Fish Pectoral Fin Hydrodynamics; Part III: Low Dimensional Models via POD Analysis

The highly complex kinematics of the pectoral fin and the resulting hydrodynamics does not lend itself easily to analysis based on simple notions of pitching/heaving/paddling kinematics or lift/drag based propulsive mechanisms. A more inventive approach is needed to dissect the fin gait and gain insight into the hydrodynamic performance of the pectoral fin. The focus of the current work is on the hydrodynamics of the pectoral fin of a bluegill sunfish in steady forward motion. The 3D, time-dependent fin kinematics is obtained via a stereo-videographic technique. We employ proper orthogonal decomposition to extract the essential features of the fin gait and then use CFD to examine the hydrodynamics of simplified gaits synthesized from the POD modes. The POD spectrum shows that the first two, three and five POD modes capture 55{\%}, 67{\%}, and 80{\%} of the motion respectively. The first three modes are in particular highly distinct: Mode-1 is a ``cupping'' motion where the fin cups forward as it is abducted; Mode-2 is an ``expansion'' motion where the fin expands to present a larger area during adduction and finally Mode-3 involves a ``spanwise flick'' of the dorsal edge of the fin. Numerical simulation of flow past fin gaits synthesized from these modes lead to insights into the mechanisms of thrust production; these are discussed in detail.