Mathematical modeling and simulation of aquatic and aerial animal locomotion T.Y. Hou a, * ,1 , V.G. Stredie a , T.Y. Wu b a Applied and Computational Mathematics, Caltech, Pasadena, CA 91125, United States b Division of Engineering and Applied Science, Caltech, Pasadena, CA 91125, United States Received 22 January 2006; received in revised form 13 December 2006; accepted 10 February 2007 Available online 24 February 2007 Abstract In this paper, we investigate the locomotion of fish and birds by applying a new unsteady, flexible wing theory that takes into account the strong nonlinear dynamics semi-analytically. We also make extensive comparative study between the new approach and the modified vortex blob method inspired from Chorin’s and Krasny’s work. We first implement the mod- ified vortex blob method for two examples and then discuss the numerical implementation of the nonlinear analytical mathematical model of Wu. We will demonstrate that Wu’s method can capture the nonlinear effects very well by applying it to some specific cases and by comparing with the experiments available. In particular, we apply Wu’s method to analyze Wagner’s result for a wing abruptly undergoing an increase in incidence angle. Moreover, we study the vorticity generated by a wing in heaving, pitching and bending motion. In both cases, we show that the new method can accurately represent the vortex structure behind a flying wing and its influence on the bound vortex sheet on the wing. Ó 2007 Elsevier Inc. All rights reserved. PACS: 47.85.Gj; 47.32.C; 47.15.Km Keywords: Aerodynamics; Vortex dynamics; Potential flows 1. Introduction The subject of animal locomotion has fascinated human minds for generations. Many experts have made important contributions to the theory of animal locomotion. Starting with the pioneering works of Sir James Gray (the Head of Cambridge University’s Zoology Department, 1937–1961), the theory of animal locomo- tion stimulated Sir G.I. Taylor to make two important investigations, one involving the swimming of snakes and eels, while the other initiated hydrodynamic studies on ciliary propulsion. However, the main contribu- tions to this field came later from Sir James Lighthill and Prof. Theodore Wu. Lighthill laid a theoretical 0021-9991/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2007.02.015 * Corresponding author. E-mail addresses: hou@acm.caltech.edu (T.Y. Hou), gaby@acm.caltech.edu (V.G. Stredie), tywu@its.caltech.edu (T.Y. Wu). 1 The research of T.Y. Hou was in part supported by a NSF FRG Grant No. DMS-0353838 and a NSF ITR Grant No. ACI-0204932. Journal of Computational Physics 225 (2007) 1603–1631 www.elsevier.com/locate/jcp