Convective shutdown in a porous medium at high Rayleigh number

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra\mathit{Ra}. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu\mathit{Nu} from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu=2.75+0.0069Ra\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO2{\mathrm{CO} }_{2} in a saline aquifer is discussed

Internally heated porous convection: an idealised model for Enceladus' hydrothermal activity

Recent planetary data and geophysical modelling suggest that hydrothermal activity is ongoing under the ice crust of Enceladus, one of Saturn's moons. According to these models, hydrothermal flow in the porous, rocky core of the satellite is driven by tidal deformation that induces dissipation and volumetric internal heating. Despite the effort in the modelling of Enceladus' interior, systematic understanding---and even basic scaling laws---of internally-heated porous convection and hydrothermal activity are still lacking. In this article, using an idealised model of an internally-heated porous medium, we explore numerically and theoretically the flows that develop close and far from the onset of convection. In particular, we quantify heat-transport efficiency by convective flows as well as the typical extent and intensity of heat-flux anomalies created at the top of the porous layer. With our idealised model, we derive simple and general laws governing the temperature and hydrothermal velocity that can be driven in the oceans of icy moons. In the future, these laws could help better constraining models of the interior of Enceladus and other icy satellites.Comment: 23 pages, 13 figure

High-Rayleigh-number convection in porous-fluid layers

We present a numerical study of convection in a horizontal layer comprising a fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven by a vertical, destabilising temperature difference applied across the whole system, as in the canonical Rayleigh-B\'enard problem. Numerical simulations are carried out using a single-domain formulation of the two-layer problem based on the Darcy-Brinkman equations. We explore the dynamics and heat flux through the system in the limit of large Rayleigh number, but small Darcy number, such that the flow exhibits vigorous convection in both the porous and the unconfined fluid regions, while the porous flow still remains strongly confined and governed by Darcy's law. We demonstrate that the heat flux and average thermal structure of the system can be predicted using previous results of convection in individual fluid or porous layers. We revisit a controversy about the role of subcritical "penetrative convection" in the porous medium, and confirm that such induced flow does not contribute to the heat flux through the system. Lastly, we briefly study the temporal coupling between the two layers and find that the turbulent fluid convection above acts as a low-pass filter on the longer-timescale variability of convection in the porous layer.Comment: Accepted for publication in Journal of Fluid Mechanics, 25 pages, 13 figure

Convective shutdown in a porous medium at high Rayleigh number

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra\mathit{Ra}. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu\mathit{Nu} from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu=2.75+0.0069Ra\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO2{\mathrm{CO} }_{2} in a saline aquifer is discussed

Flow-induced compaction of a deformable porous medium.

Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.D.R.H. was supported by a Killam Postdoctoral Fellowship and a Research Fellowship at Gonville and Caius College, Cambridge. During the experimental part of this project, J.S.N. was supported by the division of Engineering Science, University of Toronto. J.A.N. is partly supported by a Royal Society University Research Fellowship.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.02311

One-dimensional compression of a saturated elastoviscoplastic medium

A theoretical and experimental study is presented of the one-dimensional compression of a networked suspension. Particular attention is given to relatively rapid compression where we extend previous works by including an elastoviscoplastic constitutive relation. Solutions of a one-dimensional model are presented, and asymptotic limits explored, for compressions controlling either displacement or load. The results are compared to complementary laboratory experiments using cellulose fiber suspensions, with the material functions appearing in the model calibrated by independent experiments. Measurements of load and local solid velocity as a function of displacement during compression and unloading gauge the importance of elastic effects. The comparison between experiment and theory is satisfying, demonstrating a dramatic improvement over existing inelastic constitutive models in reproducing the observed differential spatial compaction

Optimal face-to-face coupling for fast self-folding kirigami

Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer folding times in the presence of fluctuations. Here, we study the effect of rotational coupling between levels on the self-folding of two-level kirigami designs driven by thermal noise in a fluid. Naturally present due to hydrodynamic resistance, we find that optimization of this coupling as control parameter can significantly improve a structure's self-folding rate and yield