On reduced models for gravity waves generated by moving bodies

Abstract

In 1983, 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 (Proceedings of the 14th Symposium on Naval Hydrodynamics, 1983, 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, 30 years later, we will revive Tulin’s observations, and explain how an asymptotically consistent framework allows us to address these concerns. Most notably, we demonstrate, 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 a new and powerful methodology for the study of geometrically nonlinear wave–body interactions.