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 (Journal of Experimental Biology, 1933). 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 used for the complex orthogonal decomposition of modes. This method was applied to a normal whiting and an amputated whiting, both of Gray’s paper. The fish motions were well represented by a single complex mode, which was used as a modal filter. The modal coordinate was also extracted. The mode and modal coordinate were used to estimate the frequency, wavelength, and wave speed. The amputated fish was compared to the non-amputated fish, and the different amount of traveling in the respective waveforms was quantified.

Propulsion at low Reynolds numbers by multiple traveling waves

“…A vector field of the mean active power flow per unit area is a measure for the magnitude and direction of the mechanical energy flowing in a structure due to traveling waves. 22 A mathematical approach exploiting proper orthogonal decomposition based identification of propagating vibrations was proposed in Feeny 23 and Feeny and Feeny 24 and demonstrated for simulated vibration patterns. But, the abovementioned approaches do not provide the required information for the present case as will be shown below.…”