Experimental observation of thermoacoustic turbulence and universal properties at the quasiperiodic transition to chaos

Publisher Website
Google Scholar
Abstract
In this paper, we report experimental results of strongly nonlinear phenomena observed in the thermoacoustic system which we have termed ‘‘Taconis oscillation’’ [W. H. Keesom, Helium (Elsevier, New York, 1942), p. 174; C. F. Squire, Low Temperature Physics (McGraw-Hill, New York, 1953), p. 23; K. W. Taconis, J. J. M. Beenaker, A. O. C. Nier, and L. T. Aldrich, Physica 15, 733 (1949) (see footnote on p. 738)]. The system exhibits quasiperiodic and chaotic dynamics in spontaneous states and states forced by external oscillation. In spontaneous states, we observed that three clearly defined stable modes with incommensurate frequencies can be excited simultaneously, and that competition between them leads to chaotic motion near the overlapping regions of the stability curves. Experimental time series of chaotic oscillations are analyzed by theories of nonlinear dynamical systems, and the dimension and entropy of chaotic attractors are determined. In forced thermoacoustic states, a spontaneous oscillation is periodically perturbed by a mechanical force with amplitude and frequency externally controlled. Nonlinear coupling between thermally and mechanically driven oscillators leads to quasiperiodicities, frequency-locking, and the onset of chaos within a certain bandwidth. The global and local universal properties for the quasiperiodic transition to chaos are experimentally studied and compared with circle map universality.