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

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 30, 2006
Accession Number
ADA612395

Entities

People

  • A. R. Osborne

Organizations

  • University of Turin

Tags

DTIC Thesaurus Topics

  • Deep Water
  • Differential Equations
  • Dynamics
  • Equations
  • Euler Equations
  • Fourier Analysis
  • Fourier Series
  • Frequency
  • Inverse Problems
  • Mathematics
  • Numerical Integration
  • Partial Differential Equations
  • Shallow Water
  • Surface Waves
  • Water
  • Water Waves
  • Waves

Readers

  • Calculus or Mathematical Analysis
  • Distributed Systems and Data Platform Development
  • Marine Hydrodynamics