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

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.We present experimental results for universal scaling properties at the onset of chaos in order to examine the applicability of the map to certain aspects of thermoacoustic systems such as (1) the self-similar hierarchical structure and scaling power spectrum at a particular winding number (the golden mean), (2) the fractal dimension of the set of locked states on the critical line, and (3) the multifractal spectrum. In particular, the scaling power law of the spectrum is found to change from f⁴ to f² as the system approaches the onset of chaos. We provide numerical support for the hypothesis that the change of the scaling power law is attributed to the drastic change of the Poincar\'e cross section from a mild to a sharp wrinkle. The experiment demonstrates that the thermoacoustic system belongs to the same universality class as the simple map, at least up to the onset of chaos, in spite of the complexity of the system.