  Despite the presence of strong fluctuations, many turbulent systems such as
Rayleigh-B\'{e}nard 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-B\'{e}nard convection.
