Reduced Order Modeling of Near-Wall and Roughness Sublayer Turbulence Using Resolvent Analysis

Modeling near-wall and roughness sublayer turbulence using physics-based methods remains a topic of paramount importance, since most engineering-relevant flows are turbulent and most surfaces are not smooth. While today there exists a wide range of empirical, data-driven modeling approaches for turbulence, these methods are limited because fully resolved turbulence data remains expensive to generate and burdensome to store and analyze. Therefore, the ability to predict out-of-sample is important, and since data-driven methods struggle to extrapolate, developing physics-based approximations that give useful, inexpensive predictions remains necessary. Yet the complexity of near-wall turbulence makes developing theoretical models difficult. This thesis tackles two main challenges. First, methods for reduced order modeling of the sensitivity of turbulence to multiscale, engineering-relevant roughness geometries are developed. In particular, a physics-based method for incorporating a drag-scaled, Reynolds-decomposed volume penalization into resolvent analysis yields a linear reduced order model that gives computationally inexpensive estimates for roughness sublayer fluctuations and dispersive stresses given a surface geometry and the mean flow profile in a rough wall channel flow. Then, an iterative method is developed to predict the mean flow profile, equivalent sand grain roughness, and Hama roughness function that utilizes the discovered relationship between the fluctuations and the mean flow. That model yields a closed-loop system for predicting roughness sublayer turbulence and the mean response given only a scan of the roughness geometry and a bulk Reynolds number in a rough wall channel flow. Second, a methodology for generating spatiotemporal representations of near-wall turbulence with very few degrees of freedom is developed. It utilizes a coarse-graining approach to reduce the number of modes required to describe a turbulent flow, selection criteria for picking descriptive modes, and Reynolds number scaling to provide predictions for an out-of-sample, higher Reynolds number flow. A spatiotemporal representation is generated, and results from Piomelli et al. that incorporate the modal representation into the wall layer of a wall modeled large eddy simulation are presented. Overall, this thesis contributes new reduced order modeling approaches that make use of physics-based insights to tackle outstanding problems in the prediction of near-wall and roughness sublayer turbulence.