Suspension of a Point-Mass-Loaded Filament in Non-Uniform Flows: Passive Dynamics of a Ballooning Spider

Abstract

AbstractSpiders utilize their fine silk fibres for their aerial dispersal, known as ballooning. With this method, spiders can disperse hundreds of kilometres, 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. The previous study (Rouse model: without taking into account anisotropic drag of a fibre) suggested that the flexible and extendible fibres reduce the settling speed of the ballooning model in homogeneous turbulence. However, the exact cause of the reduction of the settling speed is not explained and the assumed isotropic drag of a fibre is not realistic in the low Reynolds number flow. Here we introduce a bead-spring model that takes into account the anisotropic drag of a fibre to investigate the passive behaviour of the ballooning model in the various non-uniform flows (a shear flow, a periodic vortex flow field and 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 means the ratio of Stokes’ fluid-dynamic force on a fibre by the non-uniform flow field to the gravitational force of a body at the end of the fibre. Our simulation shows that the settling speed of the present model in the homogeneous turbulent flows shows the biased characters of slow settling as the influence of the turbulent flow increases. The causes of this slow settling are investigated by simulating it in a wide range of shear flows. We revealed that the cause of this is the drag anisotropy of the filament structure (spider silk). In more detail, the cause of reduced settling speed lies not only in the deformed geometrical shape of the ballooning silk but also in its generation of fluid-dynamic force in a non-uniform flow (shear flow). Additionally, we found that the ballooning structure could become trapped in a vortex flow. This seemed to be the second reason why the ballooning structure settles slowly in the homogeneous turbulent flow. These results can help deepen our understanding of the passive dynamics of spiders ballooning in the atmospheric boundary layer.