Doubly Periodic Circular Couette Flow: Experiments Compared with Predictions from Dynamics and Symmetry

Our experiments on doubly periodic wavy vortex flow show that the second spectral frequency corresponds to a modulation of the $m$ azimuthal traveling waves. We use spacetime symmetry to classify the possible modulation patterns and to predict a basic period $\tau$ such that in the frame rotating with the angular velocity of the waves the wave pattern at times $t$ and $t+\tau$ will differ only by a rotation through an integral multiple of $\frac{2\pi }{m}$. Measurements on the twelve observed modulation patterns agree with this prediction.