Waves generated by a load moving on an ice sheet over water

• Main Author: Nugroho, Widijanto Satyo
• Other Authors: Milinazzo, F.
• Format: Thesis
• Language: English
• Published: 1997
• Subjects: Plates (Engineering); Mathematical models; Fluid dynamics; Finite element method; Mathematical analysis; Ice Sheet
• Online Access: https://dspace.library.uvic.ca//handle/1828/9774

A load moving on a floating ice sheet produces a deflection of the ice sheet. In this Dissertation, three problems associated with mathematical models of the ice water system are examined. A mathematical model involving a steadily moving rectangular load on an ice sheet where the supporting fluid is of infinite depth is analyzed. The solution is written as a Fourier integral and is estimated using an asymptotic method. The results show that the amplitude of the ice deflection is similar to the case where the supporting fluid is of finite depth. The only significant difference is that, in contrast to the case where the supporting fluid is of finite depth where a quiescent zone appears behind the load when its speed exceeds the speed of gravity waves on shallow water, waves appear behind the load for all supercritical load speeds. A mathematical model of an ice plate that takes into account the thickness of the ice is derived by assuming that the vertical shearing forces vary linearly through the ice plate. The equations obtained are similar to those used to describe a mathematical model using a thin plate approximation subjected to in-plane forces. A comparison of the dispersion relation is carried out between the mathematical model of an ice plate that takes into account the plate thickness, the mathematical model of an ice plate using the thin plate approximation, and the mathematical model of an ice plate using the thin plate approximation subjected to in-plane forces. The results show that taking the ice thickness into consideration decreases the minimum phase speed. However, this effect is small. The major contribution of this Dissertation is the determination of the large time response of the deflection of an ice sheet caused by the steady motion of an impulsively-started point load. The results obtained are new. The solution of the ice deflection is written as a Fourier integral and asymptotic methods are used to estimate the large time behaviour of the rate of change of the ice deflection with respect to ...