Room: 5-314
Speaker Name:
Max Pierce
Affiliation:
MIT Ocean Engineering
Abstract:
A moving load on a floating ice sheet (e.g. a cargo truck driving on an ice road) generates a wake pattern that deviates substantially from the Kelvin wake of a ship moving in open water largely due to the flexural term in the dispersion relation. Understanding this wake pattern is important because it determines the dynamic stress in the ice, related to ice fracture. While wake predictions using linear wave theory are well established, finite-amplitude nonlinear effects are known to qualitatively affect the wake at certain speeds. Here, for the 2D problem, we consider the nonlinear triad interaction that occurs at the double-frequency condition where the wavelength of the trailing wave is double that of the leading wave. Using multiple-scales perturbation analysis, we obtain amplitude evolution equations governing the leading-order, steady-state response. We complement the theoretical predictions with direct numerical simulations of the initial-boundary value problem using a high-order spectral (HOS) method accurate to arbitrary order. Our results show that the double-frequency interaction can cause the trailing wave amplitude to decay with distance from the load, with its energy transferred to its second harmonic which radiates forward to coherently interfere with the leading wave. Depending on the length and orientation of the load, the resonant interaction can, in some cases, cause the wave drag to become vanishingly small or, in other cases, nearly double the maximum bending strain compared to the linear prediction. We also consider the effect of a small ambient wave which can cause the response to become a steady, localised wave packet containing two mutually trapped wave components, leading to vanishing wave drag.