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Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech. , vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$ , due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces. [ABSTRACT FROM AUTHOR]

Most existing models for fluid transportation within a single rock fracture tend to use a channel with two smooth parallel plates, whereas real fracture surfaces are usually rough and tortuous, which can produce a flow field significantly different from the smooth plate model. For fluid flow in a rough fracture, there are surface concave areas (SCA), where the fluid velocity is extremely low, contributing little to the fluid transportation. It is of great significance to quantitatively evaluate the impact of rough surfaces on fluid flow. Therefore, a numerical model for simulating Newtonian fluid through rough fractures is proposed, where synthetic surfaces are generated according to statistical analysis of natural rock fractures and can be quantified by several characteristic parameters. Equivalent hydraulic aperture (EHA) is proposed as one quantitative indicator for evaluating the impact of fracture roughness. Systematic studies were conducted for evaluating EHAs of rough fractures, which, combined with characteristic parameters of fractures, are used to build surrogate models for EHA prediction. It is found that the EHA is directly correlated with the fracture roughness, the mean mechanical aperture, and the standard deviation of aperture distribution. The developed surrogate models were verified to have a high accuracy for EHA prediction. Key words: rock fracture, roughness, tortuosity, equivalent hydraulic aperture (EHA), artificial neural network (ANN). La plupart des modeles existants de transport de fluide dans une fracture unique dans la roche utilisent generalement un canal avec deux plaques lisses paralleles, alors que les surfaces de fracture reelles sont generalement rugueuses et tortueuses, ce qui peut produire un champ d'ecoulement tres different du modele a plaques lisses. Pour un ecoulement de fluide dans une fracture rugueuses, il existe des zones concaves de surface (ZCS), ou la vitesse du fluide est extremement faible, contribuant peu au transport du fluide. Il est tres important d'evaluer quantitativement l'impact des surfaces rugueuses sur le debit des fluides. Par consequent, un modele numerique pour simuler le fluide newtonien a travers des fractures rugueuses est propose, ou les surfaces synthetiques sont generees selon l'analyse statistique des fractures naturelles de roches et peuvent etre quantifiees par plusieurs parametres caracteristiques. L'ouverture hydraulique equivalente (OHE) est proposee comme indicateur quantitatif permettant d'evaluer l'impact de la rugosite de fracture. Des etudes systematiques ont ete menees pour evaluer les OHE des fractures rugueuses, qui, combines aux parametres caracteristiques des fractures, permettent de creer des modeles de substitution pour la prediction des OHE. On constate que l'OHE est directement correlee a la rugosite de rupture, a l'ouverture mecanique moyenne et a l'ecart type de la distribution d'ouverture. Les modeles de substitution developpes ont ete verifies et ils ont une grande precision au niveau de la prediction de l'OHE. [Traduit par la Redaction] Mots-cles: fracture de roche, rugosite, tortuosite, ouverture hydraulique equivalente (OHE), reseau de neurones artificiels (RNA)., 1. Introduction Rock fractures in nature are rough and tortuous, and the fracture surfaces are found to be fractal and self-affine (Hsiung et al. 1993; Mandelbrot 1985; Odling 1994; Power [...]