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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.

On the turbulent boundary layer of a dry granular avalanche down an incline. II – closure model and numerical simulations

Fang C.

Journal of Theoretical and Applied Mechanics

2016

Vol. 54 nr 4

1245--1256

Dynamic responses of the closure relations, specific turbulent Helmholtz free energy and turbulent viscosity are postulated followed by experimental calibrations. The established closure model is applied to analyses of a gravity-driven stationary avalanche with incompressible grains down an incline. While the mean velocity and volume fraction increase from their minimum values on the plane toward maximum values on the free surface exponentially, two-fold turbulent kinetic energies and dissipations evolve in a reverse manner. Most two-fold turbulent kinetic energies and dissipations are confined within the thin turbulent boundary layer immediately above the plane, with nearly vanishing two-fold turbulent kinetic energies and finite two-fold turbulent dissipations in the passive layer. The two layers are similar to those of Newtonian fluids in turbulent boundary layer flows, and are preferable recognized by the distributions of turbulent kinetic energies and dissipations.