Bumblebee Flight in Heavy Turbulence

High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments, or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.

Figure 1

Bumblebee in turbulent flow. (a) Visualization of the prescribed wingbeat, where $T$ is period time. (b)–(d) Time evolution of horizontal (b) and vertical (c) force, and aerodynamic power (d) under laminar, moderately turbulent ($\mathrm{Tu}=0.33$) and highly turbulent ($\mathrm{Tu}=0.99$) conditions. Circular markers represent cycle-averaged values. (e)–(f) Flow visualization by means of isosurfaces of normalized vorticity magnitude $\parallel \underset{\_}{\omega }\parallel$. (e) Perspective view for a realization with $\mathrm{Tu}=0.33$. The purple and blue isosurfaces visualize stronger and weaker vortices, respectively, and weaker vortices are shown only for $3.7R\le y\le 4R$. (f) Top view, with the upper half showing flow at elevated turbulent ($\mathrm{Tu}=0.99$), and the lower half at moderate turbulent ($\mathrm{Tu}=0.33$) intensity. Weaker vortices, i.e., smaller values of $\parallel \underset{\_}{\omega }\parallel$, are shown only for $0\le z\le 0.3R$.

Figure 2

Slab averaged turbulence intensity as a function of the axial coordinate, with the insect drawn to scale for orientation. The black line is the laminar case. The gray shaded areas mark regions where the inflow and outflow is imposed.

Figure 3

Top: Isosurface of normalized absolute vorticity, $\parallel \underset{\_}{\omega }\parallel =100$, in the vicinity of the right wing at $t/T=0.3$. Snapshots of instantaneous vorticity distribution during laminar and turbulent inflow are shown on the left. Phase- and ensemble-averaged vorticity from 16 and 108 wingbeats and at $\mathrm{Tu}=0.17$ and $\mathrm{Tu}=0.99$, respectively, is shown on the right. Bottom: averaged $\parallel \underset{\_}{\omega }\parallel =50$ isolines at midspan for all values of Tu. The leading edge vortex persists on average even under the strongest inflow perturbations.

Figure 4

rms value of the final roll angular velocity ${\mathrm{\Omega }}_{\text{roll}}$ versus the inflow turbulence intensity, calculated over all flow realizations. The colors correspond to different response delay times $\tau$. The gray shaded area represents the limit of sensor saturation, estimated from the behavioral measurements available for honeybees [4] and fruit flies [27].