Structure interactions in a reduced-order model for wall-bounded turbulence

Abstract

Reduced-order models are derived for a simplified description of transition and turbulence in Waleffe and Couette flow. Twelve nonlinear ordinary differential equations model the dynamics of coherent structures in fair agreement with direct numerical simulation. Compared to previous models, these low order systems display longer turbulence lifetimes and lower transition thresholds. Two spanwise wavelengths, ${L}_{z}$ and ${L}_{z}/2$, for roll and streak modes is a key feature. The models show that interaction between structures with either wavelength is crucial to maintain longer turbulence lifetimes, as a neglect of such interaction leads to order-of-magnitude lifetime reductions.