## Abstract

The authors consider the transport velocity in boundary layer flows driven by either noisy monochromatic progressive or standing waves. The central issue addressed here is whether such flows are capable of sustaining a transport velocity when noise is present in the wave field and, if so, in what ways the noise affects the transport velocity, the mean wall shear stress, and the total mass flux.

Specifically, the effect of noise due to unresolved processes is addressed. The study is motivated by the fact that in the natural setting it is the norm rather than the exception that noise is present in the wave field. The authors find that when noise is added to standing waves, the transport in the boundary layer leads to a nonzero mass flux. On the other hand, noise due to progressive waves reduces the mass flux. Further, the drift velocity will have two components: a deterministic one and a diffusive one.

*Corresponding author address:* Prof. Juan M. Restrepo, Department of Mathematics, Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721. Email: restrepo@math.arizona.edu