When vortices stick: an aerodynamic transition in tiny insect flight

Abstract

We have used computational fluid dynamics to study changes in lift generation and vortex dynamics for Reynolds numbers (Re) between 8 and 128. The immersed boundary method was used to model a two-dimensional wing through one stroke cycle. We calculated lift and drag coefficients as a function of time and related changes in lift to the shedding or attachment of the leading and trailing edge vortices. We find that the fluid dynamics around the wing fall into two distinct patterns. For Re> or =64, leading and trailing edge vortices are alternately shed behind the wing, forming the von Karman vortex street. For Re< or =32, the leading and trailing edge vortices remain attached to the wing during each 'half stroke'. In three-dimensional studies, large lift forces are produced by 'vortical asymmetry' when the leading edge vortex remains attached to the wing for the duration of each half stroke and the trailing edge vortex is shed. Our two-dimensional study suggests that this asymmetry is lost for Re below some critical value (between 32 and 64), resulting in lower lift forces. We suggest that this transition in fluid dynamics is significant for lift generation in tiny insects.