Structured input-output analysis of oblique turbulent bands in Waleffe flow

Abstract

This work employs structured input-output analysis (SIOA) to study Waleffe flow. The SIOA framework employs structured uncertainty to include the componentwise structure of nonlinearity in Navier-Stokes equations, and SIOA quantifies the flow response using structured singular values. The structured input-output analysis identifies the wavelength and inclination angle of oblique turbulent bands observed in large-domain direct numerical simulations. The structured input-output response scales over Reynolds number as $\sim R{e}^{1.7}$.

arXiv comment2 pages, 3 figures, accepted to LSU Symposium on Control, Learning, and Intelligent Systems 2026