title: A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents.
abstract: The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel.
authors: Oxford Centre for Industrial and Applied Mathematics , Mathematical Institute, University of Oxford , Oxford OX2 6GG, UK.
authors: Philippe H
authors: 0000-0003-3227-1844
authors: PH
authors: Trinh
keywords: Stokes phenomenon; exponential asymptotics; steepest descent; surface gravity waves; wave/free-surface flows; wave–structure interactions