Coherent structures in high-reynolds number wall-bounded turbulence: invariant solutions and scale interaction

Abstract

This work seeks to address some of the outstanding issues in the theoretical description of high-Reynolds number wall-bounded turbulence, with an emphasis on coherent structures and their dynamics. An inner-scaled shear stress-driven flow is introduced as a model of independent mesolayer turbulence as the friction Reynolds number tends to infinity, given that the effects of the flow geometry are negligible in this limit. The universal mesolayer dynamics are subsequently investigated from a dynamical systems perspective and through statistical analysis. Fifteen invariant solutions are computed in the minimal unit of near-wall turbulence, which capture all three stages of the self-sustaining process that underpins the dynamics at each integral lengthscale of motion. The temporal dynamics of near-wall flow with two integral lengthscales of motion are then analysed from a statistical perspective, with a focus on scale interaction. It is observed that the dynamics of the energy cascade from large to small scales are entirely determined by the large-scale self-sustaining process, while the feeding of energy from small to large scales is impelled by the small-scale self-sustaining process. Furthermore, a new scale interaction process is discovered, namely that wall-normal energy transfer from large to small scales drives small-scale turbulent production through the Orr mechanism. Finally, this minimal unit of multi-scale near-wall turbulence is also analysed from a dynamical systems perspective and twenty-eight invariant solutions are computed, which represent either the large- or small-scale self-sustaining processes. A solution that captures the feeding of streamwise energy from small to large scales and the resulting localised large-scale turbulent production is presented, both of which are supported by the subharmonic sinuous streak instability mode. However, none of the reported solutions fully capture the turbulent dynamics and in the absence of multi-scale invariant solutions, the dynamical systems description of the minimal unit of multi-scale near-wall turbulence is inadequate.