| Contents |
| A numerical investigation on the Navier-Stokes equations with both the slip and no-slip boundary condition
is carried out for an incompressible 2d flow.
When the classical no-slip boundary condition is applied at the boundaries, the flow
exhibits the phenomenon of the unsteady separation and, according to the $Re$ number,
two kind of interaction acting over different length scale develop in the boundary layer flow.
Moreover all the interactions are characterized by the presence of several complex singularities
in the wall shear stress at the boundary.
By using a slip boundary condition, such
as the Navier boundary condition whereby the slip velocity is proportional to the tangential viscous stress,
the flow evolution exhibits a different behavior from the no-slip case.
We show how this boundary condition acts on the separation evolution
and on the characterization of the complex singularities of the wall shear.
We carry out numerical simulations by using an efficient mixed spectral-finite differences numerical scheme as used in [1].
[1] F. Gargano. M. Sammartino, V. Sciacca, K.W. Cassel , {\em Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions}, J. Fluid. Mech, Accepted, 2014 |
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