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

TL;DR

This paper investigates the wave patterns of multi-cornered ships in the low-speed limit, deriving explicit formulas relating hull geometry to wave formation and confirming predictions through numerical simulations.

Contribution

It extends previous work by analyzing more complex hull geometries with multiple corners using exponential asymptotics and numerical methods.

Findings

Multi-cornered ships cannot be made waveless in the low-speed limit.

Derived explicit formulas linking hull geometry to wave patterns.

Numerical results confirm analytical predictions.

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.