An Approximate Inertial Manifold (AIM) Based Closure for Turbulent Flows

Maryam Akram, Malik Hassanaly, Venkat Raman

Research output: Contribution to journalArticlepeer-review

5 Scopus Citations


A closure model for turbulent flows is developed based on a dynamical system theory. An appropriately discretized formulation of the governing equations is considered for this process. The key ingredient is an approximation of the system's attractor, where all the trajectories in phase space are confined. This approximate inertial manifold based approach provides a path to track trajectories of the system in a lower-dimensional subspace. Unlike conventional coarse-graining approaches, the turbulent field is decomposed into resolved and unresolved dynamics using the properties of the governing equations. The novelty of the approach relies on the reconstruction of the unresolved field constrained by the governing equations. A posteriori tests for homogeneous isotropic turbulence and the Kuramoto-Sivashinsky equation show promising results for considerable dimension reduction with strong convergence properties. The proposed model outperforms the dynamic Smagorinsky model, and the computational overhead is competitive with similar approaches.

Original languageAmerican English
Article number075118
Number of pages13
JournalAIP Advances
Issue number7
StatePublished - 1 Jul 2022

Bibliographical note

Publisher Copyright:
© 2022 Author(s).

NREL Publication Number

  • NREL/JA-2C00-81633


  • approximate inertial manifold
  • reduced-order modeling
  • turbulence


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