DYNAMICS AND SELECTION OF GIANT SPIRALS IN RAYLEIGH-BENARD CONVECTION
Spiral patterns are found in many pattern-forming sys- tems (1). Famous examples include cardiac arrhythmias of the heart (2), the aggregation of starving slime mold amoebae (3), and the Belousov-Zhabotinsky chemical re- action (4). Many of these systems can be classified as excitable media in which the core of the spiral, like a pacemaker, selects the temporal and spatial evolution of the outward travelling spiral waves (4). In this Letter we present a detailed experimental study of a driven, dissi- pative system in which the formation of spirals can be attributed to a qualitatively different mechanism acting far away from the spiral's core. In particular, we show for Rayleigh-Benard convection (RBC) of a small Prandtl number fluid that the rotation of giant, multi-armed spi- rals can be captured using concepts based on nonlinear phase equations (5-9,13). These concepts should be uni- versal and preliminary evidence indicates that similar reasoning may also apply to the spiral pattern formation in vibrating granular layers (10) and in gas discharges (11). As stated earlier (12), the rigid rotation of a giant, fi- nite spiral of radius rd necessitates that the spiral waves which propagate from the spiral's core are annihilated at r = rd by a circular motion of the outer defect. Thus, the pattern simply consists of stationary, concentric rolls for r > rd. This balancing mechanism has been placed on a more precise theoretical framework by Cross and Tu (7,8) (CTC). They argue that the rotation of a spiral requires the reconciliation of two competing selection principles acting far away from the spiral's core: (1) wavelength se- lection by climb of the outer defect and (2) the emission of radially travelling waves due to target selection. These arguments have been successfully tested within general- ized Swift-Hohenberg (SH) models for axisymmetric spi- rals (7-9,13) and have also been extended to multi-armed spirals (9). However, the generalized SH-model used in these studies contains ad hoc parameters, and its stabil- ity regime deviates substantially from that for RBC (14). As Cross (8) has pointed out in his concluding remarks, serious conceptual uncertainties remain as well. In this Letter, we present the first quantitative exper- imental and theoretical analysis of giant rotating spi- rals in RBC. For axisymmetric, multi-armed spirals in large aspect-ratio cells we find good quantitative agree- ment between experimental measurements and theoret- ical predictions. However, for the frequent case of non- axisymmetric spirals our measurements are in conflict with the proposed target selection mechanism and, as a consequence, CTC's "Invasive Chaos" idea as a tentative explanation of Spiral Defect Chaos (SDC) (15) requires refinement.