"Catenaries in Viscous Fluid"

James Hanna, Department of Biomedical Engineering and Mechanics, Virginia Tech

This talk is about certain dynamical equilibria of curves related to towed cables, sedimenting filaments, and other marine, microfluidic, or industrial structures.  I will present analytical results detailing the configurations of a translating and axially moving string subjected to a uniform body force and local, linear, anisotropic drag forces.  Generically, these configurations comprise a five-parameter family of planar shapes determined by the ratio of tangential (axial) and normal drag coefficients, the angle between the translational velocity and the body force, the relative magnitudes of translational and axial drag forces with respect to the body force, and a scaling parameter.  This five-parameter family of shapes is, in fact, a degenerate six-parameter family of equilibria in which inertial forces rescale the tension in the string without affecting its shape.  Each configuration is represented by a first order dynamical system for the tangential angle of the body, which can be classified by the presence and location of fixed points and poles in the corresponding phase portrait.  I will also discuss the behavior of the tension in the string, which can display qualitatively different behavior even between similar configurations.  All of this information will be conveyed through colorful cuts and projections of the parameter space.

James Hanna joined the department of Engineering Science and Mechanics (now merged into the new department of Biomedical Engineering and Mechanics) at Virginia Tech as an assistant professor in 2013, after a few years doing physics at UMass Amherst, and prior stints in fluids and materials.  His interests span theoretical and experimental classical mechanics.  He is currently thinking about nonlinear oscillators, as well as thin, flexible bodies and their dynamical equilibria, discontinuities, and defects.

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