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-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.
Keywords
Cite
@article{arxiv.1909.10814,
title = {Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection},
author = {Gregor Ibbeken and Gerrit Green and Michael Wilczek},
journal= {arXiv preprint arXiv:1909.10814},
year = {2019}
}