A Resolvent-based Model for Roughness-induced Scale Interactions in a Turbulent Boundary Layer

By modeling a turbulent boundary layer as a low-order linear system with random background forcing, we are able to qualitatively predict the effect of a rough wall on the individual scales of the turbulence.

Turbulent boundary layers are the thin regions surrounding airplanes, ships, and other moving bodies where the fluid is dragged along by friction. In most practical applications, this region is turbulent, meaning that the fluid contains many swirls and eddies in a wide variety of sizes. When the surface of the body is roughened by corrosion or manufacturing defects, the roughness interacts with all these different-sized eddies in a complicated way to change the physics of the boundary layer. This work models the eddies as pairs of eddies with the same time scale which are highly favored by the linear system, and which interact with the roughness in known ways. We can predict how this will cause a change in the spatial distribution of turbulent energy for different time scales, and compare it to experimental results from a real turbulent boundary layer. We are able to accurately predict the shape and locations of the spatial distibutions of energy.

Figure: Spatial variation of the temporal power spectrum of a rough-wall boundary layer, Re_tau=1200 a)measured b)predicted

Jonathan Morgan
Adviser: Prof. Beverley McKeon 

Funding
ONR grant # N000141310739