Laminar flow past the bottom with obstacles - a porous medium approximation
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Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland
Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland
Włodzimierz Bielski   

Theoretical Geophysics, Institute of Geophysics, Księcia Janusza 64, 01-452, Warszawa, 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
Journal of Theoretical and Applied Mechanics 2022;60(3):509–520
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.
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