Browsing by Author "Huang, Zhi-Feng"

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    Exploring spiral defect chaos in generalized Swift-Hohenberg models with mean flow
    Karimi, A.; Huang, Zhi-Feng; Paul, Mark R. (American Physical Society, 2011-10-28)
    We explore the phenomenon of spiral defect chaos in two types of generalized Swift-Hohenberg model equations that include the effects of long-range drift velocity or mean flow. We use spatially extended domains and integrate the equations for very long times to study the pattern dynamics as the magnitude of the mean flow is varied. The magnitude of the mean flow is adjusted via a real and continuous parameter that accounts for the fluid boundary conditions on the horizontal surfaces in a convecting layer. For weak values of the mean flow, we find that the patterns exhibit a slow coarsening to a state dominated by large and very slowly moving target defects. For strong enough mean flow, we identify the existence of spatiotemporal chaos, which is indicated by a positive leading-order Lyapunov exponent. We compare the spatial features of the mean flow field with that of Rayleigh-Bénard convection and quantify their differences in the neighborhood of spiral defects. © 2011 American Physical Society.
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    Spiral defect chaos in Rayleigh-Benard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals
    Vitral, Eduardo; Mukherjee, Saikat; Leo, Perry H.; Vinals, Jorge; Paul, Mark R.; Huang, Zhi-Feng (American Physical Society, 2020-09-10)
    Rotating spiral patterns in Rayleigh-Bénard convection are known to induce azimuthal flows, which raises the question of how different neighboring spirals interact with each other in spiral chaos and the role of hydrodynamics in this regime. Far from the core, we show that spiral rotations lead to an azimuthal body force that is irrotational and of magnitude proportional to the topological index of the spiral and its angular frequency. The force, although irrotational, cannot be included in the pressure field as it would lead to a nonphysical multivalued pressure. We calculate the asymptotic dependence of the resulting flow and show that it leads to a logarithmic dependence of the azimuthal velocity on distance r away from the spiral core in the limit of negligible damping coefficient. This solution dampens to approximately 1/r when accounting for no-slip boundary conditions for the convection cell's plate. This flow component can provide additional hydrodynamic interactions among spirals including those observed in spiral defect chaos. We show that the analytic prediction for the azimuthal velocity agrees with numerical results obtained from both two-dimensional generalized Swift-Hohenberg and three-dimensional Boussinesq models and find that the velocity field is affected by the size and charges of neighboring spirals. Numerically, we identify a correlation between the appearance of spiral defect chaos and the balancing between the mean-flow advection and the diffusive dynamics related to roll unwinding.