Linear and Non-Linear Interactions Involving Large-Scale Structures in Turbulence

Abstract

This thesis performs a linear resolvent analysis (McKeon and Sharma, 2010), and a novel quantitative non-linear analysis of the triadic interactions, to study the largescale structures in wall-bounded turbulence.

First, resolvent analysis is applied to a flow over spanwise periodic roughness, to model the large-scale counter-rotating rolls. The experimental data (Wangsawijaya et al., 2020) is utilized to examine both the predictive and data compression capabilities of the resolvent. The improvements by the inclusion of an eddy viscosity and a crude boundary geometry model are also demonstrated. Standard resolvent is able to qualitatively predict the shape of the counter-rotating rolls. The inclusion of eddy viscosity improves the quantitative predictions and combined with the boundary geometry model is able to efficiently represent the data with small differences using only a fraction of the degree of freedom.

Next, we developed a novel framework to quantitatively analyze the triadic non-linear contributions in a turbulent channel. We incorporated the linear resolvent operator to provide the missing link from energy transfer between modes to the effect on the spectral turbulent kinetic energy. The coefficients highlight the importance of interactions involving large-scale structures, for both the large and small-scale forcing and response, providing a natural connection to the modeling assumptions of the quasi-linear (QL) and generalized quasi-linear (GQL) analyses. Specifically, it is revealed that QL and GQL are efficiently capturing important triadic interactions in the flow, and the inclusion of small amounts of wavenumbers into the GQL large-scale base flow quickly captures most of the important triadic interactions.

Finally, by performing spatio-temporal analyses of the triadic contributions to a single mode, we demonstrated the spatio-temporal nature of the triadic interactions and the effect of the resolvent operator. It is shown that the energetic triadic interactions are concentrated in temporal frequencies around a plane where all three wavespeeds are the same, allowing for a truncation of the important triadic interactions. We also demonstrated the linear amplification mechanism of the resolvent, allowing certain triadic interactions to generate a stronger response even with a weak forcing, underscoring the different perspectives offered by the inclusion of the linear resolvent operator into the analyses of the non-linear triadic interactions.