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

TL;DR

This paper applies structured input-output analysis to Waleffe flow, identifying key features of oblique turbulent bands and their scaling behavior with Reynolds number.

Contribution

It introduces a structured input-output analysis framework that captures the nonlinearity structure in Navier-Stokes equations for turbulent flow analysis.

Findings

Identifies the wavelength and inclination angle of oblique turbulent bands.

Quantifies the flow response scaling as approximately Re^{1.7}.

Demonstrates the effectiveness of structured input-output analysis in turbulent flow studies.

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 $\sim Re^{1.7}$.