Water wave transients in an ice-covered channel

Abstract

Many studies show that the propagation of a breakup water surge in impeded rivers (ice cover present) differs from the unimpeded case. Some of the differences are due to ice sheet breaking into pieces as the wave travels downstream while others are due to the effect of a fissured but otherwise intact ice cover’s resistance to motion. This is the subject of this paper: water waves that are sufficiently strong to break the cover away from the banks but not strong enough to create transverse cracks. Although some analytical solutions exist for the propagation of these transients for simple cases, for the first time in the literature, this paper introduces numerical solutions using a FEM model (HYDROBEAM) that simulates this interaction using the one-dimensional Saint-Venant equations appropriately written for rivers having an intact fissured floating ice cover coupled with a classic beam equation subject to hydrostatic loads (often referred to as a beam on an elastic foundation). The governing equations are numerically expressed and are solved using a finite element method (FEM) for the hydrodynamic and ice beam equations separately. A coupling technique is used to converge to a unique solution at each time step (for more information on the numerical characteristics of the model, see companion paper presented by the authors in this issue). The coupled model, gives a first and unique opportunity to compare the simplified analytical solutions to the full numerical solutions. A parametric analysis is herein presented that quantifies the impact of the ice cover's presence and stiffness on wave attenuation and wave celerity as well as to quantify tensile stresses generated in the ice sheet as a function of ice properties (thickness and strength) and channel shape (rectangular and trapezoidal). In general, for rectangular channels, it was found that the simplified analytical solutions are quite representative of the phenomenon namely that short wave transients are affected by the cover’s stiffness but long waves (>400 m) are not.