The mechanical scaling of coasting in zebrafish (Danio rerio)

Many fish species span two or three orders of magnitude in length during the growth from larvae to adults, and this change may have dramatic consequences for locomotor performance. We measured how the performance of coasting changes over the life history of zebrafish (Danio rerio) and examined the scaling of mechanics underlying this change. Adult zebrafish coast disproportionately further and faster and maintain their speed for a longer duration than do larvae and juveniles. Measurements of drag on tethered dead fish suggest that adult fish operate in an inertial regime by coasting at relatively high Reynolds numbers (Re > 1000), and in vivo drag measurements showed adults to operate with a drag coefficient (Cinert approximately 0.024) that was consistent with previously published estimates. However, drag scaled differently at lower Re values than those assumed in previous studies. We found a viscous regime at Re < 300, which corresponds to the routine coasting of larvae and juveniles. Despite these changes in hydrodynamics over growth, a mathematical model of coasting mechanics suggests that the disproportionately longer coasting of adults is caused primarily by their large body mass and high speed at the beginning of coasting. We therefore propose that changes in coasting performance with growth are dictated primarily by the scaling of momentum rather than resulting from hydrodynamic changes. These results provide an opportunity for new interpretations of function in the growth and evolution of fish.