Three-dimensional nonlinear responses of a floating ice sheet to moving loads

We investigate the three-dimensional responses of a floating ice sheet on an ideal fluid subjected to moving loads. This study considers the effects of nonlinearity, viscoelasticity and inertia. We develop a fully dispersive model that incorporates quadratic and cubic nonlinearities by using the Taylor expansion of the Dirichlet–Neumann operator within the boundary conditions; we refer to this model as the cubic model. By using the multiple-scale expansion method at the minimum phase speed, we derive the corresponding envelope equation, known as the Benney–Roskes–Davey–Stewartson (BRDS) system. We also examine the bifurcation diagrams of solitary waves within the cubic model and justify it by comparing the bifurcation mechanism to the BRDS theory. Through numerical simulations, we compare the predictions of the cubic model with previous field observations and find strong agreement, confirming its effectiveness. Furthermore, we explore how the ice sheet responds to moving loads at varying velocities. Our findings indicate that both acceleration and deceleration processes increase ice deflection when the target or initial speed of the load exceeds the minimum phase speed. Finally, we verify the reliability of the cubic model in addressing scenarios involving variable load speeds through comparisons with the analytical solution derived from linear theory.