A simplified derivation of the ordinary differential equations for the free-surface Green functions. (January 2020)

• Record Type: Journal Article
• Authors: Newman, J.N.
• Is Part Of: Applied ocean research. Volume 94(2020)
• Publication Date: 2020-01
• Subjects: Free-surface Green function -- Infinite depth -- Frequency domain -- Time domain -- Ordinary differential equation; Ocean engineering -- Periodicals; 620.416205
• DOI: 10.1016/j.apor.2019.101973
• Languages: English
• ISSNs: 0141-1187

Abstract

Abstract: Ordinary differential equations (ODEs) are derived for the free-surface Green functions and their gradients, in a fluid of infinite depth. The cases of harmonic time-dependence in the frequency domain and impulsive motion in the time domain are considered separately. These ODEs were derived originally by Clément, starting with fourth-oder equations in the time domain and using Fourier transforms to derive a second-order ODE in the frequency domain. In the present work a simpler procedure is followed independently in each domain, transforming the governing Laplace equation to an ordinary differential equation. The results are consistent with the ODEs derived using Clément's method.