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Statistical Dynamics and Subgrid Modelling of Turbulence: From Isotropic to Inhomogeneous
by
Jorgen S. Frederiksen
Jorgen S. Frederiksen 1,*,
Vassili Kitsios
Vassili Kitsios 1
and
Terence J. O’Kane
Terence J. O’Kane 2
1
CSIRO Environment, Aspendale, Melbourne 3195, Australia
2
CSIRO Environment, Hobart 7004, Australia
*
Author to whom correspondence should be addressed.
Atmosphere 2024, 15(8), 921; https://doi.org/10.3390/atmos15080921 (registering DOI)
Submission received: 30 June 2024
/
Revised: 20 July 2024
/
Accepted: 26 July 2024
/
Published: 31 July 2024
Abstract
Turbulence is the most important, ubiquitous, and difficult problem of classical physics. Feynman viewed it as essentially unsolved, without a rigorous mathematical basis to describe the statistical dynamics of this most complex of fluid motion. However, the paradigm shift came in 1959, with the formulation of the Eulerian direct interaction approximation (DIA) closure by Kraichnan. It was based on renormalized perturbation theory, like quantum electrodynamics, and is a bare vertex theory that is manifestly realizable. Here, we review some of the subsequent exciting achievements in closure theory and subgrid modelling. We also document in some detail the progress that has been made in extending statistical dynamical turbulence theory to the real world of interactions with mean flows, waves and inhomogeneities such as topography. This includes numerically efficient inhomogeneous closures, like the realizable quasi-diagonal direct interaction approximation (QDIA), and even more efficient Markovian Inhomogeneous Closures (MICs). Recent developments include the formulation and testing of an eddy-damped Markovian anisotropic closure (EDMAC) that is realizable in interactions with transient waves but is as efficient as the eddy-damped quasi-normal Markovian (EDQNM). As a similarly efficient closure, the realizable eddy-damped Markovian inhomogeneous closure (EDMIC) has been developed. Moreover, we present subgrid models that cater to the complex interactions that occur in geophysical flows. Recent progress includes the determination of complete sets of subgrid terms for skilful large-eddy simulations of baroclinic inhomogeneous turbulent atmospheric and oceanic flows interacting with Rossby waves and topography. The success of these inhomogeneous closures has also led to further applications in data assimilation and ensemble prediction and generalization to quantum fields.
Share and Cite
MDPI and ACS Style
Frederiksen, J.S.; Kitsios, V.; O’Kane, T.J.
Statistical Dynamics and Subgrid Modelling of Turbulence: From Isotropic to Inhomogeneous. Atmosphere 2024, 15, 921.
https://doi.org/10.3390/atmos15080921
AMA Style
Frederiksen JS, Kitsios V, O’Kane TJ.
Statistical Dynamics and Subgrid Modelling of Turbulence: From Isotropic to Inhomogeneous. Atmosphere. 2024; 15(8):921.
https://doi.org/10.3390/atmos15080921
Chicago/Turabian Style
Frederiksen, Jorgen S., Vassili Kitsios, and Terence J. O’Kane.
2024. "Statistical Dynamics and Subgrid Modelling of Turbulence: From Isotropic to Inhomogeneous" Atmosphere 15, no. 8: 921.
https://doi.org/10.3390/atmos15080921
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