Application of proper orthogonal decomposition (POD) to investigate a turbulent boundary layer in a channel with rough walls

Abstract

Snapshot proper orthogonal decomposition (POD) is used to investigate a rough-wall turbulent boundary layer in a channel. One- and two-dimensional POD decompositions have been performed using 3D velocity database from direct numerical simulations (DNS). DNS of a turbulent channel flow with rough walls consisting of 3D roughness elements have been performed at Re_τ = 180. 1D analysis has revealed that convergence of the POD for a rough wall is slower compared to the smooth wall, which is attributed to the increase in range of length scales due to roughness. For the egg-carton roughness elements, the depth of a roughness sublayer (ζ_mode ⁿ ) for POD mode n decays with increasing mode number in an exponential manner as ζ_mode ⁿ = 14e ^{−0.86 n} h for roughness of height h. The reconstruction of turbulence intensities and shear stress has revealed that the inner layer which includes the roughness sublayer is well captured by first 10 POD modes. 2D POD analysis has revealed that roughness alters the size and spacing of the large scale, energy containing structures of the flow.

Keywords:

• Roughwall
• Direct numerical simulation
• Turbulent boundary layers