  The dynamical equation of the boundary vorticity has been obtained, which
shows that the viscosity at a solid wall is doubled as if the fluid became more
viscous at the boundary. For certain viscous flows the boundary vorticity can
be determined via the dynamical equation up to bounded errors for all time,
without the need of knowing the details of the main stream flows. We then
validate the dynamical equation by carrying out stochastic direct numerical
simulations (i.e. the random vortex method for wall-bounded incompressible
viscous flows) by two different means of updating the boundary vorticity, one
using mollifiers of the Biot-Savart singular integral kernel, another using the
dynamical equations.

Fluid Dynamics;Numerical Analysis;Analysis of PDEs;Numerical Analysis;Probability