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An Isaac Newton Institute Workshop

Pattern Formation in Fluid Mechanics

Spatially periodic pattern selection in the Faraday problem

Author: Skeldon, A (University of Surrey )

Abstract

A wide variety of different patterns have been observed in the Faraday wave experiment. In the case of spatially periodic patterns, symmetry and bifurcation theory along with the idea of resonant triad interactions have been used to help explain the underlying mechanisms of pattern selection. Here, we will discuss a weakly nonlinear analysis of the Navier-Stokes equations that enables the calculation of the coefficients in the relevant amplitude equations for spatially periodic patterns. The implications for pattern selection will be discussed and comparisons made with some experimental data.