Leading-edge vortex stability in insect wings.

An analytical study is presented to determine if the persistency of the leading-edge vortex in an insect wing can be explained as the balance between vorticity generation at the leading edge and advection plus effects of vorticity stretching and tilting by the flow along the wing span. It is found that a spanwise flow of the required magnitude is produced by the simple rotation of the wing about its root at a constant angle of attack (no supination or pronation), and that the regions where this equilibrium exists in stable form are well localized, independent of the rotation velocity, almost independent of the position along the wing, and weakly dependent on the angle of attack, for angles below approximately equal to 70 degrees. In contrast, extended regions of vorticity are expected for angles of attack above approximately equal to 75 degrees.

Unsteady two-dimensional theory of a flapping wing.

An analytical evaluation of the hydrodynamic force on a single flapping wing is presented, based on the two-dimensional inviscid theory, with the addition of an attached leading-edge vortex. The explicit expression of the force is given and compared with some of the measurements by Dickinson et al. [Science 284, 1954 (1999)] and Sane and Dickinson [J. Expl. Biol. 204, 2607 (2001)] for a fruit fly model wing.

Formulation of subgrid stresses for large-scale fluid equations.

A formulation is presented based on a previously derived self-consistent procedure for obtaining subgrid scale models for complex system of equations. Using linear stability analysis and numerical simulations of the one-dimensional Burgers equation the formulation is shown to be very stable numerically and to reproduce accurately the large-scale flow of a high-resolution, direct simulation. Moreover, the resulting equation has a structure very similar to the viscous Camassa-Holm equation recently introduced in the modeling of turbulent flows.