Features of the attached-eddy hypothesis in one-dimensional turbulence models of turbulent boundary layers
Phys. Rev. Fluids 11, 014604 – Published 13 January, 2026
DOI: https://doi.org/10.1103/l8xs-nnjt
Abstract
The complexity of wall-bounded turbulent flows has given rise to a variety of models that capture the essence of this physical problem, yet many of these models are built on different modeling assumptions. A plausible model is Townsend's attached eddy model (AEM), which is predicated on the assumption that the eddies have a geometric scaling with the distance from the wall and a constant characteristic velocity. With a limited set of modeling assumptions, AEM has shown potential to capture many of the preponderant features of the turbulent boundary layer (TBL) such as the log layer and Reynolds stress distributions. Other models, such as the stochastic one-dimensional turbulence (ODT) model from A. R. Kerstein, J. Fluid Mech. 392, 277 (1999) are built on a completely different set of modeling assumptions, yet show similarly convincing agreement when modeling the TBL. In this work, we rewrite the ODT formulation as a Markov process and simplify some modeling assumptions, which allows us to recast the equations into a form analogous to AEM. By distilling and simplifying ODT, we highlight the implicit similarities in the modeling assumptions found in AEM, which underscores the importance of (i) the eddy-probability estimation and (ii) the functions associated with the displacement and velocity induced by the eddy events. Comparison of the stochastic ODT model with a structural AEM model helps to identify the key features in TBL modeling along with some of the shortcomings in each of these models.
