Waveless ships in the low speed limit: Results for multi-cornered hulls

Abstract

In the low-speed limit, a blunt ship modeled as two-dimensional semi-infinite body with a single corner can never be made waveless. This was the conclusion of the previous part of our work in Trinh et al. (2011), which focused on the Dagan & Tulin (1972) model of ship waves in the low speed limit. In this accompanying paper, we continue our investigations with the study of more general, piecewise-linear, or multi-cornered ships. The low-speed or low-Froude limit, coupled with techniques in exponential asymptotics allows us to derive explicit formulae relating the geometry of the hull to the form of the waves. Configurations with closely spaced corners present a non-trivial extension of the theory, and we present the general methodology for their study. Lastly, numerical computations of the nonlinear ship-wave problem are presented in order to confirm the analytical predictions.

References in corpus (3)

• New gravity-capillary waves at low speeds. Part 1: Linear geometries
• New gravity-capillary waves at low speeds. Part 2: Nonlinear geometries
• Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves

Cited by in corpus (5)

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• Exponential asymptotics and problems with coalescing singularities
• Three-dimensional capillary waves due to a submerged source with small surface tension
• A topological study of gravity waves generated by moving bodies using the method of steepest descents