On precisely locating the inertial sublayer in turbulent channel flow

The spatial inertial sublayer in wall-bounded turbulent flows, which also coincides with the logarithmic mean velocity profile, factors importantly in physical, conceptual and mathematically-based flow characterizations. In this regard, studies that seek to predict or describe wall-flow structure are often assessed via the estimation of statistical and/or structural properties on the inertial sublayer. In the interest of obtaining the highest fidelity estimates, it is thus advantageous to have well-justified and precise bounds of the inertial sublayer. Toward this aim, inertial sublayer inner and outer bounds are developed for turbulent channel flow. The Reynolds number dependent bounds are independently founded in the properties of the mean dynamical equation and are set prior to estimating the statistical quantity of interest. The outer bound is shown to depend on the Reynolds shear stress profile curvature, and thus data accuracy sensitivities are important to this bound. With increasing Reynolds number, the inner bound is shown to move to increasing y⁺ and the outer bound moves to decreasing y/δ, where y⁺ and y/δ are the inner and outer normalized wall-distances, respectively. Once established, mean flow properties are estimated and assessed on the inertial sublayer using DNS channel data across a friction Reynolds number range 2,000 < δ⁺ < 16,000.