Journal of Fluid Mechanics


Low-dimensional models and performance scaling of a highly deformable fish pectoral fin

M. BOZKURTTASa1 p1, R. MITTALa1 c1, H. DONGa1 p2, G. V. LAUDERa2 and P. MADDENa2

a1 Department of Mechanical and Aerospace Engineering, The George Washington University, 801 22nd St NW, Washington DC 20052, USA

a2 Organismic and Evolutionary Biology, 26 Oxford St, Harvard University, Cambridge, MA 02138, USA


The hydrodynamics of a highly deformable fish pectoral fin used by a bluegill sunfish (Lepomis macrochirus) during steady forward swimming are examined in detail. Low-dimensional models of the fin gait based on proper orthogonal decomposition (POD) are developed, and these are subjected to analysis using an incompressible Navier–Stokes flow solver. The approach adopted here is primarily motivated by the quest to develop insights into the fin function and associated hydrodynamics, which are specifically useful for the design of a biomimetic, pectoral fin propulsor. The POD analysis shows that the complex kinematics of the pectoral fin can be described by a few (<5) POD modes and that the first three POD modes are highly distinct. The significance of these modes for thrust production is examined by synthesizing a sequence of fin gaits from these modes and simulating the flow associated with these gaits. We also conduct a scale study of the pectoral fin in order to understand the effect of the two key non-dimensional parameters, Reynolds number and Strouhal number, on the propulsive performance. The implications of the POD analysis and performance scaling on the design of a robotic pectoral fin are discussed.

(Received July 29 2008)

(Revised March 11 2009)


c1 Email address for correspondence:

p1 Present address: Exa Corporation, 55 Network Drive, Burlington, MA 01803, USA

p2 Present address: Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA