L1-Based Sparsification of Reduced Order Models of High Reynolds Number Turbulent Flows
Abstract
Turbulence is a multi-scale phenomenon exhibiting a wide hierarchy of spatial and temporal scales. This property, coupled with the intrinsic nonlinearity of the governing equations, poses considerable difficulties to its modelling and analysis. One of the major challenges to obtain a satisfactory mathematical description of this phenomenon arises from the fact that the dynamics of flow structures at a particular length or time scale cannot be examined in isolation without also considering at the same time the whole hierarchy of complementary scales [Domaradzki et al., 1994]. In fact, nonlinear interactions between triads of scales play a fundamental role as they are the main driver of energy transfer between coherent structures [Pope, 2001, Moffatt, 2014]. In turn, the organisation of triadic interactions has a direct influence on the physics of a number of flow phenomena, such as direct and inverse energy cascades [Kolmogorov, 1991] or transition to turbulence [Craik, 1971, Rempfer and Fasel, 1994a,b] in different flow configurations [Schmidt, 2020]. Overall, this property makes the development of computationally efficient and physically-interpretable reduced order dynamical models a challenging task. Historically, the study of triadic interactions has been conducted by first employing an appropriate decomposition technique to educe coherent structures from the turbulent motion and then characterising the intensity of the inter-modal couplings through the perspective of the resulting Galerkin model [Noack et al., 2008]. One of the key findings of such studies is that energy transfers are not uniformly distributed in modal space. In fact, not all interactions have the same importance and energy flows along preferential directions. Specifically, there is evidence suggesting that the nonlinear interaction pattern among coherent structures is often sparse.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 17, 2022
- Accession Number
- AD1165518
Entities
People
- Andrea Da Ronch
- Davide Lasagna
- Riccardo Rubini
Organizations
- University of Southampton