Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction

TL;DR

This paper investigates the energy transfer mechanisms and mean-flow interactions in patterned shear turbulence, revealing how turbulence structures influence energy budgets during transition from uniform turbulence to laminar flow.

Contribution

It provides a detailed analysis of energy balances and transfer processes in patterned shear turbulence, highlighting mechanisms driving pattern formation and transition.

Findings

Mean flow is strongly modulated in patterns.

Energy transfer from small to large scales occurs via negative spectral production.

Negative production is also present in uniform turbulence.

Abstract

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of spatially intermittent turbulent structures. In plane shear flows, these appear as a regular pattern of alternating turbulent and quasi-laminar flow. Both the physical and the spectral energy balance of a turbulent-laminar pattern in plane Couette flow are computed and compared to those of uniform turbulence. In the patterned state, the mean flow is strongly modulated and is fuelled by two mechanisms: primarily, the nonlinear self-interaction of the mean flow (via mean advection), and secondly, the extraction of energy from turbulent fluctuations (via negative spectral production, associated with an energy transfer from small to large scales). Negative production at large scales is also found in the uniformly turbulent state. Important features of the energy budgets are surveyed as a function of $Re$ through the transition between uniform turbulence and turbulent-laminar patterns.