A question about Peclet number

Zhong Lei

I have a simple problem which I have not understood.

It is well known that the Peclet number ( Peclet = u dx / \nu) must be smaller than 2.0 to maintain numerical stability in a linear convective-diffusive problem, where the convective velocity remains constant. However for a nonlinear problem such as boundary layer flows, as the flow goes away from the wall, the local velocity is increased. To satisfy the condition of Peclet number < 2, does it mean that the spatial size dx should be decreased? Certaninly, it does not. But why?