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Updated: May 18, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Propulsive performance of a body with a traveling-wave surface
Fang-Bao Tian1, Xi-Yun Lu, Haoxiang Luo
1Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Place, Nashville, TN 37235-1592, USA. fangbao.tian@vanderbilt.edu
Abstract:
A body with a traveling-wave surface (TWS) is investigated by solving the incompressible Navier-Stokes equation numerically to understand the mechanisms of a novel propulsive strategy. In this study, a virtual model of a foil with a flexible surface which performs a traveling-wave movement is used as a free swimming body. Based on the simulations by varying the traveling-wave Reynolds number and the amplitude and wave number of the TWS, some propulsive properties including the forward speed, the swimming efficiency, and the flow field are analyzed in detail. It is found that the mean forward velocity increases with the traveling-wave Reynolds number, the amplitude, and the wave number of the TWS. A weak wake behind the free swimming body is identified and the propulsive mechanisms are discussed. Moreover, the TWS is a "quiet" propulsive approach, which is an advantage when preying. The results obtained in this study provide a novel propulsion concept, which may also lead to an important design capability for underwater vehicles.
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