The significance of intermediate Reynolds number flows to biological form and development

Intermediate Reynolds number (Re) flows set physical limits to the kinds of organisms observed in nature. For example, such flows determine a lower size limit for flapping flight and undulatory swimming. A fish that uses pectoral fin locomotion could not swim at very low Reynolds numbers. Such a fish would move forward during the downstroke but slide back into its original position during the upstroke. Intermediate-Re flows also define a lower size limit to peristaltic and chambered pumps. For example, a valve and chambered heart could not pump fluid at very low Reynolds numbers. Recent studies also suggest that intermediate-Re flows play a crucial role in the regulation of chamber morphogenesis in developing embryonic hearts. In fact, research on kidney, lung, and heart development suggests that fluid flow is a key regulator of organogenesis.

In this presentation, I will discuss how fluid dynamic transitions determine a lower size limit for insect flight. I explored flight aerodynamics over a range of Re using the immersed boundary method to numerically solve the two-dimensional Navier-Stokes equations with moving, flexible boundaries. For the smallest flying insects, my work has shown that flight becomes very inefficient as relative lift forces decrease and relative drag forces increase with decreasing Re. This effect is related to the behavior of the vortex wake behind the wing. At lower Re, neither leading nor trailing edge vorticity separates from the wings until stroke reversal. Tiny insects use the Weis-Fogh mechanism (also known as clap and fling) to augment the lift forces generated during flight. My work has shown that there is, however, a large aerodynamic cost for this behavior. At lower Re, very large drag forces are required to perform the clap and fling. This negative effect can be reduced with wing flexibility and wing bristles.