Modelling and simulation of waves in three-layer porous media

Abstract. The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a weakly nonlinear Boussinesq-type diffusion equation for the wave height, with coefficients dependent on the conductivities and depths of each layer. In the limit of equal conductivities of all layers, the equation reduces to the single-layer result recorded in the literature. The model equations are numerically integrated in the case of an incident monochromatic wave hitting the layers. The results exhibit dissipation and also a downstream net height rise at infinity. Wave transmission coefficient in three-layer porous media with conductivity of mangrove is discussed. Numerically, propagation of an initial solitary wave through a porous medium shows the emergence of wave reflection and transmission that both evolve as permanent waves. Additionally we examine the impact of a solitary gravity wave on a porous medium breakwater.

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Modelling and Simulation of Waves in Three-Layer Porous Media

10.31227/osf.io/v928j ◽

2018 ◽

Author(s):

Sri Redjeki Pudjaprasetya

Keyword(s):

Porous Media ◽

Solitary Wave ◽

Gravity Waves ◽

Asymptotic Theory ◽

Wave Reflection ◽

Single Layer ◽

Monochromatic Wave ◽

Weakly Nonlinear ◽

The Impact ◽

Wave Transmission Coefficient

The propagation of gravity waves in an emerged three-layerporous medium is considered in this paper. Based onthe assumption that the flow can be described by Darcy’sLaw, an asymptotic theory is developed for small amplitudelong waves. This leads to a weakly nonlinear Boussinesq-typediffusion equation for the wave height, with coefficientsdepend on the conductivities and depths of each layer. In thelimit of equal conductivities of all layers, the equation reducesto the single layer result recorded in the literature. Themodel equations are numerically integrated in the case of anincident monochromatic wave hitting the layers. The resultsexhibit dissipation and also a downstream net height rise atinfinity. Wave transmission coefficient in three layer porousmedia with conductivity of mangrove is discussed. Numerically,propagation of an initial solitary wave through a porousmedium show the emergence of wave reflection and transmissionthat both evolve as permanent waves. Additionallywe examine the impact of a solitary gravity wave on a porousmedium breakwater.

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Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽

10.3390/math8091448 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1448

Author(s):

Anand Kumar ◽

Vinod K. Gupta ◽

Neetu Meena ◽

Ishak Hashim

Keyword(s):

Heat Transfer ◽

Porous Medium ◽

Prandtl Number ◽

Heat Transport ◽

Viscoelastic Fluid ◽

Rotational Speed ◽

Weakly Nonlinear ◽

Speed Modulation ◽

The Stability ◽

The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

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Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media

Entropy ◽

10.3390/e22111214 ◽

2020 ◽

Vol 22 (11) ◽

pp. 1214 ◽

Cited By ~ 1

Author(s):

Kun Yang ◽

Wei Huang ◽

Xin Li ◽

Jiabing Wang

Keyword(s):

Heat Transfer ◽

Porous Medium ◽

Porous Media ◽

Nusselt Number ◽

Double Layer ◽

Entropy Generation ◽

Single Layer ◽

Entropy Generation Rate ◽

Total Entropy ◽

Interfacial Radius

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.

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On Internal Waves Propagating across a Geostrophic Front

Journal of Physical Oceanography ◽

10.1175/jpo-d-18-0056.1 ◽

2019 ◽

Vol 49 (5) ◽

pp. 1229-1248 ◽

Cited By ~ 3

Author(s):

Qiang Li ◽

Xianzhong Mao ◽

John Huthnance ◽

Shuqun Cai ◽

Samuel Kelly

Keyword(s):

