Abstract:
Extensible membranes are soft materials that undergo significant stretching in a fluid flow. Examples include textile fabric, rubber, or the skin of swimming and flying animals. We study rectangular membranes with deflections that have significant spanwise nonuniformity when immersed in a 3-D inviscid fluid flow. We determine how these spanwise variations in membrane deflection depend on various material and geometric parameters. We use both a spanwise-symmetric and spanwise-asymmetric initial perturbation and find that the motions differ for long times but eventually reach the same steady state in most cases. At large times, we find interesting spanwise symmetric and asymmetric oscillations, with the latter more common. With the membrane's side-edges free, traveling waves along the span frequently exist but oscillations in the form of “side-to-side” and other standing wave motions along the span, also occur.
Biography:
Christiana Mavroyiakoumou received a BSc in Mathematics at Imperial College London. She then attended the University of Oxford where she completed her MSc in Mathematical Modeling and Scientific Computing and worked with Ian Griffiths and Peter Howell on modeling the manufacture of microstructured optical fibers. She received her PhD in 2022 from the University of Michigan where she worked with Silas Alben on the dynamics of extensible membranes in inviscid flow. She is now a Courant Instructor at the Courant Institute (NYU) working in the Applied Math Lab, primarily with Leif Ristroph and Jun Zhang.
Seminar by the NYU-ECNU Institute of Physics at NYU Shanghai