Modal decomposition of nonlinear interactions in wall turbulence

Ugur Karban, Eduardo Martini, André V. G. Cavalieri, Peter Jordan

Published 2023-01-03Version 1

Coherent structures are found in many different turbulent flows and are known to drive self-sustaining processes in wall turbulence. Identifying the triadic interactions which generate coherent structures can provide insights beyond what is possible in the framework of linearized models. There are infinite possible interactions that may generate a given structure. Thus a method to systematically study those, ranking them in terms of their contribution to the structure of interest, is essential. We here use the resolvent-based extended spectral proper orthogonal decomposition (RESPOD) approach (Karban, U. et al. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. Journal of Fluid Mechanics 969, A36) to rank the triadic interactions which give rise to wall-attached structures in a minimal Couette flow at Reynolds number 400. Our analysis identifies that six triadic interactions dominate the most-energetic wall-attached structure, revealing the capability of the methodology to identify and rank nonlinear interactions responsible for a given coherent structure. The approach can be used to analyse the energy exchange in turbulent flows and may guide the construction of reduced-order models based on the interplay between different flow modes.