Internal Wave ◽

Internal Waves ◽

Wave Reflection ◽

Wave Theory ◽

Horizontal Shear ◽

Mixing Rate ◽

Reflection And Transmission ◽

Topographic Slope ◽

Virtual Boundary ◽

The Impact

AbstractReflection and transmission of normally incident internal waves propagating across a geostrophic front, like the Kuroshio or Gulf Stream, are investigated using a modified linear internal wave equation. A transformation from depth to buoyancy coordinates converts the equation to a canonical partial differential equation, sharing properties with conventional internal wave theory in the absence of a front. The equation type is determined by a parameter Δ, which is a function of horizontal and vertical gradients of buoyancy, the intrinsic frequency of the wave, and the effective inertial frequency, which incorporates the horizontal shear of background geostrophic flow. In the Northern Hemisphere, positive vorticity of the front may produce Δ ≤ 0, that is, a “forbidden zone,” in which wave solutions are not permitted. Thus, Δ = 0 is a virtual boundary that causes wave reflection and refraction, although waves may tunnel through forbidden zones that are weak or narrow. The slope of the surface and bottom boundaries in buoyancy coordinates (or the slope of the virtual boundary if a forbidden zone is present) determine wave reflection and transmission. The reflection coefficient for normally incident internal waves depends on rotation, isopycnal slope, topographic slope, and incident mode number. The scattering rate to high vertical modes allows a bulk estimate of the mixing rate, although the impact of internal wave-driven mixing on the geostrophic front is neglected.

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Throughflow and G-Jitter Effects on Oscillatory Convection in a Rotating Porous Medium

Advanced Science Engineering and Medicine ◽

10.1166/asem.2020.2580 ◽

2020 ◽

Vol 12 (6) ◽

pp. 781-791

Author(s):

S. H. Manjula ◽

Palle Kiran ◽

B. S. Bhadauria

Keyword(s):

Heat Transfer ◽

Porous Medium ◽

Heat Transport ◽

Landau Equation ◽

Nonlinear Stability Analysis ◽

Periodic Mode ◽

Ginzburg Landau ◽

Weakly Nonlinear ◽

Weakly Nonlinear Analysis ◽

The Impact

The impact of vertical throughflow and g-jitter effect on rotating porous medium is investigated. A feeble nonlinear stability analysis associate to complex Ginzburg-Landau equation (CGLE) has been studied. This weakly nonlinear analysis performed for a periodic mode of convection and quantified heat transport in terms of the Nusselt number, which is governed by the non-autonomous advanced CGLE. Each idea, rotation and throughflow is used as an external mechanism to the system either to extend or decrease the heat transfer. The results of amplitude and frequency of modulation on heat transport are analyzed and portrayed graphically. Throughflow has dual impact on heat transfer either to increase or decrease heat transfer in the system. Particularly the outflow enhances and inflow diminishes the heat transfer. High centrifugal rates promote heat transfer and low centrifugal rates diminish heat transfer. The streamlines and isotherms area portrayed graphically, the results of rotation and throughflow on isotherms shows convective development.

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A homogenised model for flow, transport and sorption in a heterogeneous porous medium

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.938 ◽

2021 ◽

Vol 932 ◽

Author(s):

L.C. Auton ◽

S. Pramanik ◽

M.P. Dalwadi ◽

C.W. MacMinn ◽

I.M. Griffiths

Keyword(s):

Porous Medium ◽

Porous Media ◽

Multiple Scales ◽

Effective Diffusivity ◽

Rectangular Lattice ◽

Mathematical Framework ◽

Anisotropic Flow ◽

Flow And Transport ◽

Soft Porous Media ◽

The Impact

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

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Closed-Form Expressions of Plane-Wave Reflection and Transmission Coefficients at a Planar Interface of Porous Media with a Normal Incident Fast P-Wave

Pure and Applied Geophysics ◽

10.1007/s00024-019-02383-1 ◽

2020 ◽

Vol 177 (6) ◽

pp. 2605-2617

Author(s):

Dongyong Zhou ◽

Xingyao Yin ◽

Zhaoyun Zong

Keyword(s):

Porous Media ◽

Plane Wave ◽

Closed Form ◽

Wave Reflection ◽

Planar Interface ◽

P Wave ◽

Reflection And Transmission Coefficients ◽

Reflection And Transmission ◽

Transmission Coefficients

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Diffusion limited mixing in heterogeneous porous media

10.5194/egusphere-egu21-15721 ◽

2021 ◽

Author(s):

Mayumi Hamada ◽

Pietro de Anna

Keyword(s):

