Turbulent solutions of the Navier-Stokes equations are characterized by a deep hierarchy of structures, spanning a wide range of spatiotemporal scales. Identifying relevant energy transfer paths between structures across this hierarchy is therefore a challenging task. In particular, in large Galerkin reduced-order models, the third-order tensor representing nonlinear interactions is dense, hindering the interpretation of the underlying physics. Here, we employ l1-based regression techniques to sparsify the third order tensor, pruning weak triadic interactions and identify uniquely the subset of interactions contributing most prominently to the dynamics. Crucially, the l1-based regression is a convex problem with a unique solution, and can be solved efficiently using ADMM-type methods. We demonstrate the approach on a family of large reduced-order models of 2D lid-driven cavity flow at Re = 2 ×104 constructed from Proper Orthogonal Decomposition (POD) and Spectral POD modes. Depending on the modal decomposition, the l1 regression sparsifies the dynamics in agreement with the established picture of scale interactions in 2D turbulence. Specifically, for the small scales, non-local interactions are preserved, while small-small/scale interactions are truncated.USAF, AFRL DUNS AF OFFICE OF SCIENTIFIC RESEARCH Grant Number FA9550-17-1-0324.
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 2019