Structural ensemble dynamics theory for engineering turbulenc models

For decades, turbulence models are built upon dimensional arguments with numerous empirical coefficients, which yield two problems:absence of physical interpretation for parameters (thus limited adaptability to complex flows) and poor prediction accuracy (relying on experimental calibration). Only a deep understanding of the similarity principle in realistic engineering flows can make a fundamental change. After a review of current research on wall turbulence, we suggest a new symmetry-based approach, the so-called structure ensemble dynamics (SED) theory, which aims at discovering universal symmetry principle imposed by the presence of wall. The theory gives rise to a universal multi-layer description of all Reynolds stresses (hence a unified description for both the mean velocity and turbulence intensities) for canonical wall-bounded turbulent flows, based on the concepts of length order function, generalized dilation-invariance ansatz under a novel Lie-group analysis framework. Five steps of the SED analysis are proposed to renovate the aerodynamics studies, including collecting data, verifying symmetry, defining order functions, determining multi-layer parameters, and developing adequate turbulence models, respectively. The framework opens a new avenue for analyzing empirical data from experiments and numerical simulations, then developing new turbulence models with a physical parameterization and much more accurate prediction.