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The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(1):85-106; doi:10.1093/qjmam/54.1.85
© 2001 by Oxford University Press
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The forward motion of an unsymmetric surface-piercing cylinder: the solvability of a nonlinear problem in the supercritical case

Carlo D. Pagani1 and Dario Pierotti1

( 1 Dipartimento di Matematica del Politecnico, Piazza L. da Vinci, , 32, 20133, Milano, Italy )

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.

Received 30 March, 1999. Revised 8 January, 2000.


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