Secondary instability mode of a roll pattern and transition to spatiotemporal chaos in the Taylor-Dean system

The secondary instability mode and transition to a weak chaotic regime in a one-dimensional roll pattern have been investigated in the Taylor-Dean system. The spatiotemporal modulation of a roll pattern, called a triplet state in Phys. Rev. Lett. 64, 1729 (1990), is quantitatively characterized using the demodulation technique by the Hilbert transform. A triplet pattern arises from the primary structure by a periodic modulation of the phase both in space and time. The amplitude of the modulation, chosen as an order parameter, has been measured, and it grows as a square root of the reduced control parameter. The correlation length and time of the triplet pattern are maximal near the threshold, and decrease to values comparable to the size and period of a triplet in the chaotic regime. In the chaotic regime, regular oscillations of triplets are observed with a finite frequency, suggesting a phase modulation of the triplet pattern: itself.