The flow around the butterfly

The Mathematical Butterfly: Simulations Provide New Insights On Flight | Inside Science

The researchers ran three different simulations of this mathematical butterfly, and found that the insect used the forces from teensy whirlpools in the air created during each flap of its wings to create lift. They noticed that the butterfly's flight was bumpy as it moved through the air, with lots of ups and downs as it pushed itself forward. 
There were some surprises in the tiny flows of air surrounding the butterflies. "The flow around the butterfly is much more turbulent than expected," says Yokoyama.

The researchers surmised that the minute bumpiness of the air causes butterflies' signature flit, and also may help protect them against predators – the more they duck and weave, the harder it is to catch them. The research was published earlier this year in the journal Physics of Fluids

High speed video - Painted Lady butterfly (front) - YouTube

High speed video recorded at 3000 fps.
See www.jhuinsectflight.com for more information on Tiras Lin's research project at Johns Hopkins University.

Mathematical butterflies provide insight into how insects fly

Using data from observations of butterfly flight in wind tunnels, the researchers conducted three different types of simulations with their model that were defined by the position and attitude of the thorax: tethered (where the thorax is fixed), prescribed (where the thorax is programmed to move in an expected manner) and free-flight (where the thorax movement is unrestricted). They found that their mathematical butterfly did -- as predicted -- make use of the tiny, swirling vortices that form in the direction of travel during a downward flap, pushing air down and providing lift. However, they also observed that the flow around the butterfly is much more turbulent than expected. This turbulent flow triggers the complex trajectories characteristic to the flights of butterflies that may be one of the strategies by which the insects avoid predators.

Phys. Fluids (1994-Present) - Physics of Fluids

Naoto Yokoyama, Kei Senda, Makoto Iima, and Norio Hirai
Phys. Fluids 25, 021902 (2013); http://dx.doi.org/10.1063/1.4790882 (24 pages)
Online Publication Date: 21 February 2013