Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method.

摘要

LONG-TERM GOALS: 1. Application of multidimensional Fourier analysis for the extremely fast numerical integration of the partial differential equations of surface water waves is the long-term goal of this work. The approach is a generalization of linear Fourier analysis and therefore is a hyperfast extension of the fast Fourier transform (FFT) to the nonlinear Euler water wave equations. 2. The present report discusses progress made in both the shallow and deep-water environments, anticipating the marriage of the two in the coming year for a complete, higher order, hyperfast integration to Euler. An important application of the approach is possibility of the on-board computation of wave properties as derived from shipboard direct wave and/or radar measurements of the sea surface, leading to prediction of sea state conditions, including the presence of rogue waves in real time.