Since 1963
ARTICLE
Laminar flow past the bottom with obstacles - a porous medium approximation
1
Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland
2
Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland
Submission date: 2021-09-17
Final revision date: 2022-05-11
Acceptance date: 2022-06-20
Online publication date: 2022-07-14
Publication date: 2022-07-30
Corresponding author
Włodzimierz Bielski
Theoretical Geophysics, Institute of Geophysics, Księcia Janusza 64, 01-452, Warszawa, Poland
Theoretical Geophysics, Institute of Geophysics, Księcia Janusza 64, 01-452, Warszawa, Poland
Journal of Theoretical and Applied Mechanics 2022;60(3):509-520
KEYWORDS
TOPICS
ABSTRACT
We provide a model of a stationary laminar flow in a channel at the bottom of which plants
grow in a dense layer. Since this layer of plants is dense, we treat it as a porous medium
and we propose to describe the flow in such a medium by Brinkman’s equation. The flow
in the fluid layer located above (infiltrated by water) the layers of plants is described by
the Stokes equation. We show that such a model gives results consistent with experimental
observations. We indicate also that this new model complements the previously given model
in which the benthonic plants were considered as a suspension, so the previous model referred
to the channel at the bottom of which the plants grew rare. For high permeability of the
porous medium, we arrive at the results obtained for the medium filled with a liquid with a
suspension.
REFERENCES (25)
1.
Auriault J.-L., 2009, On the domain of validity of Brinkman’s equation, Transport in Porous Media, 79, 215-223.
2.
Bielski W., Wojnar R., 2008, Homogenisation of flow through double scale porous medium, [In:] Analytic Methods of Analysis and Differential Equations: AMADE 2006, A.A. Kilbas and S.V. Rogosin (Edit.), Cambridge Scientific Publishers, 27-44.
3.
Bielski W., Wojnar R., 2021, Long gravity waves in a canal with a corrugated bottom in the asymptotic description, Journal of Theoretical and Applied Mechanics, 59, 3, 443-454.
4.
Brinkman H.C., 1949, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Applied Scientific Research, 1, 1, 27-34.
5.
Caroppi G., Västilä K., Järvelä J., Rowiński P.M., Giugni M., 2019, Turbulence at water-vegetation interface in open channel flow: Experiments with natural-like plants, Advances in Water Resources, 127, 180-191.
6.
D’Ippolito A., Calomino F., Alfonsi G., Lauria A., 2021, Flow resistance in open channel due to vegetation at reach scale: A review, Water, 13, 116.
7.
D’Ippolito A., Lauria A., Alfonsi G., Calomino F., 2019, Investigation of flow resistance exerted by rigid emergent vegetation in open channel, Acta Geophysica, 67, 971-986.
8.
Evangelos K., 2012, The impact of vegetation on the characteristics of the flow in an inclined open channel using the PIV method, Water Resources and Ocean Science, 1, 1, 1-6.
9.
Ghisalberti M., Nepf H., 2006, The structure of the shear layer in flows over rigid and flexible canopies, Environmental Fluid Mechanics, 6, 3, 277-301.
10.
Huai W., Wang W., Zeng Y., 2013, Two-layer model for open channel flow with submerged flexible vegetation, Journal of Hydraulic Research, 51, 6, 708-718.
11.
Joodi A.S., Sizaret S., Binet S., Bruand A., Alberic P., Lepiller M., 2010, Development of a Darcy-Brinkman model to simulate water flow and tracer transport in a heterogeneous karstic aquifer (Val d’Orléans, France), Hydrogeology Journal, 18, 2, 295-309.
12.
Kubrak E., Kubrak J., Kiczko A., 2015, Experimental investigation of kinetic energy and momentum coefficients in regular channels with stiff and flexible elements simulating submerged vegetation, Acta Geophysica, 63, 5, 1405-1422.
13.
Kubrak E., Kubrak J., Rowiński P.M., 2012, Influence of a method of evaluation of the curvature of flexible vegetation elements on vertical distributions of flow velocities, Acta Geophysica, 60, 4, 1098-1119.
14.
Kubrak E., Kubrak J., Rowiński P.M., 2013, Application of one-dimensional model to calculate water velocity distributions over elastic elements simulating Canadian waterweed plants (Elodea canadensis), Acta Geophysica, 61, 1, 194-210.
15.
Malevich A.E., Mityushev V., Adler P., 2006, Stokes flow through a channel with wavy walls, Acta Mechanica, 182, 151-182.
16.
Marchenko V.A., Khruslov E.Ya., 1974, Boundary Value Problems in Domains with a Fine Grained Boundary, Naukova Dumka, Kiev.
17.
Morad M.R., Khalili A., 2009, Transition layer thickness in a fluid-porous medium of multi-sized sperical beads, Experiments in Fluids, 46, 323-330.
18.
Nepf H.M., 2012, Hydrodynamics of vegetated channels, Journal of Hydraulic Research, 50, 3, 262-279.
19.
Nikora V., Goring D., McEwan I., Griffiths G., 2001, Spatially averaged open-channel flow over rough bed, Journal of Hydraulic Engineering, 127, 2, 123-133.
20.
Pu J.H., Hussain A., Guo Y.K., Vardakastanis N., Hanmaiahgari P.R., Lam D., 2019, Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction, Water Science and Engineering, 12, 2, 121-128.
21.
Tang X., 2019, Evaluating two-layer models for velocity profiles in open-channels with submerged vegetation, Journal of Geoscience and Environment Protection, 7, 68-80.
22.
Valdes-Parada F.J., Ochoa-Tapia J.A., Alvarez-Ramirez J., 2007, On the effective viscosity for the Darcy-Brinkman equation, Physica A, Statistical Mechanics and its Applications, 385, 1, 69-79.
23.
Wojnar R., Bielski W., 2015, Laminar flow past the bottom with obstacles – a suspension approximation, Bulletin of the Polish Academy of Sciences, 63, 3, 685-695.
24.
Yang W., Choi S.-U., 2009, Impact of stem flexibility on mean flow and turbulence structure in depth-limited open channel flows with submerged vegetation, Journal of Hydraulic Research, 47, 4, 445-454.
25.
Yang W., Choi S.-U., 2010, A two-layer approach for depth-limited open-channel flows with submerged vegetation, Journal of Hydraulic Research, 48, 4, 466-475.
| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
