Deflection of Nonperiodic Ice Sheet Due to Wave Interaction in the Presence of Current

Abstract A two-dimensional mathematical model for wave scattering induced by the interaction of a wave with a nonperiodic variable ice sheet with the inclusion of current is presented, primarily focusing on the ice sheet deflection arising from this interaction. The perturbation approach is initially used to solve the associated boundary value problem (BVP), followed by the Fourier transform technique. The main aim of this study is to derive an explicit analytical expression for the first-order deflection of the ice sheet and to examine its behavior for different physical parameters. Moreover, the surface strain of the ice sheet is also examined. For numerical simulations, an elastic plate having a Gaussian oscillatory shape is explored for its deflection under uniform current in connection to various physical parameters such as the spreading parameter, frequency parameter, and channel depth Froude number (current speed parameter). One significant observation is the emergence of an updrifting pattern in the deflection of ice sheet for very small spreading parameter values. In addition, the subharmonic peaks begin to transition into harmonic peaks as the Froude number increases. The findings of this study could be potentially useful to marine engineers and geologists while building coastal structures based on physical oceanographic conditions.