A Michell Oseen-Flow Theory for Thin Ships

Citation

Wilson, Michael Barron (1971) A Michell Oseen-Flow Theory for Thin Ships. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4ZZV-F953. https://resolver.caltech.edu/CaltechETD:etd-03262007-154052

Abstract

A linear theory is developed for the steady free surface flow of a viscous fluid past a general system of submerged flow disturbances (a point mass source and three orthogonal point forcelets). The viscous character of the flow is approximated by using the Oseen linearization of the Navier-Stokes equations.

Solution of the fundamental problem (point flow disturbances) using double Fourier transforms furnishes formal representations of all the interesting flow quantities: the wave height, the three components of the perturbation velocity, and the dynamic pressure. Asymptotic expansions are presented for the 'free' or propagating parts of the flow quantities as they would appear far downstream.

Centerplane distributions of the flow disturbance singularities are used to model the flow about a symmetric thin ship. From the application of the momentum theorem, general formulae are derived for the total fluid drag on a ship in a viscous flow. These results are then specialized for use with the Oseen equations. The wave resistance formulae are of particular interest because they contain the strengths of the three forcelet distributions as well as the mass source distribution.

A numerical example of a wave resistance calculation is presented in which the four distribution functions are prescribed. The results are compared to known experimental curves. These indicate that significant features in the character of ship wave resistance can be qualitatively described by including the strengths of local viscous forces acting on the body.

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