing Boussinesq model to investigate the maximum momentum flux in the solitary wave runup zone over back-reef slopes.…”