Rankine-type cylinders having zero wave resistance in infinitely deep flows

Abstract

We prove the existence of a family of immersed obstacles that have zero wave resistance in the context of the 2D Neumann–Kelvin problem. We first build a waveless potential by superposing a source and a sink in a uniform flow for an appropriate choice of parameters. The obstacle is obtained by a combination of streamlines of the waveless potential. Numerical simulations show that the construction is valid for a large set of parameters.

Continuity with respect to the speed for optimal ship forms based on Michell's formula

“…325-326] (cf. also [16]). The model here is more complex regarding the geometry, so that the length Froude number F r L is not exactly constant.…”

“…Continuity of the optimal hull with respect to the parameters. In this section, we show that "the" solution u of problem (P + D ) depends continuously (up to uniqueness) on the parameters (F r, C F ) where F r is the Froude number (20) and C F is the viscous drag coefficient defined in (16). The dependence on F r (i.e.…”

“…This allows us to define the nondimensional version of the problem and to introduce the Froude number. In the definition of the total resistance (16), we also consider the viscous drag coefficient as an independent parameter.…”