A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.
Original languageEnglish
Article number20150833
Number of pages20
JournalProceedings of the Royal Society A
Volume472
Early online date1 Jul 2016
DOIs
Publication statusPublished - 13 Jul 2016

Fingerprint Dive into the research topics of 'A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents'. Together they form a unique fingerprint.

Cite this