Space-scale-time dynamics of liquid–gas shear flow

Thiesset, Fabien; Ménard, Thibaut; Dumouchel, Christophe

doi:10.1017/jfm.2020.1152

Cited by 3 publications

(41 citation statements)

References 51 publications

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“…(2.12) Equation (2.12) is the general expression for the unaveraged squared increments (δφ) 2 . It generalizes the equation derived by Thiesset et al ( , 2021 to the case where S d / = 0 and/or ∇ x • u / = 0. Compared with the equations detailed by Thiesset et al ( , 2021, where only the unsteady and the two transfer terms (in r and X space) were present, (2.12) reveals an additional source term which notably depends on the correlation between a quantity related to the bulk phase φ and a surface quantity, namely S d |∇ x φ|.…”

Section: General Two-point Equationsmentioning

confidence: 72%

“…Here, the main originality of the present work is that this morphological descriptor is supplemented by an exact transport equation which allows the different physical processes acting on the iso-scalar volumes to be characterized. It generalizes the equation proposed by and Thiesset, Ménard & Dumouchel (2021) firstly dedicated to two-phase flows, to cases where the interface possesses an intrinsic displacement speed (as for premixed flames or diffusive scalars). The machinery for obtaining two-point statistical equations is the same as the one used to derive the scale-by-scale budgets of the dynamical or scalar field (see Hill (2002) and Danaila, Antonia & Burattini (2004), among others).…”

Section: Introductionmentioning

confidence: 75%

“…Here, H and G are the mean and Gaussian curvatures, respectively; • s is used to denote the surface area weighted average. Berryman (1987) and Thiesset et al (2021) proved that (2.17) remains valid in anisotropic media by applying an additional angular average to (δφ) 2 R . When |r| → ∞, Thiesset et al ( , 2021 showed that lim…”

Section: General Two-point Equationsmentioning

confidence: 98%

“…For scales larger than the reach, (δφ) 2 R contains information about the morphology of the structures under hand. In this respect, Adler et al (1990), Torquato (2002 and Thiesset et al (2021) showed that the scale distribution φ + φ − R or (δφ) 2 R widens when the morphological content (or its tortuousness) of a given set increases. Similarly, the fractal facets of aggregates are often appraised by use of the correlation function of the phase indicator at intermediate scales (see, e.g.…”

Section: General Two-point Equationsmentioning

confidence: 99%

“…Because the flows under consideration can be turbulent, it is worth supplementing (2.9) and (2.12) by some averaging operators. The choice of a specific average generally depends on the flow situations (Hill 2002;Thiesset et al , 2021. One can simply apply an ensemble average operator, noted • E , which has the advantage of commuting with time t, spatial X and scale r derivatives.…”

Section: General Two-point Equationsmentioning

confidence: 99%

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Structure of iso-scalar sets

et al. 2022

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An analytical framework is proposed to explore the structure and kinematics of iso-scalar fields. It is based on a two-point statistical analysis of the phase indicator field which is used to track a given iso-scalar volume. The displacement speed of the iso-surface, i.e. the interface velocity relative to the fluid velocity, is explicitly accounted for, thereby generalizing previous two-point equations dedicated to the phase indicator in two-phase flows. Although this framework applies to many transported quantities, we here focus on passive scalar mixing. Particular attention is paid to the effect of Reynolds (the Taylor based Reynolds number is varied from 88 to 530) and Schmidt numbers (in the range 0.1 to 1), together with the influence of flow and scalar forcing. It is first found that diffusion in the iso-surface tangential direction is predominant, emphasizing the primordial influence of curvature on the displacement speed. Second, the appropriate normalizing scales for the two-point statistics at either large, intermediate and small scales are revealed and appear to be related to the radius of gyration, the surface density and the standard deviation of mean curvature, respectively. Third, the onset of an intermediate ‘scaling range’ for the two-point statistics of the phase indicator at sufficiently large Reynolds numbers is observed. The scaling exponent complies with a fractal dimension of 8/3. A scaling range is also observed for the transfer of iso-scalar fields in scale space whose exponent can be estimated by simple scaling arguments and a recent closure of the Corrsin equation. Fourth, the effects of Reynolds and Schmidt numbers together with flow or scalar forcing on the different terms of the two-point budget are highlighted.

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Section: General Two-point Equationsmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 75%

Section: General Two-point Equationsmentioning

confidence: 98%

Section: General Two-point Equationsmentioning

confidence: 99%

Section: General Two-point Equationsmentioning

confidence: 99%

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Structure of iso-scalar sets

et al. 2022

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Morphology of contorted fluid structures

Dumouchel

Thiesset

Ménard

2022

International Journal of Multiphase Flow

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Structure of iso-density sets in supersonic isothermal turbulence

Thiesset¹,

Federrath²

2023

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Context. The gas density structure of the cold molecular phase of the interstellar medium is the main controller of star formation. Aims. A theoretical framework is proposed to describe the structural content of the density field in isothermal supersonic turbulence. Methods. It makes use of correlation and structure functions of the phase indicator field defined for different iso-density values. The relations between these two-point statistics and the geometrical features of iso-density sets such as the volume fraction, the surface density, the curvature, and fractal characteristics are provided. An exact scale-by-scale budget equation is further derived revealing the role of the turbulent cascade and dilation on the structural evolution of the density field. Although applicable to many flow situations, this tool is here first invoked for characterising supersonic isothermal turbulence, using data from the currently best-resolved numerical simulation. Results. We show that iso-density sets are surface fractals rather than mass fractals, with dimensions that markedly differ between dilute, neutral, and dense regions. The surface–size relation is established for different iso-density values. We further find that the turbulent cascade of iso-density sets is directed from large towards smaller scales, in agreement with the classical picture that turbulence acts to concentrate more surface into smaller volumes. Intriguingly, there is no range of scales that complies with a constant transfer rate in the cascade, challenging our fundamental understanding of interstellar turbulence. Finally, we recast the virial theorem in a new formulation drawing an explicit relation between the aforementioned geometrical measures and the dynamics of iso-density sets.

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Space-scale-time dynamics of liquid–gas shear flow

Abstract: Abstract

Cited by 3 publications

References 51 publications

Structure of iso-scalar sets

Structure of iso-scalar sets

Morphology of contorted fluid structures

Structure of iso-density sets in supersonic isothermal turbulence

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