Turbulent superstructures in the turbulent cascade of Reynolds stresses

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Vortical structures with different characteristic length scales coexist and interact reciprocally in wall-bounded turbulence. They range from very large-scale structures away from the wall to small-scale eddies in the wall vicinity. The large-scale motions are called turbulent superstructures - TSS in the following – and have length scales much larger than those of the near-wall vortices. TSS play an important role in the dynamics of turbulent flows, where they cause strong velocity fluctuations with a characteristic length scale of many times the largest length scale of the flow, for instance the thickness of a turbulent boundary layer. TSS are responsible for a significant fraction of total turbulent kinetic energy and increased friction drag at the wall, through their contribution to the Reynolds shear stress. Presently, no agreed-upon description of the dynamics of TSS exists, especially concerning their mutual interaction with other scales. While the effect of TSS on the small scale structures at the wall has been documented in literature, there is contrasting evidence regarding an influence in the opposite direction, i.e. an influence of the small scale structures onto the TSS. In particular, it is still unclear whether the small scale structures play a determinant role in the origin of TSS. Understanding the mutual influence of TSS and the other scales of the flow is of great importance not only from a theoretical point of view, but also because it greatly affect our ability to model and control a turbulent flow.In the present proposal we investigate the interaction between TSS and the other smaller scale structures of the flow. We apply a new theoretical framework, the Anisotropic Generalized Kolmogorov Equations, in order to describe how the separate component of the Reynolds stress tensor are produced, dissipated and transported through structures at different length scales and across physical space in the turbulent flow. In this framework, the result of the interaction between scales is a measurable transport of Reynolds stresses across scales and space, that constitutes the so-called turbulent cascade of Reynolds stresses.We develop a series of numerical experiments, in which the physics of turbulent flows in channels is let develop naturally or purposely altered, in order to highlight or quench some aspects of TSS. Through an analysis of how Reynolds stresses are transported through different scales, we can highlight the relationship between TSS and other structures of the turbulent flow.