Temporal dynamics of the alignment of the turbulent stress and strain rate

Ballouz, Joseph G.; Johnson, Perry L.; Ouellette, Nicholas T.

doi:10.1103/physrevfluids.5.114606

Temporal dynamics of the alignment of the turbulent stress and strain rate

Journal Article · Fri Nov 13 00:00:00 EST 2020 · Physical Review Fluids (Online)

DOI:https://doi.org/10.1103/physrevfluids.5.114606· OSTI ID:1850299

Ballouz, Joseph G. ^[1]; Johnson, Perry L. ^[2]; ^[3]

Stanford Univ., CA (United States); OSTI
Univ. of California, Irvine, CA (United States)
Stanford Univ., CA (United States)

We report that the flux of energy between scales in turbulence can be cast as the result of the interaction between a turbulent stress and a rate of strain. Efficient energy transfer requires that these two tensors be oriented properly relative to each other, but previous work has shown that the instantaneous alignment between them is poor. Here, we consider the temporal dynamics of this alignment in a direct numerical simulation of isotropic turbulence. We show that the orientation of the stress lags behind that of the strain rate, both at a single location and along trajectories. However, the timescale of the reorientation of the stress in these cases does not follow the expected dynamical scaling with length scale. To capture the proper dynamical scaling, we reformulate the energy flux between scales using the right Cauchy-Green strain tensor and the second Piola-Kirchhoff stress tensor. Our results highlight the key role played by the deformation of fluid elements in the physics of the energy cascade, and suggest that their irreversible deformation is a Lagrangian manifestation of the cascade's broken time-reversal symmetry.

View Accepted Manuscript (DOE)

Research Organization:: Stanford Univ., CA (United States); Univ. of California, Irvine, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0002373

OSTI ID:: 1850299

Journal Information:: Physical Review Fluids (Online), Journal Name: Physical Review Fluids (Online) Journal Issue: 11 Vol. 5; ISSN 2469-990X

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Temporal dynamics of the alignment of the turbulent stress and strain rate

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