On reduced models for gravity waves generated by moving bodies

TL;DR

This paper revisits Tulin's 1982 reduced model for gravity waves generated by moving bodies, using asymptotic methods to clarify wave regimes and improve understanding of nonlinear wave-body interactions.

Contribution

It revives and extends Tulin's framework with asymptotic analysis, addressing previous unresolved issues about wave regimes and low-speed applicability.

Findings

Relation of free-surface wave production to integration contours

Visual and intuitive method for nonlinear wave-body interaction analysis

Clarification of weak and strong wave-making regimes

Abstract

In 1982, Marshall P. Tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form [Proc. 14th Symp. on Naval Hydrodynamics, 1982, pp.19-51]. Several new and puzzling issues were highlighted by Tulin, notably the existence of weak and strong wave-making regimes, and the paradoxical fact that the theory seemed to be applicable to flows at low speeds, "but not too low speeds". These important issues were left unanswered, and despite the novelty of the ideas, Tulin's report fell into relative obscurity. Now thirty years later, we will revive Tulin's observations, and explain how an asymptotically consistent framework allows us to address these concerns. Most notably, we will explain, using the asymptotic method of steepest descents, how the production of free-surface waves can be related to the arrangement of integration contours connected to the shape of the moving body. This approach provides an intuitive and visual procedure for studying nonlinear wave-body interactions.