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2 Journal of Theoretical and Applied Mechanics

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Laminar flow past the bottom with obstacles - a porous medium approximation

Bielski Włodzimierz, Wojnar Ryszard

Journal of Theoretical and Applied Mechanics

2022

Vol. 60 nr 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.

Long gravity waves in a canal with a corrugated bottom in the asymptotic description

Bielski Włodzimierz, Wojnar Ryszard

Journal of Theoretical and Applied Mechanics

2021

Vol. 59 nr 3

443–-454

We consider the classic Lagrange long gravitational wave of a homogeneous incompressible fluid in a shallow canal with a corrugated bottom. We use the asymptotic expansion method to find the effective depth of a one-dimensional canal and, hence, the effective wave velocity. A flow in a two-dimensional tank with a corrugated bottom is also studied by this method.