Water wave interaction with ice-sheet of variable geometry in the presence of uniform current

Abstract

We propose an asymptotic method to solve the problem of flexural-gravity wave scattering by an ice sheet of variable geometry in the presence of uniform currents. The significance of the article resides in the development of first and second-order solutions via the use of asymptotic expansion and the Fourier transform technique. We consider two different shape functions for the plate geometry, namely, Gaussian and Gaussian oscillatory. For both shape functions, the first and second-order solutions result in a major impact of depth Froude numbers in hydrodynamic coefficients, emphasizing the crucial function of the higher-order solutions in understanding the current responsiveness. We also observe the occurrence of Bragg resonance for the Gaussian oscillatory shape. The depth Froude number alters the frequency of wave components that are most reflected, and wave action conservation causes a rise in the energy of reflected waves. The depth Froude numbers can induce a unique minimum in reflection coefficient, which is close to 0. An examination of plate deflection reveals that the elevation amplitude is substantially higher near the point where there is a peak of elastic plate's shape. The pressure exerted by the plate is also concentrated near this point, highlighting the significance of the elastic plate's shape. The collective numerical observations for both shapes provide insight into resonance phenomena, the role of plate shape, and the intricate relationship between wave characteristics and varying plate properties. The findings from this study could assist geologists and marine engineers in designing and managing ice sheets, ports, and harbor infrastructure.