scholarly journals On the form of the viscous term for two dimensional Navier-Stokes flows

2014 ◽  
Vol 67 (2) ◽  
pp. 205-228 ◽  
Author(s):  
A. D. Gilbert ◽  
X. Riedinger ◽  
J. Thuburn
Keyword(s):  
Navier Stokes ◽  
Two Dimensional ◽  
Stokes Flows ◽  
Viscous Term

scholarly journals Correlation between No-Slip and Slip Boundary Conditions Associated with A Two-Dimensional Navier-Stokes Flows in a Plane Diffuser

2021 ◽  
Vol 65 (1) ◽  
pp. 1-23
Author(s):  
Ranis Ibragimov ◽  
◽  
Vesselin Vatchev ◽  
Keyword(s):  
Boundary Conditions ◽  
Small Perturbation ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Viscous Effects ◽  
Stokes Flows ◽  
Slip Boundary ◽  
Two Parameters

We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro- parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.

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