scholarly journals Attracting curves on families of stationary solutions in two‐dimensional Navier-Stokes and reduced magnetohydrodynamics

1998 ◽  
Vol 454 (1973) ◽  
pp. 1407-1444 ◽  
Author(s):  
Gianne Derks ◽  
Tudor Ratiu
Keyword(s):  
Stationary Solutions ◽  
Navier Stokes ◽  
Two Dimensional

ON STABILITY OF PHYSICALLY REASONABLE SOLUTIONS TO THE TWO-DIMENSIONAL NAVIER–STOKES EQUATIONS

2019 ◽  
pp. 1-52
Author(s):  
Yasunori Maekawa
Keyword(s):  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Domain Modeling ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Spatial Infinity ◽  
Navier Stokes Equations ◽  
Unique Existence ◽  
Fundamental Object

The flow past an obstacle is a fundamental object in fluid mechanics. In 1967 Finn and Smith proved the unique existence of stationary solutions, called the physically reasonable solutions, to the Navier–Stokes equations in a two-dimensional exterior domain modeling this type of flows when the Reynolds number is sufficiently small. The asymptotic behavior of their solution at spatial infinity has been studied in detail and well understood by now, while its stability has remained open due to the difficulty specific to the two-dimensionality. In this paper, we prove that the physically reasonable solutions constructed by Finn and Smith are asymptotically stable with respect to small and well-localized initial perturbations.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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