Title: Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Abstract

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluatemore » the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.« less

Authors:

Tian, Yifeng  ^[1];

• Search DOE PAGES for author "Tian, Yifeng"
• Search DOE PAGES for ORCID "0000-0002-1668-7770"

Lin, Yen Ting  ^[1];

• Search DOE PAGES for author "Lin, Yen Ting"
• Search DOE PAGES for ORCID "0000-0001-6893-8423"

Anghel, Marian  ^[1];

• Search DOE PAGES for author "Anghel, Marian"
• Search DOE PAGES for ORCID "0000-0003-3495-4235"

Livescu, Daniel  ^[1]

• Search DOE PAGES for author "Livescu, Daniel"
• Search DOE PAGES for ORCID "0000-0003-2367-1547"

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+ Show Author Affiliations

1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Thu Dec 09 00:00:00 EST 2021

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:

1874192

Alternate Identifier(s):

OSTI ID: 1834961

Report Number(s):

LA-UR-21-28283
Journal ID: ISSN 1070-6631; TRN: US2307113

Grant/Contract Number:  

89233218CNA000001

Resource Type:

Accepted Manuscript

Journal Name:

Physics of Fluids

Additional Journal Information:

Journal Volume: 33; Journal Issue: 12; Journal ID: ISSN 1070-6631

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; turbulence simulations; nonequilibrium statistical mechanics; computational fluid dynamics; turbulent flows; Navier Stokes equations; turbulence theory and modelling; nonlinear systems