Multiscale quasi time-periodic coherent structures in shear flows

TL;DR

This paper demonstrates that capturing multiscale shear-flow turbulence requires considering quasi-time-periodic solutions, which can be efficiently approximated using a quasi-linear model to reveal vortex structures consistent with the Taylor frozen-flow hypothesis.

Contribution

It introduces a quasi-linear modeling approach to efficiently approximate multiscale quasi-time-periodic states in shear flows, advancing turbulence analysis.

Findings

Quasi-linear models effectively approximate complex shear-flow states.

Multiscale critical layers produce vortices consistent with Taylor's hypothesis.

Capturing quasi-time-periodic solutions enhances understanding of shear turbulence.

Abstract

Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as complex as quasi-time-periodic solutions. Approximations of these states can be computed efficiently using a quasi-linear model, consistent with the large-Reynolds-number asymptotic analysis. The quasi-linear structure is key to producing multiscale critical layers that generate vortices obeying Taylor frozen-flow hypothesis.