The hydrodynamic genesis of linear karren patterns

Bertagni, Matteo Bernard; Camporeale, Carlo Vincenzo

doi:10.1017/jfm.2021.39

Cited by 6 publications

(26 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…then the representation (4) satisfies the Stokes equations with the required boundary conditions (1). We solve (7) by discretizing γ and Γ at equispaced collocation points, and then replacing the integrals with quadrature rules. This results in a linear system with a mesh-independent condition number, and it is solved iteratively with GMRES.…”

Section: Boundary Integral Equation and Cauchy Integral Formulationmentioning

confidence: 99%

“…The overall accuracy of our method is determined by the quadrature rule applied to equation (7). Since we have written the Stokes double-layer potential velocity (11), deformation tensor (12), and vorticity (13) as a sum of Cauchy integrals and their derivatives, the overall accuracy hinges on the computation of a general Cauchy integral…”

Section: Quadrature For Cauchy Integralsmentioning

confidence: 99%

“…Flow-induced erosion acts across a range of scales in the natural world, from massive geological structures sculpted by wind or water [1,28,20,32,19], to mesoscopic patterns formed by surface or internal flows [6,7,36], and down to granular and porous networks slowly disintegrating in groundwater flows [10,34,22,15,8,11,37]. The associated nonlinear feedback between changing shapes and the surrounding flows can imprint across all of these scales, affecting large-scale features as well as small-scale ones, such as the microstructure of porous materials.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

How fluid-mechanical erosion creates anisotropic porous media

Moore¹,

Cherry²,

Chiu³

et al. 2022

Preprint

View full text Add to dashboard Cite

Using a Cauchy integral formulation of the boundary integral equations, we simulate the erosion a porous medium comprised of up to 100 solid bodies embedded in a Stokes flow. The grains of the medium are resolved individually and erode under the action of surface shear stress. Through nonlinear feedback with the surrounding flow fields, microscopic changes in grain morphology give way to larger-scale features in the medium such as channelization. The Cauchy-integral formulation and associated quadrature formulas enable us to resolve dense configurations of nearly contacting bodies. We observe substantial anisotropy to develop over the course of erosion; that is, the configurations that result from erosion generally permit flow in the longitudinal direction more easily than in the transverse direction by up to a factor of six. These results suggest that the erosion of solid material from groundwater flows may contribute to previously observed anisotropy of natural porous media.

show abstract

Section: Boundary Integral Equation and Cauchy Integral Formulationmentioning

confidence: 99%

Section: Quadrature For Cauchy Integralsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

How fluid-mechanical erosion creates anisotropic porous media

Moore¹,

Cherry²,

Chiu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…2005; Camporeale & Ridolfi 2012) and flutings in limestone caves (Camporeale 2015; Bertagni & Camporeale 2017; Ledda et al. 2021) and due to solidification and melting of water (Camporeale 2015), while physical or chemical erosion leads to scallops (Meakin & Jamtveit 2010) or linear karren (Bertagni & Camporeale 2021) patterns. Gravity currents, widely encountered in environmental fluid dynamics, are flows driven by gravity differences typically imputed to the presence of one phase heavier than the other which spreads on a substrate.…”

Section: Introductionmentioning

confidence: 99%

“…Such formation of elongated structures along the streamwise direction is also typical of contact-line-driven instabilities, often called fingering, and occurs when a fluid spreads on a dry substrate (Oron, Davis & Bankoff 1997;Kondic 2003;Weinstein & Ruschak 2004;Craster & Matar 2009). Such patterns are identified as the physical origin for several geological structures such as stalactites (Short et al 2005;Camporeale & Ridolfi 2012) and flutings in limestone caves (Camporeale 2015;Bertagni & Camporeale 2017;) and due to solidification and melting of water (Camporeale 2015), while physical or chemical erosion leads to scallops (Meakin & Jamtveit 2010) or linear karren (Bertagni & Camporeale 2021) patterns. Gravity currents, widely encountered in environmental fluid dynamics, are flows driven by gravity differences typically imputed to the presence of one phase heavier than the other which spreads on a substrate.…”

Section: Introductionmentioning

confidence: 99%

Gravity-driven coatings on curved substrates: a differential geometry approach

et al. 2022

View full text Add to dashboard Cite

Drainage and spreading processes in thin liquid films have received considerable attention in the past decades. Yet, our understanding of three-dimensional cases remains sparse, with only a few studies focusing on flat and axisymmetric substrates. Here, we exploit differential geometry to understand the drainage and spreading of thin films on curved substrates, under the assumption of negligible surface tension and hydrostatic gravity effects. We develop a solution for the drainage on a local maximum of a generic substrate. We then investigate the role of geometry in defining the spatial thickness distribution via an asymptotic expansion in the vicinity of the maximum. Spheroids with a much larger (respectively smaller) height than the equatorial radius are characterized by an increasing (respectively decreasing) coating thickness when moving away from the pole. These thickness variations result from a competition between the variations of the substrate's slope and mean curvature. The coating of a torus presents larger thicknesses and a faster spreading on the inner region than on the outer region, owing to the different curvatures in these two regions. In the case of an ellipsoid with three different axes, spatial modulations in the drainage solution are observed as a consequence of a faster drainage along the short principal axis, faithfully reproduced by a three-dimensional asymptotic solution. Leveraging the conservation of mass, an analytical solution for the average spreading front is obtained. The solutions are in agreement with numerical simulations and experimental measurements obtained from the coating of a curing polymer on diverse substrates.

show abstract