Suspension of a point-mass-loaded filament in non-uniform flows: Passive dynamics of a ballooning spider

Abstract

Spiders utilize their fine silk fibers for their aerial dispersal, known as ballooning. With this method, spiders can disperse hundreds of kilometers, reaching as high as 4.5 km. However, the passive dynamics of a ballooning model (a highly flexible filament and a spider body at the end of it) are not well understood. Here, we introduce a bead–spring model that takes into account the anisotropic drag of a fiber to investigate the passive dynamics by the various non-uniform flows: (i) a shear flow, (ii) a periodic vortex flow field, and (iii) a homogeneous turbulent flow. For the analysis of the wide range of parameters, we defined a dimensionless parameter, which is called “a ballooning number.” The ballooning number is defined as the ratio of Stokes’ fluid-dynamic force on a fiber by the non-uniform flow field to the gravitational force of a body. Our simulations show that the present model in a homogeneous turbulent flow exhibits the biased characteristic of slow settling with increasing turbulence. Upon investigating this phenomenon for a shear flows, it was found that the drag anisotropy of the filament structure is the main cause of the slow settling. Particularly, the cause of slow settling speed lies not only in the deformed geometrical shape but also in its generation of fluid-dynamic force in a non-uniform flow. Additionally, we found that the ballooning structure could become trapped in a vortex flow. These results help deepen our understanding of the passive dynamics of spiders ballooning in the atmospheric boundary layer.