Research at the Experimental Hydrodynamics Laboratory

Impulse generated during unsteady maneuvering of swimming fish B. P. Epps & A. H. Techet Summary The relationship between the maneuvering kinematics of a Giant Danio (Danio aequipinnatus) and the resulting vortical wake were investigated for a rapid, ‘C’-start maneuver using fully time-resolved (500 Hz) particle image velocimetry (PIV). PIV illuminates the two distinct vortices formed during the turn. The fish body rotation is facilitated by the initial, or ‘‘maneuvering’’, vortex formation, and the final fish velocity is augmented by the strength of the second, ‘‘propulsive’’ vortex. Results confirm that the axisymmetric vortex ring model is reasonable to use in calculating the hydrodynamic impulse acting on the fish. The total linear momentum change of the fish from its initial swimming trajectory to its final swimming trajectory is balanced by the vector sum of the impulses of both vortex rings. The timing of vortex formation is uniquely synchronized with the fish motion, and the choreography of the maneuver is addressed in the context of the resulting hydrodynamic forces. Taking into account solely the linear momentum of the fish into and out of the turn, it has been shown that the net impulse of the two vortex rings is close to the total change in momentum of the fish. In this particular maneuver, the initial velocity is quite low, and thus the fish body is not able to use its initial forward momentum to significantly aid in the turn. Were the fish moving at a sufficiently high initial velocity, such that slight changes in body orientation away from the forward motion could generate a lifting force on either the anterior or posterior sections of the body and thus a turning moment, the need for this ‘‘maneuvering’’ vortex might be lessened. The transitions between maneuvering stages become important when only considering one of the vortices or certain segments of the turn. Here, the question arises as to which parts of the turn should be considered when determining scaling laws: should the entire turn be considered (using both the maneuvering and propulsive vortex), or only the formation of the final vortex ring? Triantafyllou et al. (2005) suggests that a scaling law can be determined using the time to develop a full vortex ring as the principal parameter controlling rapid maneuvering and fast-starting, in a similar fashion to the Strouhal law for steadily flapping foils and the formation number in impulsive started jets. In order to determine scaling laws for maneuvering fish, considering the maneuver from stage one through stage three taking into account only the linear momentum of the fish’s body at the beginning and end of the turn, there will be cases where both the first ‘‘maneuvering’’ vortex jet as well as the second ‘‘propulsive’’ vortex jet may need to be considered in order to balance the total change in momentum of the fish. There may also be cases where the first vortex is negligible or non-existent due to the initial conditions of the turn. References Triantafyllou, M. S., F. S. Hover, A. H. Techet, and D. K. P. Yue “Review of Scaling Laws in Aquatic Locomotion and Fish-like Swimming,” Applied Mechanics Review, 58(4):226-237, July 2005. Epps, B. P. and A. H. Techet, “Impulse Forces Generated During Unsteady Maneuvering of Swimming Fish,” Experiments in Fluids, 43(5), 691-700, November 2007. [doi:10.1007/s00348-007-0401-4] ** Publications.htmlshapeimage_1_link_0

Fish Swimming & Maneuvering

Live Fish Maneuvering     Biomimetic Propulsion     Salp Propulsion     Prey Capture

Sequence of six instantaneous vorticity fields determined using PIV for a 105 degree C-start. Every 15th frame is presented (dt =  0.030s). Anticlockwise (positive) vorticity is shown in red and clockwise (negative) in blue.  The four vortices shed during the maneuver are labeled Γ1A, Γ1B, Γ2A, and Γ2B.

Giant Danio

(Danio aequipinnatus)

Dye visualization of a 3:1 aspect ratio foil that has impulsively flapped once to the right on the page and back to the position shown in a continuous motion, as viewed from behind the trailing edge, reveals a directional vortex ring formation similar to that formed by a maneuvering fish.