Self-similar solution to a problem of axisymmetric motion of gas through a porous medium in the case of a quadratic law of resistance

1983 ◽  
Vol 17 (4) ◽  
pp. 631-634 ◽  
Author(s):  
N. A. Kudryashov ◽  
V. V. Murzenko
Keyword(s):  
Porous Medium ◽  
Similar Solution ◽  
Axisymmetric Motion ◽  
Self Similar Solution ◽  
Self Similar

Self-similarity in coupled Brinkman/Navier–Stokes flows

2012 ◽  
Vol 699 ◽  
pp. 94-114 ◽  
Author(s):  
Ilenia Battiato
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flexural Rigidity ◽  
Similar Solution ◽  
Navier Stokes ◽  
Self Similar Solution ◽  
Hydrodynamic Shear ◽  
Self Similar ◽  
Definition Of ◽  
Similar Solutions

AbstractIn this paper we derive self-similar solutions of flows through both a porous medium and a pure fluid. Self-similar filtration velocity and hydrodynamic shear profiles are obtained by means of asymptotic analysis in the limit of infinitely small permeability, and for both laminar and turbulent regimes over the porous medium. We show that a spatial length scale, related to the porous layer thickness, naturally emerges from the limiting process and suggests a more formal definition of thick and thin porous media. We finally specialize the analysis to porous media constituted of patterned cylindrical obstacles, which can freely deflect under the aerodynamic shear exerted by the fluid flowing through and over the forest. A self-similar solution for the bending profile of the elastic cylindrical obstacles is obtained as intermediate asymptotics, and applied to carbon nanotube (CNT) forests’ response to aerodynamic stresses. This self-similar solution is successfully used to estimate flexural rigidity of CNTs by linear fit of appropriately rescaled maximum deflection and average velocity measurements.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

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