Complex Modal Analysis of the Swimming Motion of a Whiting

Abstract

The kinematics of the transverse motion of a swimming fish are analyzed using a complex modal decomposition. Cinematographic images of a swimming whiting (Gadus merlangus) were obtained from the work of Sir James Gray (1933, “Studies in Animal Locomotion III. The Propulsive Mechanism of the Whiting (Gadus merlangus),” J. Exp. Biol., 10, pp. 391–402). The position of the midline for each image was determined and used to produce planar positions of virtual markers distributed along the midline of the fish. Transverse deflections of each virtual marker were then used for the complex orthogonal decomposition of modes. This method was applied to images of a whiting before and after amputation in a Newtonian frame of reference and an “anterior-body-fixed” frame as well. The fish motions were well represented by a single complex mode, which was then used as a modal filter. The extracted mode and modal coordinate were used to estimate the frequency, wavelength, and wave speed. The amputated fish was compared to the nonamputated fish, and the amount of traveling in the respective waveforms was quantified. The dominant complex mode shape and the estimated modal frequency were employed to reanimate the fish motion.