Whirling skirts and rotating cones

TL;DR

This paper models the complex patterns on spinning skirts using a minimal, symmetry-based approach, revealing the importance of Coriolis forces and providing solutions that resemble observed skirt patterns.

Contribution

It introduces a novel minimal model capturing skirt patterns through traveling waves on a rotating conical sheet, emphasizing the role of Coriolis effects and topological quantization.

Findings

Coriolis forces are crucial for skirt-like solutions.

Solutions with three-fold symmetry resemble observed patterns.

The model reduces dynamics to a particle in a potential, enabling analysis.

Abstract

Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a three-parameter family of potentials. One parameter is associated with the stress in the sheet, aNoether is the current associated with rotational invariance, and the third is a Rossby number which indicates the relative strength of Coriolis forces. Solutions are quantized by enforcing a topology appropriate to a skirt and a particular choice of dihedral symmetry. A perturbative analysis of nearly axisymmetric cones shows that Coriolis effects are essential in establishing skirt-like solutions. Fully non-linear solutions with three-fold symmetry are presented which bear a suggestive resemblance to the observed patterns.