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- Title
The forward motion of an unsymmetric surface-piercing cylinder: the solvability of a nonlinear problem in the supercritical case.
- Authors
PAGANI, CARLO D.; PIEROTTI, DARIO
- Abstract
We consider the wave-resistance problem for a 'slender' cylinder semisubmerged in a heavy fluid and moving at uniform, supercritical speed in the direction orthogonal to its generators. By a hodograph transformation, the problem (originally set up in a domain with a free boundary) reduces to the determination of a function, holomorphic in a fixed domain, satisfying some nonlinear boundary conditions depending on two (unknown) parameters. The problem in the hodograph plane is solved via the implicit function theorem; then, the two parameters are fixed by the requirement that the free boundary and the cylinder profile (which is assumed convex and reasonably smooth) form a single smooth (C¹) streamline. Furthermore, the free boundary is monotone increasing downstream, monotone increasing upstream and lies under the level of calm water.
- Subjects
WAVE resistance (Hydrodynamics); SUPERCRITICAL fluids; NONLINEAR theories; IMPLICIT functions; MONOTONE operators; HODOGRAPH equations
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2001, Vol 54, Issue 1, p85
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/54.1.85