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Abstract

Despite the presence of strong fluctuations, many turbulent systems such as Rayleigh-Benard 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-Benard convection.