The Navier wall law at a boundary with random roughness

Details The Navier wall law at a boundary with random roughness The Navier wall law at a boundary with random roughness

2007-11-22

arxiv.org/abs/0711.3610v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00220-008-0597-z

We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size $\eps \ll 1$. In a parent paper, we derived a homogenized boundary condition of Navier type as $\eps \to 0$. We show here that for a large class of boundaries, this Navier condition provides a $O(\eps^{3/2} |\ln \eps|^{1/2})$ approximation in $L^2$, instead of $O(\eps^{3/2})$ for periodic irregularities. Our result relies on the study of an auxiliary boundary layer system. Decay properties of this boundary layer are deduced from a central limit theorem for dependent variables.

Affiliated with

Also associated with

No associations

Rating

The Navier wall law at a boundary with random roughness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Navier wall law at a boundary with random roughness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Navier wall law at a boundary with random roughness will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-311125