A general framework for computing the turbulence structure tensors

Good measures of the turbulence structure are important for turbulence modeling, flow diagnostics and analysis. Structure information is complementary to the componentality anisotropy that the Reynolds stress tensor carries, and because structures extend in space, structure information is inherently non-local. Given access to instantaneous snapshots of a turbulence field or two-point statistical correlations, one can extract the structural features of the turbulence. However, this process tends to be computationally expensive and cumbersome. Therefore, one-point statistical measures of the structural characteristics of turbulence are desirable. The turbulence structure tensors are one-point statistical descriptors of the non-local characteristics of the turbulence structure and form the mathematical framework for constructing Structure-Based Models (SBM) of turbulence. Despite the promise held by SBM, the tensors have so far been available only in a small number of DNS databases of rather simple canonical flows. This inhibits further SBM development and discourages the use of the tensors for flow analysis and diagnostics. The lack of a clear numerical recipe for computing the tensors in complex domains is one the reasons for the scarce reporting of the structure tensors in DNS databases. In particular, the imposition of proper boundary conditions in complex geometries is non-trivial. In this work, we provide for the first a time a rigorous and well-documented description of a mathematical and computational framework that can be used for the calculation of the structure tensors in arbitrary turbulent flow configurations.