Abstract

The multi-layer structure is a statistical (mean-field) structure of a turbulent boundary layer (TBL), which will be shown to stand as the true similarity structure of TBL . It includes the famous log-law layer as a part, but extends to cover the entire (thin) boundary layer. For quite a while, one focus only on the logarithmic layer, leaving many key issues undetermined, such as their accurate locations and how they may impact on our understanding of TBL in general. We will discuss a recently developed symmetry-based multi-layer description of TBL , which has three remarkable features. The first concerns with its universal similarity nature, owing to wall-induced dilation symmetry-breakings. Thus, it applies not only in the wall normal direction, for explaining sublayer, buffer layer, log-layer, etc., but also yields accurate description in the streamwise direction for laminar-turbulence transitions, since all transitions between different layers/regimes obey universal rule dictated by a Lie-group ansatz. The second is its ability to be extended from equilibrium TBL to non-equilibrium (engineering) TBL , the latter simply involves more symmetry-breakings with spatially varying multi-layer parameters. The third is its intimate connection to global properties such as skin friction, heat flux, etc.; in other words, knowing multi-layer structure precisely will enable to make unprecedentedly accurate predictions of practical properties which engineers are interested in. This talk will present these features, with recent accomplishment in developing accurate models for such engineering flows as: 1) a variety of transitional flows from laminar to turbulence; 2) high speed flows around flat plate from transonic to hypersonic; 3) aeronautic flows around wing or cone; 4) shock-induced separated flows, etc.