Statistical properties of defect turbulence in two and three dimensions
Date
2015-04-06
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Abstract
Spatiotemporal chaos in oscillatory and excitable media is often characterized by the presence of phase singularities called defects. Understanding such defect mediated turbulence is an important challenge in nonlinear dynamics. This is especially true in the context of ventricular fibrillation in the heart, where the mechanism leading to ventricular fibrillation, and the importance of the thickness of the ventricular wall, is contentious. Here, we study defect mediated turbulence arising in many regimes of conceptual models of oscillatory and excitable media and investigate the statistical properties of the turbulent state that results.
Two central ideas are put under scrutiny. First, that the turbulence is driven, and its observables influenced, by the mechanism of breakup and second, that the dimensionality of the medium leads to a different, potentially more complex, turbulence. We find evidences that support the idea of instability driven turbulence for different 2-dimensional instabilities. Furthermore, breakup from purely 3-dimensional instabilities offers a completely different mechanism. For 2D mechanisms in 3D media, we find that the thickness of the medium does not have a significant influence far from onset in fully developed turbulence while there is a clear transition in behavior if the system is close to a spiral instability. We further provide clear evidence that the observed transition is purely a consequence of the dimensionality of the medium. Using 3D defect tracking, we show that the statistical properties arising from 2D instability driven turbulence are different from those in turbulent regimes arising from 3D instabilities, but only close to onset.
As a consequence of this study, we are lead to the counterintuitive conclusion that even in the absence of pure 3D instabilities, 3D simulations may be necessary to capture even the simplest statistical feature of the turbulent behaviour of real 3D systems. However, even if the 3D statistics are different from the 2D ones, they are not distinguishable in a general context, a conclusion that opposes a previous conjecture.
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Condensed Matter, Statistics
Citation
St-Yves, G. (2015). Statistical properties of defect turbulence in two and three dimensions (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27878