Self-similar bending in a flow: The axisymmetric case

We study how sheets roll up into conical configurations when exposed to fluid flows using simulations and analysis. The simulations couple the bending of thin sheets to axisymmetric flows with vortex shedding. We find quasisteady flows with vortex ring wakes in which the radii of the rings scale with the radii of the cone bases. The cone angles scale with the dimensionless flow speed raised to the power -1/3. The drag coefficients for the cones scale with flow speed to the power -1. We find good agreement with the previously published experimental results. The scalings we have found result from a self-similar behavior of the flow at the outer edges of the cones, with length scales set by the radii of the vortex rings in the wakes. (c) 2010 American Institute of Physics. [doi:10.1063/1.3467494]