Two-Dimensional Stokes Flows

2012 ◽  
pp. 43-62
Keyword(s):  
Two Dimensional ◽  
Stokes Flows

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.

On angles of separation in Stokes flows

1983 ◽  
Vol 133 ◽  
pp. 427-442 ◽  
Author(s):  
M. E. O'Neill
Keyword(s):  
Circular Cylinder ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stokes Flows ◽  
Eddy Structure ◽  
Toroidal Vortices ◽  
Mathematical Equivalence ◽  
Infinite Sets

A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established.

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