Spontaneous generation of spiral waves by a hydrodynamic instability

¹  Laboratoire de Physique Statistique, UMR 8550 CNRS, École Normale Supérieure - 24, rue Lhomond, 75231 Paris Cedex 05, France
²  Institute for Advanced Studies in Basic Sciences (IASBS) - Zanjan 45195-1159, Iran
³  Institut de Physique du Globe de Paris and Université de Paris-7, CNRS, Tour 14 - 2, place Jussieu, 75005 Paris, France
⁴  Van der Waals-Zeeman Institute, University of Amsterdam - Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

Received: 25 April 2007
Accepted: 4 December 2007

Abstract

The coiling of a thin filament of viscous fluid falling onto a surface is a common and easily reproducible hydrodynamic instability. Here we report for the first time that this instability can generate regular spiral patterns, in which air bubbles are trapped in the coil and then advected horizontally by the fluid spreading on the surface. We present a simple model that explains how these beautiful patterns are formed, and how the number of spiral branches and their curvature depends on the coiling frequency, the frequency of rotation of the coiling center, the total flow rate, and the thickness of the spreading fluid film.