Nonlinear Interaction of Surge Waves with Ice Cover in River Channels

摘要

The interaction of water waves with an ice cover in river channels is studied using one-dimensional governing equations which describe fluid continuity, momentum, and the ice cover response. The ice cover is assumed to be a continuous, thin elastic plate. Both linearized and nonlinear forms of the above three equations are analyzed in this study. The effects of a constant compressive axial force along an ice cover on the propagation characteristics of linear water waves, i.e., celerity, attenuation, and group velocity, are first investigated over the entire spectrum of wavelengths on the basis of linear stability theory. It is found that only when an axial force approaches a critical value and the wavelength is around 2-pi-l, where l is the characteristic length of the cover, the effect of the axial force is significant. The nonlinear terms in the water equation, which are ignored in the linear theory, become significant in highly unsteady flows such as surges caused by ice jam releases. An analytical solution for the nonlinear shallow wave equations is obtained. The effects of ice inertia and an axial force on the nonlinear waves are examined. The stresses induced in ice cover by both linear and nonlinear waves obtained from the above mentioned analysis are used to investigate the possible formation of closedly-spaced transverse cracks often observed during ice cover breakups. The formation of closedly-spaced transverse cracks is the key mechanism for river ice breakup and the initiation of breakup ice runs. The validity of the linear theory is found to be very limited. The nonlinear analysis provides results in close agreement with field observations. These results provide basic explanation of the formation mechanism of transverse cracks which initiate the breakup ice runs.