Porous Medium ◽

Porous Media ◽

Flow Field ◽

Fast Diffusion ◽

Pore Scale ◽

Mixing Processes ◽

Local Flow ◽

Gaussian Shape ◽

Diffusion Limited ◽

The Impact

A pore-scale description of the transport and mixing processes is particularly relevant when looking at biological and chemical reactions. For instance, a microbial population growth is controlled by local concentrations of nutrients and oxygen, and chemical reaction are driven by molecular-scale concentration gradients. The heterogeneous flow field typically found in porous media results from the contrast of velocities that deforms and elongates the mixing fronts between solutes that often evolves through a lamella-like topology. For continuous Darcy type flow field a novel framework that describes the statistical distribution of concentration being transported was recently developed (Le Borgne et al., JFM 2015). In this model, concentrations in each lamella are distributed as a Gaussian-like profile which experiences diffusion in the transverse direction while the lamella is elongated by advection along the local flow direction. The evolving concentration field is described as the superposition of each lamella. We hypothesize that this novel view, while perfectly predicting the distribution of concentration for Darcy scale mixing processes, will breakdown when the processes description is at the pore scale. Indeed the presence of solid and impermeable boundaries prevents lamella concentration to diffuse freely according to the a Gaussian shape, and therefore changes the mixing front profile, the lamella superposition and elongation rules. Previous work (Hamada et al, PRF, 2020) demonstrated that the presence of solid boundaries leads to an enhanced diffusion and thus fast homogenization of concentrations. In a purely diffusive process the local mixing time is reduced by a factor of ten with respect to the continuous case and concentration gradient are dissipated exponentially fast while a power law decrease is observed in continuous medium. To investigate the impact of these mechanisms on mixing we developed an experimental set-up to visualize and quantify the displacement of a conservative tracer in a synthetic porous medium. The designed apparatus allows to obtain high resolution concentration measurements at the pore scale. We show that the resulting mixing measures, computed in terms of concentration probability density function and dilution index values, diverge qualitatively and quantitatively from what happens in a continuous domain. These observations suggest that description of pore-scale diffusion-limited mixing requires model that takes into account the confined nature of porous medium, otherwise we will tend to overestimate concentration value and neglect the fast diffusion dynamic taking place at microscopic level.

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Adhesion of Colloids and Bacteria to Porous Media: A Critical Review

Reviews of Adhesion and Adhesives ◽

10.7569/raa.2019.097314 ◽

2019 ◽

Vol 7 (4) ◽

pp. 417-460 ◽

Cited By ~ 1

Author(s):

Runwei Li ◽

Changfu Wei ◽

Hefa Cheng ◽

Gang Chen

Keyword(s):

Porous Medium ◽

Porous Media ◽

Bacterial Adhesion ◽

Fate And Transport ◽

Theoretical Models ◽

Water Interface ◽

Subsurface Soil ◽

Air Water Interface ◽

Surface Physicochemical Properties ◽

The Impact

Adhesion of colloids and bacteria to various surfaces is important for a variety of environmental phenomena including microbial biofouling and contamination prevention. Under saturated conditions, both colloids and bacteria have the opportunity to attach to porous medium surfaces. Under water unsaturated conditions or in the presence of the air-water interface, besides the porous medium surfaces, colloids and bacteria can also attach to the air-water interface, including the air-water-solid threephase interface. The magnitudes of adhesion of colloids and bacteria are correlated to the interactions of the colloids and bacteria with the surfaces, which are a function of their surface physicochemical properties. In this review, adhesion theories are revisited and adhesion of colloids and bacteria to porous media and the air-water interface is discussed. The interaction forces are quantified using various theoretical models including the DLVO models and used to interpret related adhesion. The impact of surfactants on colloid and bacterial adhesion is also discussed. The review also includes the implementation of the adhesion theory in interpreting colloid and bacterial fate and transport in the subsurface soil.

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Propagation of acoustic waves in layered porous media

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2007.1.020 ◽

2007 ◽

Vol 5 ◽

pp. 169-175

Author(s):

V.L. Dmitriev ◽

Е.А. Ponomareva

Keyword(s):

Porous Medium ◽

Porous Media ◽

Dispersion Relation ◽

Acoustic Waves ◽

Saturated Liquid ◽

Reflection And Transmission ◽

Transmission Coefficients ◽

Layered Porous Media ◽

The Media

The paper considers the processes of reflection and transmission acoustic waves at the interface between two porous media, saturated liquid or gas. The cases of a porous medium whose layers have the same porosity, but are saturated with different fluids. Based The dispersion relation and the conditions at the interface between the media are obtained reflection and transmission coefficients. The possibility determination of the parameters of the porous material and its saturating fluid based on the signal reflected from the interface.

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