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 Taylo r-Dean system. The spatiotemporal modulation of a roll pattern, called a triplet state in Phys. Rev. Lett. 64, 1729 (1990), is quantitativel y characterized using the demodulation technique by the Hilbert transf orm. 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 gr ows 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 triple t in the chaotic regime. In the chaotic regime, regular oscillations o f triplets are observed with a finite frequency, suggesting a phase mo dulation of the triplet pattern: itself.