Fracture of River Ice Covers by River Waves

Abstract

The stresses induced in ice covers by river waves are investigated as a possible mechanism for causing transverse cracks during breakup. The maximum stress levels that river waves can cause in the ice cover are determined over the entire spectrum of waves that may be present at breakup. The ice cover is analyzed as a continuous elastic plate. For a given wave amplitude, the amplitude of ice-cover bending stress has two possible maximums: one when the wavelength is equal to 2πl (where l is the characteristic length of the ice cover), and a second when the celerity of the propagating wave equals the celerity of a free (homogeneous) wave of the same wavelength. The present calculations indicate that the celerities of propagating waves are always less than the celerity of free waves of the same wavelength, and, as a result, only the first maximum is possible. The global minimum wave amplitude required to cause cracks is therefore found at a wavelength of 2πl. At this wavelength, a simple expression describing the minimum wave amplitude causing cracks can be derived.