The hydrodynamics of ribbon-fin propulsion during impulsive motion

Abstract

SUMMARYWeakly electric fish are extraordinarily maneuverable swimmers, able to swim as easily forward as backward and rapidly switch swim direction, among other maneuvers. The primary propulsor of gymnotid electric fish is an elongated ribbon-like anal fin. To understand the mechanical basis of their maneuverability, we examine the hydrodynamics of a non-translating ribbon fin in stationary water using computational fluid dynamics and digital particle image velocimetry (DPIV) of the flow fields around a robotic ribbon fin. Computed forces are compared with drag measurements from towing a cast of the fish and with thrust estimates for measured swim-direction reversals. We idealize the movement of the fin as a traveling sinusoidal wave, and derive scaling relationships for how thrust varies with the wavelength, frequency, amplitude of the traveling wave and fin height. We compare these scaling relationships with prior theoretical work. The primary mechanism of thrust production is the generation of a streamwise central jet and the associated attached vortex rings. Under certain traveling wave regimes, the ribbon fin also generates a heave force, which pushes the body up in the body-fixed frame. In one such regime, we show that as the number of waves along the fin decreases to approximately two-thirds, the heave force surpasses the surge force. This switch from undulatory parallel thrust to oscillatory normal thrust may be important in understanding how the orientation of median fins may vary with fin length and number of waves along them. Our results will be useful for understanding the neural basis of control in the weakly electric knifefish as well as for engineering bio-inspired vehicles with undulatory thrusters. Supplementary material available online at

Aquatic manoeuvering with counter-propagating waves: a novel locomotive strategy

“…There are vortex structures associated with the streamwise central jet, and the tip vortex associated with the bottom edge of the fin, in addition to the vortex generated by the front and back edge of the fin. As can be observed in figure 5d and previously reported by Shirgaonkar et al [6], the streamwise central jet generates vortex ring. For inward counter-propagating waves, these vortex structures are generated from the two oppositely travelling jets and they collide in the middle section of the fin length.…”

“…The The travelling waves on the ribbon fin had a frequency, f, of 3 Hz, a wavelength, l, of 4.35 cm (for two full wavelengths along the fin) and a maximum angular deflection, u max , of 408. Those parameters are similar to those we observed in our video observations of black ghosts, and to prior studies of knifefish fin kinematics and hydrodynamics [2,6]. The fluid domain size for the computational simulation was 30 Â 5 Â 10 cm in the x, y and z directions, respectively.…”

“…This upward force prevents the fish from sinking, given that the fish is slightly more dense than the water, and is used to generate upward manoeuvers by the fish during normal locomotion. Our previous work on ribbon fin propulsion and black ghost simulations shows that the ribbon fin generates a streamwise central jet with associated vortex rings [6,13]. In this case, the inward counter-propagating wave along the ribbon fin generates two opposite fluid jets that collide at an angle.…”

“…The robot is shown in figures 1c and 4a -c. The fin length and height are 32.6 cm and 3.4 cm, respectively, to approximate the aspect ratio of the ghost knifefish. The fin aspect ratio has significant impact on the hydrodynamics [6]. The body of the robot is a 40 cm long cylinder with a diameter of 6.0 cm and hemispherical end caps at both ends (figure 4a).…”

“…First, the fish can sense objects in all directions around the body [4] through an active sensing system based on self-generated discharges of electricity. Second, the fish propels itself in a manner that facilitates rapid movement in many directions, and rapid changes in direction of movement, such as sub-second reversals in swimming direction [5,6]. Propulsion is accomplished by means of undulating an elongated fin on the belly that runs nearly the entire length of the fish.…”