ASYMMETRIC HYDRODYNAMICS OF SUSPENSIONS SUBJECTED TO THE INFLUENCE OF STRONG EXTERNAL MAGNETIC FIELDS

2012 ◽  
Vol 04 (01) ◽  
pp. 1250002
Author(s):  
MAKSYM BEREZHNYI ◽  
EUGEN KHRUSLOV
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Fluid ◽  
Symmetry Axis ◽  
Viscous Incompressible Fluid ◽  
Strain Tensor ◽  
Solid Particles ◽  
Axially Symmetric ◽  
Rotation Tensor ◽  
Small Oscillations ◽  
Homogenized Model

A viscous incompressible fluid with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of the fluid they move translationally or rotate around symmetry axis but the direction of their symmetry axes does not change. The asymptotic behavior of small oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a non-standard hydrodynamics. Namely, the homogenized stress tensor linearly depends not only on the strain tensor but also on the rotation tensor.

STEADY FLOWS OF A VISCOUS INCOMPRESSIBLE FLUID IN A POROUS HALF-SPACE

1994 ◽  
Vol 04 (05) ◽  
pp. 705-732 ◽  
Author(s):  
ARIANNA PASSERINI
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Fluid ◽  
Half Space ◽  
Viscous Incompressible Fluid ◽  
Steady Motion ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Steady Flows ◽  
Porous Half Space

In this paper we prove the existence and asymptotic behavior of solutions to the equations describing the steady motion of a viscous incompressible fluid in a porous half-space. The results are compared with those already known for the Navier-Stokes model and we find, in particular, that the behavior at large distances is strongly different depending on the value of the incoming flux through the boundary.

scholarly journals Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

2020 ◽  
Vol 5 (2) ◽  
pp. 229-238
Author(s):  
Yuri N. Skiba
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Sufficient Conditions ◽  
Vorticity Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Rotating Sphere ◽  
Bounded Set ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity

AbstractThe behavior of a viscous incompressible fluid on a rotating sphere is described by the nonlinear barotropic vorticity equation (BVE). Conditions for the existence of a bounded set that attracts all BVE solutions are given. In addition, sufficient conditions are obtained for a BVE solution to be a global attractor. It is shown that, in contrast to the stationary forcing, the dimension of the global BVE attractor under quasiperiodic forcing is not limited from above by the generalized Grashof number.

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