Wave-induced Lagrangian drift in a porous seabed

The mean drift in a porous seabed caused by long surface waves in the overlying fluid is investigated theoretically. We use a Lagrangian formulation for the fluid and the porous bed. For the wave field we assume inviscid flow, and in the seabed, we apply Darcy’s law. Throughout the analysis, we assume that the long-wave approximation is valid. Since the pressure gradient is nonlinear in the Lagrangian formulation, the balance of forces in the porous bed now contains nonlinear terms that yield the mean horizontal Stokes drift. In addition, if the waves are spatially damped due to interaction with the underlying bed, there must be a nonlinear balance in the fluid layer between the mean surface gradient and the gradient of the radiation stress. This causes, through continuity of pressure, an additional force in the porous layer. The corresponding drift is larger than the Stokes drift if the depth of the porous bed is more than twice that of the fluid layer. The interaction between the fluid layer and the seabed can also cause the waves to become temporally attenuated. Again, through nonlinearity, this leads to a horizontal Stokes drift in the porous layer, but now damped in time. In the long-wave approximation only the horizontal component of the permeability in the porous medium appears, so our analysis is valid for a medium that has different permeabilities in the horizontal and vertical directions. It is suggested that the drift results may have an application to the transport of microplastics in the porous oceanic seabed.

Stokes drift through corals

Motivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

Model of Flow Resistance Coefficient for a Fragment of a Porous Material Deposit with Skeletal Structure

The hydrodynamic conditions resulting from the permeability of porous materials are based not only on the assessment of the gas flow through these materials, but also the losses related to the pressure energy in this flow. Flow resistance is a direct measure of this loss. The aim of this experimental research was to evaluate the flow resistance of the porous material in relation to the gas flow. The research was carried out on a material with a slit-porous structure. The tests were carried out on a system for measuring gas permeability under the conditions of gas bubbling through the char. The issue of the total pressure drop process in the porous bed was considered in the Reynolds number category. The coefficient of flow resistance for the char was determined and the value of this coefficient was compared with the gas stream, and an experimental evaluation of the total pressure drop on the porous bed was made. The novelty of this article is the determination of the tortuosity and the gas permeability coefficient for a solid of any shape—a rigid skeleton.

Drying of Sisal Fiber: A Numerical Analysis by Finite-Volumes

Vegetable fibers have inspired studies in academia and industry, because of their good characteristics appropriated for many technological applications. Sisal fibers (Agave sisalana variety), when extracted from the leaf, are wet and must be dried to reduce moisture content, minimizing deterioration and degradation for long time. The control of the drying process plays an important role to guarantee maximum quality of the fibers related to mechanical strength and color. In this sense, this research aims to evaluate the drying of sisal fibers in an oven with mechanical air circulation. For this purpose, a transient and 3D mathematical model has been developed to predict moisture removal and heating of a fiber porous bed, and drying experiments were carried out at different drying conditions. The advanced model considers bed porosity, fiber and bed moisture, simultaneous heat and mass transfer, and heat transport due to conduction, convection and evaporation. Simulated drying and heating curves and the hygroscopic equilibrium moisture content of the sisal fibers are presented and compared with the experimental data, and good concordance was obtained. Results of moisture content and temperature distribution within the fiber porous bed are presented and discussed in details. It was observed that the moisture removal and temperature kinetics of the sisal fibers were affected by the temperature and relative humidity of the drying air, being more accentuated at higher temperature and lower relative humidity, and the drying process occurred in a falling rate period.

The Effects of Periodicity Assumptions in Porous Media Modelling

The effects of periodicity assumptions on the macroscopic properties of packed porous beds are evaluated using a cascaded Lattice-Boltzmann method model. The porous bed is modelled as cubic and staggered packings of mono-radii circular obstructions where the bed porosity is varied by altering the circle radii. The results for the macroscopic properties are validated using previously published results. For unsteady flows, it is found that one unit cell is not enough to represent all structures of the fluid flow which substantially impacts the permeability and dispersive properties of the porous bed. In the steady region, a single unit cell is shown to accurately represent the fluid flow across all cases studied

Gravity induced vertical motion of dense fluids into saturated granular beds

<p>Gravity currents propagating over and within porous layers occurs in natural environments and in industrial processes. The particular modes by which the dense fluid flows into the porous layer is a subject that is not sufficiently understood. To overcome this research gap, we conducted laboratory experiments aimed at describing experimentally the dynamics of the drainage flow.</p><p>The experiments were conducted in a horizontal channel with a rectangular cross-section. The channel is 3.0 m long, 0.05 m wide. The porous bottom was composed of 5 cm and 10 cm layers of 3 mm borosilicate spheres – unimodal bed – and of a mixture of 3 mm (50% in weight) and 5 mm spheres (50%) – bi-modal bed. The porosity of the unimodal bed ranged between 0.60 and 0.64 (compatible with loose packing). The porosity of the bi-modal bed ranged between 0.61 and 0.65. All gravity currents were generated by releasing suddenly denser fluid locked by a thin vertical barrier placed at 0.2 m from the channel end. The dense fluid consists in a mixture of freshwater and salt (coloured with Rhodamine) while the ambient fluid is a solution of freshwater and ethanol. The density difference between the ambient fluid and the current, and the need to maintain the same refractive index, determine the amount of salt and alcohol added in each mixture. Here we report the findings of currents with a reduced gravity of 0.06 ms<sup>-2</sup>.</p><p>Each experiment was recorded by an high-speed camera with a frame-rate of 386 Hz and a resolution of 2320 x 1726 pxxpx. Measurements were based on light absorption techniques: a LED light panel 0.3 m high and 0.61 m long was used as back illumination. All images were calibrated to ascribe, pixel by pixel, a concentration value from a 8 bit gray level. Different calibrations were performed for the porous layer and for the surface current.</p><p>Results show that, in the slumping phase, the gravity current flows with velocities compatible with those over rough beds. As the current progresses further attenuation of momentum is noticed owing to mass loss to the porous bed.</p><p>The flow in the porous bed reveals plume instability akin to a Saffman-Taylor instability. The growth of the plumes seems independent from the initial fluid height in both types of porous beds. The wavelength and the growth rate of the plumes depends on the bed material. Plumes grow faster in the case of the bi-modal bed and the wavelength of the bi-modal bed is about 1.5 as that of the unimodal bed. It is hypothesised that the gravity-induced porous flow is best parameterized by a Péclet number defined as a ratio of dispersive (mechanical diffusion) and advective modes of transport. Smaller wavelengths and slower growths are attained for stronger dispersion, characterisitic of the unimodal bed. For bimodal beds, permeability is larger, and thus also advection. This causes the flow to concentrate in faster growing but farther apart plumes.</p><p> </p><p>This research was funded by national funds through Portuguese Foundation for Science and Technology (FCT) project PTDC/CTA-OHR/30561/2017 (WinTherface).</p>