Turbulence theories and statistical closure approaches

Zhou, Ye

doi:10.1016/j.physrep.2021.07.001

Cited by 69 publications

(47 citation statements)

References 1,141 publications

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“…A recent review by Zhou [12] comprehensively summarizes the history of spectral models. The study of constant density (single fluid) homogeneous isotropic turbulence via spectral models could be said to have begun with Kraichnan's direct interaction approximation (DIA) [13] expressed as integro-differential equations for the response function and correlation of velocity fluctuations [13][14][15].…”

Section: Background and Motivation For This Surveymentioning

confidence: 99%

The local wavenumber model for computation of turbulent mixing

Kurien

Pal

2022

Phil. Trans. R. Soc. A.

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We present an overview of the current status in the development of a two-point spectral closure model for turbulent flows, known as the local wavenumber (LWN) model. The model is envisioned as a practical option for applications requiring multi-physics simulations in which statistical hydrodynamics quantities such as Reynolds stresses, turbulent kinetic energy, and measures of mixing such as density-correlations and mix-width evolution, need to be captured with relatively high fidelity. In this review, we present the capabilities of the LWN model since it was first formulated in the early 1990s, for computations of increasing levels of complexity ranging from homogeneous isotropic turbulence, inhomogeneous and anisotropic single-fluid turbulence, to two-species mixing driven by buoyancy forces. The review concludes with a discussion of some of the more theoretical considerations that remain in the development of this model. This article is part of the theme issue ‘Scaling the turbulence edifice (part 2)’.

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Section: Background and Motivation For This Surveymentioning

confidence: 99%

The local wavenumber model for computation of turbulent mixing

Kurien

Pal

2022

Phil. Trans. R. Soc. A.

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“…Relaxing these assumptions changes the prediction on the subsequent free decay model, disconnecting the value of β from the initial conditions [56,58]. Recently, new models of the turbulent free-decay have emerged, following which the turbulence decay is governed by the energy-containing scales, close to the integral one, rather than by the asymptotic behaviour at large scales [52,[66][67][68][69]. According to these findings there would be then no universal decay regime, since the details of the spectral shape near the peak are related to the turbulence production mechanism.…”

Section: Evolution Of the Velocity Field In Decaying Turbulencementioning

confidence: 99%

Generation of gravitational waves from freely decaying turbulence

Auclair,

Caprini,

Cutting

et al. 2022

Preprint

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We study the stochastic gravitational wave background (SGWB) produced by freely decaying vortical turbulence in the early Universe. We thoroughly investigate the time correlation of the velocity field, and hence of the anisotropic stresses producing the gravitational waves. By direct numerical simulation, we show that the unequal time correlation function (UETC) of the Fourier components of the velocity field is Gaussian in the time difference, as predicted by the "sweeping" decorrelation model. We introduce a decorrelation model that can be extended to wavelengths around the integral scale of the flow. Supplemented with the evolution laws of the kinetic energy and of the integral scale, this provides a new model UETC of the turbulent velocity field consistent with the simulations. We discuss the UETC as a positive definite kernel, and propose to use the Gibbs kernel for the velocity UETC as a natural way to ensure positive definiteness of the SGWB. The SGWB is given by a 4-dimensional integration of the resulting anisotropic stress UETC with the gravitational wave Green's function. We perform this integration using a Monte Carlo algorithm based on importance sampling, and find that the result matches that of the direct numerical simulations. Furthermore, the SGWB obtained from the numerical integration and from the simulations show close agreement with a model in which the source is constant in time and abruptly turns off after a few eddy turnover times. Based on this assumption, we provide an approximate analytical form for the SGWB spectrum and its scaling with the initial kinetic energy and integral scale. Finally, we use our model and numerical integration algorithm to show that including an initial growth phase for the turbulent flow heavily influences the spectral shape of the SGWB. This highlights the importance of a complete understanding of the turbulence generation mechanism.

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“…It is difficult to overstate its importance -though many have tried -and the field has attracted attention from some of the great scientists of the last 150 years (see e.g. the excellent historical perspective of Zhou 2021).…”

Section: Introductionmentioning

confidence: 99%

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

Marston¹,

Tobias²

2022

Preprint

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Understanding inhomogeneous and anisotropic fluid flows require mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence. We review some recent developments in the theory of inhomogeneous and anisotropic turbulence, placing special emphasis on several kinds of quasilinear approximations and their corresponding statistical formulations. Aspects of quasilinear theory that have received insufficient attention in the literature are discussed, and open questions are framed.

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Turbulence theories and statistical closure approaches

Cited by 69 publications

References 1,141 publications

The local wavenumber model for computation of turbulent mixing

The local wavenumber model for computation of turbulent mixing

Generation of gravitational waves from freely decaying turbulence

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

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