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An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition

Mahdi Boukrouche, Grzegorz Łukaszewicz (2005)

Banach Center Publications

We consider a free boundary problem of a two-dimensional Navier-Stokes shear flow. There exist a unique global in time solution of the considered problem as well as the global attractor for the associated semigroup. As in [1] and [2], we estimate from above the dimension of the attractor in terms of given data and the geometry of the domain of the flow. This research is motivated by a free boundary problem from lubrication theory where the domain of the flow is usually very thin and the roughness...

Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol, Francisco Ortegón Gallego (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity A ( θ , ϕ ) and nonlinear source terms of the form θ 2 | ∇ u | 2 and θ ϕ | ∇ u | 2 lying in L1. Some existence results are shown in this paper, including L ∞ -estimates and positivity for both θ and φ.

Dense Granular Poiseuille Flow

E. Khain (2011)

Mathematical Modelling of Natural Phenomena

We consider a dense granular shear flow in a two-dimensional system. Granular systems (composed of a large number of macroscopic particles) are far from equilibrium due to inelastic collisions between particles: an external driving is needed to maintain the motion of particles. Theoretical description of driven granular media is especially challenging for dense granular flows. This paper focuses on a gravity-driven dense granular Poiseuille flow...

Hydromagnetic stability of stratified shear flows in the presence of cross flow

Naresh Kumar Dua, Hari Kishan, Ruchi Goel (2011)

Annales Polonici Mathematici

The hydromagnetic stability of stratified shear flows in the presence of cross flows is discussed. The magnetic field is applied in the direction of the main flow. Some necessary conditions of instability, the growth rate of unstable modes and reduction of the unstable region are discussed.

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