Scale interactions in turbulent plane Couette flows in minimal domains

Interscale energy transfer in wall turbulence has been intensively studied in recent years, and both forward (i.e. from larger to smaller scales) and reversed transfers of turbulent energy have been found, although their corresponding physical phenomena have not been revealed. In the present study, we perform direct numerical simulations of turbulent plane Couette flow with reduced-size computational domains, where either the streamwise or the spanwise domain size is reduced to its minimal length, aiming to elucidate 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 the 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 between 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 the individual dynamics of each inner and outer structure, rather than representing their interactions.