Turbulent Flow Over Large Roughness Elements: Effect of Frontal and Plan Solidity on Turbulence Statistics and...

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Boundary Layer Theory

Background:

• Investigates fully-rough turbulent boundary layers with significant roughness relative to boundary layer thickness ($\delta /h\approx 10$).
• Complements prior work by extending analysis to turbulence statistics and spatial flow structures.

Purpose of the Study:

• To examine the impact of varying surface roughness configurations (plan solidity ${\lambda }_P$ and frontal density ${\lambda }_F$) on turbulent boundary layers.
• To identify criteria governing outer-layer similarity in turbulent flows over rough surfaces.
• To explore the presence of universal flow structures despite variations in roughness.

Main Methods:

• Conducted wind-tunnel experiments using LEGO™ bricks to create twelve distinct surface conditions.
• Employed particle image velocimetry (PIV) and floating-element drag-balance measurements.
• Utilized proper orthogonal decomposition (POD) and two-point spatial correlations for flow structure analysis.

Main Results:

• Mean velocity profiles exhibit agreement with Townsend's similarity hypothesis for varying frontal density (${\lambda }_F$), but less so for varying plan solidity (${\lambda }_P$).
• Turbulent stresses (streamwise, wall-normal, and Reynolds shear) generally lack outer-layer similarity across most cases.
• A new shelter solidity criterion effectively captures deviations in turbulence statistics from outer-layer similarity.
• POD and spatial correlations reveal consistent, universal flow structures (mode shapes, correlation fields) across all tested surfaces.

Conclusions:

• Outer-layer similarity in turbulent boundary layers over roughness depends on both roughness height and local wall morphology.
• Shelter solidity offers a promising metric for predicting the onset of outer-layer similarity breakdown.
• Despite statistical variations, underlying flow structures exhibit universality, with small-scale turbulence significantly influencing outer-layer similarity.