Fitting Conditionally Averaged Velocity Profiles in Wall-Bounded Turbulent Flows

While direct numerical simulation (DNS) and large-eddy simulation provide resolution of turbulent flows, their computational cost can be prohibitive for high Reynolds number applications. On the other hand, Reynolds-Averaged Navier-Stokes is computationally cheap, but is incapable of resolving any of the turbulent fluctuations. With the recently demonstrated proof of concept of turbulence-resolving integral simulation (TRIS) by Ragan et al. (2025), the use of instantaneous wall-normal integrals possesses great potential in the tradeoff between computational cost and physical accuracy. This study evaluates and fits the averaged velocity profiles conditioned on the wall-normal integral of the Reynolds-averaged streamwise velocity. First, the conditionally averaged velocity profiles are parametrized using Coles’ law of the wake (Coles, 1956). Then, further discussion covers how these velocity profiles are fit using ODE-based wall models. The parametrized fits are compared against data obtained from DNS of a full-channel flow at friction Reynolds numbers of 1000 and 5200, gathered from the Johns Hopkins Turbulence Database. The focus of this study is primarily placed on the wake region of the velocity profile, as it presents unique challenges in accurate fitting. Comparing the approximation of the velocity profiles to that of DNS will be instrumental in developing the models for unclosed terms in the TRIS framework to represent flow dynamics in a physically and computationally efficient manner.