Scale interactions in turbulent plane Couette flows in minimal domains

TL;DR

This study uses DNS of turbulent plane Couette flow in minimal domains to reveal how scale interactions, especially between streaks and vortices, sustain turbulence through forward and reversed energy transfers.

Contribution

It demonstrates the roles of streamwise and spanwise scale interactions in turbulence maintenance using minimal domain DNS, highlighting the importance of specific scale interactions.

Findings

Streamwise-elongated streaks and vortices are key to scale interactions.

Reversed energy transfer sustains larger-scale energy production.

Spanwise interactions are more related to individual structure dynamics.

Abstract

Interscale energy transfer in wall turbulence has been intensively studied in recent years, and both the forward (i.e. from larger to smaller scales) and reversed transfers of turbulent energy have been found whereas their corresponding physical phenomena have not been revealed. In the present study, we perform DNS of turbulent plane Couette flow with reduced-size computational domains, where either the streamwise or spanwise domain size is reduced to their minimal lengths, aiming at elucidating the role of scale interactions in each direction. Our computational results with the streamwise-minimal domain suggest that the interplays between streamwise-elongated streaks and vortices smaller than the streamwise minimal length are the essential scale interactions for both the inner and outer structures. We further show that these streamwise-independent and smaller-scale structures exchange energy through forward and reversed interscale energy transfers, and the reversed energy transfer maintains the energy production at larger scales. Based on the resemblance of the observed Reynolds-stress transport and the scenario of the self-sustaining cycle, we conjecture that the forward and reversed energy transfers mainly represent the streak instabilities and regeneration of streamwise vortices, respectively. Furthermore, the computation with the spanwise-minimal domain indicates that the interscale energy transfers observed by one-dimensional spanwise spectral analysis are likely related to individual dynamics of each inner and outer structure, rather than represent their interactions.