Fractional-Order Large-Eddy Simulation of Turbulence


Friday, 7 June, 2024 - 15:00 to 16:00

Speaker : Mohsen Zayernouri, Associate Professor

Department of Mechanical Engineering, Department of Statistics and Probability

Michigan State University (MSU), East Lansing, MI 48824

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube :

Organizers : Pavan Pranjivan Mehta* ( and Arran Fernandez** (

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Anomalous Subgrid Dynamics, Multi-Scale Modeling


Turbulence remembers and is fundamentally nonlocal. Such a longing portrait of turbulence originates from the delineation of coherent structures/motions, being spatially spotty, giving rise to interestingly anomalous spatio-temporal fluctuating signals. The statistical anomalies in such stochastic fields emerge as: sharp peaks, heavy-skirts of power-law form, long-range correlations, and skewed distributions, which scientifically manifest the non-Markovian/non-Fickian nature of turbulence at small scales. Such physical-statistical evidence highlights that ‘nonlocal features’ and ‘global inertial interactions’ cannot be ruled out in turbulence physics. On a whole different (computational) level and in addition to the aforementioned picture, the very act of filtering the Navier-Stokes and the energy/scalar equations in the large eddy simulations (LES) would make the existing hidden nonlocality in the subgrid dynamics even more pronounced, to which it induces an immiscibly mixed physical-computational nonlocal character.

This urges the development of new LES modeling paradigms in addition to novel statistical measures that can meticulously extract, pin-down, and highlight the nonlocal character of turbulence (even in the most canonical flows e.g., homogeneous isotropic turbulence) and their absence in the common/classic turbulence modeling practice. We start from the filtered Boltzmann kinetic transport equations and model the corresponding equilibrium distribution functions (for both the fluid and scalar particles) with stable heavy-tailed distributions to address and incorporate the anomalous features at small scales. Next, we derive a new class of fractional-order and tempered Laplacian models for the divergence of subgrid-scale stresses, naturally emerging as the underlying subgrid-scale (SGS) LES models. We subsequently carry out the corresponding a priori and a posteriori tests to examine the performance of each fractional SGS model. Our proposed dynamic LES modeling approach exhibits promising capabilities to effectively model and incorporate nonlocalities on the fly in the very LES (VLES) as well as the LES inertial sub-ranges. This novel LES modeling paradigm can be imperative for cost-efficient nonlocal turbulence modeling e.g., in meteorological and environmental applications. A survey of our developments in this paradigm of research is given in [1-8].

Biography: Mohsen Zayernouri is an associate professor at MSU and the director of FMATH group He obtained his 2nd PhD in Applied Mathematics at Brown University back-to-back after obtaining his 1st PhD in Mechanical Engineering at the University of Utah. He received the AFOSR Young Investigator Program (YIP) award in 2017 in addition to the ARO YIP award in 2019. He served as the MSU-PI in the ARO-MURI on Fractional PDEs for Conservation Laws and Beyond. He has also received multiple other awards from the US National Science Foundation, the US Army Research Lab (ARL) on relevant topics, including: statistical learning, uncertainty quantification, nonlocal turbulence modeling, and multi-scale (MD-to-DDD-to-Continuum) nonlocal material failure modeling.


[1] A Akhavan-Safaei, M Zayernouri, Deep Learning Modeling for Subgrid Flux in the LES of Scalar Turbulence and Transfer Learning to Other Transport Regimes, Journal of Machine Learning for Modeling & Computing, 2024, 5 (1).

[2] A Akhavan-Safaei, M Zayernouri, A Parallel Computational–Statistical Framework for Simulation of Turbulence: Applications to Data-Driven Fractional Modeling, Fractal and Fractional 7 (6), 488, 2023.

[3] A Akhavan-Safaei, M Zayernouri, A Nonlocal Spectral Transfer Model and New Scaling Law for Scalar Turbulence, Journal of Fluid Mechanics 956, A26, 2023.

[4] SH Seyedi, M Zayernouri, A Data-Driven Dynamic Nonlocal Subgrid-Scale Model for Turbulent Flows, Physics of Fluids 34 (3), 2022.

[5] SH Seyedi, A Akhavan-Safaei, M Zayernouri, Dynamic Nonlocal Passive Scalar Subgrid-Scale Turbulence Modeling, Physics of Fluids 34 (10), 2022.

[6] M Samiee, A Akhavan-Safaei, M Zayernouri, Tempered Fractional LES Modeling, Journal of Fluid Mechanics 932, A4, 2022.

[7] A Akhavan-Safaei, M Samiee, M Zayernouri, Data-Driven Fractional Subgrid-Scale Modeling for Scalar Turbulence: A Nonlocal LES Approach, Journal of Computational Physics 446, 110571, 2021.

[8] M Samiee, A Akhavan-Safaei, M Zayernouri, A fractional subgrid-scale model for turbulent flows: Theoretical formulation and a priori study, Physics of Fluids 32 (5), 2020.