scholarly journals Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion

2019 ◽  
Vol 39 (6) ◽  
pp. 3413-3441
Author(s):  
Laiqing Meng ◽  
◽  
Jia Yuan ◽  
Xiaoxin Zheng
Keyword(s):  
Global Existence ◽  
Stokes Equations ◽  
Energy Solution ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations

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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