Mechanical and Civil Engineering Seminar: PhD Thesis Defense

Abstract:

In this talk, a linear resolvent analysis (McKeon and Sharma, 2010), and a novel quantitative non-linear analysis of the triadic interactions are utilized to mainly study the large-scale structures in wall-bounded turbulence.

A novel framework is developed 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 sparse spatio-temporal nature of the triadic interactions and the effect of the resolvent operator. It is shown that the active triadic interactions are significantly localized in temporal frequencies around a plane where all three wavespeeds are the same, allowing for a very significant sparsification of the active 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.

Zoom: https://caltech.zoom.us/j/84959770424?pwd=1RkCIRnastKoTq7pvvNno4zGHHxiKH.1