Wave Patterns

Determinants of Faraday Wave-Patterns in Water Samples by Merlin Sheldrake & Rupert Sheldrake

By Merlin Sheldrake & Rupert Sheldrake

Abstract

The standing wave patterns formed on the surface of a vertically oscillated uid enclosed by a container have long been a subject of fascination, and are known as Faraday waves. In circular containers, stable, radially symmetrical Faraday wave-patterns are resonant phenomena, and occur at the vibrational modes where whole numbers of waves t exactly onto the surface of the uid sample. These phenomena make excellent systems for the study of pattern formation and complex nonlinear dynamics. We provide a systematic exploration of variables that affect Faraday wave pattern formation on water in vertical-walled circular containers including amplitude, frequency, volume (or depth), temperature, and atmospheric pressure. In addition, we developed a novel method for the quanti cation of the time taken for patterns to reach full expression following the onset of excitation. The excitation frequency and diameter of the container were the variables that most strongly affected pattern morphology. Amplitude affected the degree to which Faraday wave patterns were expressed but did not affect pattern morphology. Volume (depth) and temperature did not affect overall pattern morphology but in some cases altered the time taken for patterns to form. We discuss our findings in light of René Thom’s catastrophe theory, and the framework of attractors and basins of attraction. We suggest that Faraday wave phenomena represent a convenient and tractable analogue model system for the study of morphogenesis and vibrational modal phenomena in dynamical systems in general, examples of which abound in physical and biological systems.

Introduction

When uid enclosed by a container is subjected to a vertical oscillation, standing waves arise. These standing waves, which depend on re ections from the edge of the container, are known as Faraday waves (Miles and Henderson, 1990). At some frequencies and amplitudes they form highly ordered patterns, while at others they give rise to chaotic dynamics (Simonelli and Gollub, 1989). Faraday wave phenomena make excellent systems for the study of pattern formation because of the high degree of control compared with other pattern-forming systems such as convection or chemical reactions (Huepe et al., 2006), and the great richness and variety of pat- terns that are possible (Topaz et al., 2004; Rajchenbach and Clamond, 2015). Thus, complex nonlinear phenomena can be explored using a relatively simple experimental device.
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