Two-dimensional stationary Navier-Stokes equations with 4-cyclic symmetry

2016 ◽  
Vol 289 (17-18) ◽  
pp. 2281-2311 ◽  
Author(s):  
Masao Yamazaki
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Cyclic Symmetry ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

On nonhomogeneous boundary value problems for the stationary Navier–Stokes equations in two-dimensional symmetric semi-infinite outlets

2015 ◽  
Vol 15 (04) ◽  
pp. 543-569 ◽  
Author(s):  
M. Chipot ◽  
K. Kaulakytė ◽  
K. Pileckas ◽  
W. Xue
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Domain Boundary ◽  
Boundary Value ◽  
Symmetric Domain ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Dirichlet Integral ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

We study the stationary nonhomogeneous Navier–Stokes problem in a two-dimensional symmetric domain with a semi-infinite outlet (for instance, either paraboloidal or channel-like). Under the symmetry assumptions on the domain, boundary value and external force, we prove the existence of at least one weak symmetric solution without any restriction on the size of the fluxes, i.e. the fluxes of the boundary value [Formula: see text] over the inner and the outer boundaries may be arbitrarily large. Only the necessary compatibility condition (the total flux is equal to zero) has to be satisfied. Moreover, the Dirichlet integral of the solution can be finite or infinite depending on the geometry of the domain.

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.

Sign in / Sign up

Export Citation Format

Share Document