Hydrodynamic Convection in a Two-Dimensional Couette Cell

A two-dimensional Couette cell is formed by drawing a soap film over the annular region between an inner rotating disk and a fixed circular hole. When the inner disk is concentric, a smooth laminar flow is observed for all rotation rates. However, when the inner disk is eccentric, the film thickness $H(x,y,t)$ fluctuates in space and time. Spectral analysis of $H(x,y,t)$ reveals a power-law dependence on spatial scales that is consistent with Batchelor's calculation for turbulent dispersion of a passive scalar.