Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection

Abstract

Despite the presence of strong fluctuations, many turbulent systems such as Rayleigh-Bénard convection and Taylor-Couette flow display self-organized large-scale flow patterns. How do small-scale turbulent fluctuations impact the emergence and stability of such large-scale flow patterns? Here, we approach this question conceptually by investigating a class of pattern forming systems in the presence of random advection by a Kraichnan-Kazantsev velocity field. Combining tools from pattern formation with statistical theory and simulations, we show that random advection shifts the onset and the wave number of emergent patterns. As a simple model for pattern formation in convection, the effects are demonstrated with a generalized Swift-Hohenberg equation including random advection. We also discuss the implications of our results for the large-scale flow of turbulent Rayleigh-Bénard convection.

References in corpus (10)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Particles and fields in fluid turbulence
• High Reynolds number Taylor-Couette turbulence
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Cited by in corpus (3)

• Supergranule aggregation for constant heat flux-driven turbulent convection
• Resolved energy budget of superstructures in Rayleigh-Bénard convection
• Gauge symmetry and dimensionality reduction of the anisotropic pressure Hessian