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LIT-1259: Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism

1 min read

Properties5
StatusActive — read 2026-10-20 (NOTE-973) in full; worth reading for the clearest working example of a Mori–Zwanzig memory term turned into a finite Markovian augmentation (Stinis's finite-memory closure: the resolved modes plus a relaxing subgrid-force field), tested against filtered DNS on Burgers and four Navier–Stokes flows. Read it knowing that the augmentation's error is not bounded, the memory length is fitted or preset, the zero-variance projection makes the formalism a deterministic trajectory closure, "finite support" is exponential decay, and the comparisons are plots without error norms. THEORY-760 (Active) and THEORY-747 (Proposed) are filed from it.
Version2
Tagsnatural-sciences, mathematics
Cited as “paper” byNOTE-973 — Parish and Duraisamy — Non-Markovian closure for LES via Mori–Zwanzig
Cited as “source” byTHEORY-747 — In Fourier–Galerkin large-eddy simulation, a first-order finite-memory Mori–Zwanzig closure tracks filtered-DNS energy decay and dissipation on the viscous Burgers equation and on the incompressible Taylor–Green vortex, isotropic turbulence and channel flow about as well as dynamic Smagorinsky where that model is at home and better than Smagorinsky and the t-model on the transitional Taylor–Green vortex; the memory length that fits it is set by the cutoff, not by the flow alone, scaling in Burgers roughly as 0.2 over the spectral radius of the resolved variables' Jacobian, THEORY-760 — The finite-memory Mori–Zwanzig closure that Parish and Duraisamy take from Stinis, truncated at order m with one trapezoidal sub-interval and constant memory lengths, is a finite-dimensional Markovian augmentation: m + 1 auxiliary variables per resolved mode, each relaxing at rate 2/τ; at first order it replaces the memory integral by the kernel 2e^{−2s/τ₀} acting on the first-order term, which tends to τ₀ times that term, the t-model with t replaced by τ₀, when τ₀ is short against the resolved dynamics; its kernel is twice the true one at zero lag for every τ₀, so it is not exact even where the true memory is a single exponential, and nothing in the construction bounds its error

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Parish, E. J. & Duraisamy, K. (2017). Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism. Physical Review Fluids 2(1): 014604. doi:10.1103/PhysRevFluids.2.014604. Preprint: arXiv:1611.03311 (10 November 2016).

Read in full on 2026-10-20 (NOTE-973). The reading’s findings for the record are THEORY-760, on what the closure is (a finite Markovian augmentation with uncontrolled error), and THEORY-747, on how well it did against DNS.

Why this is here

A3 cited it as the turbulence literature’s own use of Mori–Zwanzig for unresolved scales. Bears on QUESTION-222.

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