Flying Spiders: Simulating and Modeling the Dynamics of Ballooning

Spiders use a type of aerial dispersal called “ballooning” to move from one location to another. In order to balloon, a spider releases a silk dragline from its spinnerets and when the movement of air relative to the dragline generates enough force, the spider takes flight. We have developed and implemented a model for spider ballooning to identify the crucial physical phenomena driving this unique mode of dispersal. Mathematically, the model is described as a fully coupled fluid– structure interaction problem of a flexible dragline moving through a viscous, incompressible fluid. The immersed boundary method has been used to solve this complex multi-scale problem. Specifically, we used an adaptive and distributedmemory parallel implementation of immersed boundary method (IBAMR). Based on the nondimensional numbers characterizing the surrounding flow, we represent the spider as a point mass attached to a massless, flexible dragline. In this paper, we explored three critical stages for ballooning, takeoff, flight, and settling in two The original version of this chapter was revised. An erratum to this chapter can be found at https://doi.org/10.1007/978-3-319-60304-9_13 L. Zhao ( ) Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA e-mail: [email protected] I.N. Panayotova Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA e-mail: [email protected] A. Chuang • K.S. Sheldon Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, USA e-mail: [email protected]; [email protected] L. Bourouiba The Fluid Dynamics of Disease Transmission Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02130, USA e-mail: [email protected] L.A. Miller Departments of Mathematics and Biology, University of North Carolina, Chapel Hill, NC 27599, USA e-mail: [email protected] © The Author(s) and the Association for Women in Mathematics 2017 A.T. Layton, L.A. Miller (eds.), Women in Mathematical Biology, Association for Women in Mathematics Series 8, DOI 10.1007/978-3-319-60304-9_10 179