Multiple leading edge vortices of unexpected strength in freely flying hawkmoth

Abstract

The Leading Edge Vortex (LEV) is a universal mechanism enhancing lift in flying organisms. LEVs, generally illustrated as a single vortex attached to the wing throughout the downstroke, have not been studied quantitatively in freely flying insects. Previous findings are either qualitative or from flappers and tethered insects. We measure the flow above the wing of freely flying hawkmoths and find multiple simultaneous LEVs of varying strength and structure along the wingspan. At the inner wing there is a single, attached LEV, while at mid wing there are multiple LEVs, and towards the wingtip flow separates. At mid wing the LEV circulation is ~40% higher than in the wake, implying that the circulation unrelated to the LEV may reduce lift. The strong and complex LEV suggests relatively high flight power in hawmoths. The variable LEV structure may result in variable force production, influencing flight control in the animals.

Figure 1. Velocity fields (U_∞ subtracted), showing every third vector, and vorticity field, around the inner (a) (Moth 9), mid (b) (Moth 2) and distal (c) (Moth 2) part of a wing of a M. stellatarum flying at 2 m/s.

Flight direction is to the right. a and b are at mid downstroke, and c at beginning of downstroke. Velocity is scaled according to the reference vector and vorticity according to the colorbar below the graphs. The velocity and vorticity fields are superimposed on the original images showing the wing profile as a gray area in the masked region (white). Cartoons to the right show the position of the laser along the span. The gray area shows the region where the structure and strength of the LEV changes along the wing length.

Figure 2. A zoomed in view of Fig. 1b showing the streamlines on top of the swirling strength (a measure of rotation) colorcoded according to the colorbar below.

Free-stream flow not subtracted. The swirling strength indicates two distinct LEVs separated by areas of zero swirl.

Figure 3. Velocity and vorticity plots of the LEV structure at mid wing at mid downstroke at three additional wingbeats from the same flight sequence as Fig. 1b of Moth 2 showing the diversity of the flow structure.

(a–c) show every second vector (free stream subtracted), scaled according to the vector below, on top of the vorticity, scaled according to the upper scale of the colorbar below the figure. (d–f) show the velocity, including the free stream flow, on top of the swirl strength scaled according to the lower scale of the colorbar below (zero swirl). Data from additional individuals and from further inwards on the wing are available in the Supplementary Figs. S1–S6.

Figure 4. Circulation normalized by the local speed and chord of the LEV (closed) and TEV (open) along the length of the wing (0 at base, 1 at tip) at 1 m/s (a) and 2 m/s (c) flight speed.

Γ_LEV/Γ_TEV along the length of the wing at 1 m/s (b) and 2 m/s (d) flight speed. A ratio above one suggests that the LEV is stronger than the circulation found in the wake. The gray area indicates the location along the wing where we find an increase in Γ_LEV and Γ_LEV/Γ_TEV. Values are means ± 2*SEM. Colors are beginning of downstroke (blue), mid downstroke (red) and end of downstroke (green).