Direct Numerical Simulation of Turbulent Boundary Layer over Cubical Roughness Elements

Abstract

The present study explores turbulence statistics in turbulent flow over urban-like terrain using direct numerical simulation (DNS). DNS is performed in a turbulent boundary layer (TBL) over 3D cubic roughness elements. The turbulence statistics at Reτ = 816 are compared with those of experimental and numerical studies for validation, where Reτ is the friction Reynolds number. The flow exhibits wake interference characteristics similar to k-type roughness. Logarithmic variations in streamwise and spanwise Reynolds stresses and a plateau in Reynolds shear stress are observed, reminiscent of Townsend’s attached-eddy hypothesis. The energy at long wavelengths near the top of elements extends to smaller scales, indicating a two-scale behavior and a potential link to amplitude modulation. The quadrant analysis of Reynolds shear stress is employed, revealing significant changes in the contributions of ejection and sweep events near the top of elements. The results of quadrant analysis in the outer region closely resemble those of a TBL over a smooth wall, aligning with Townsend’s outer-layer similarity. The analysis of the transport equation of turbulent kinetic energy highlights the role of the roughness elements in energy transfer, especially pressure transport. Streamwise energy is mainly reduced near upstream elements and redirected in other directions.

Keywords

• direct numerical simulation
• turbulent boundary layer
• cubical roughness
• turbulence statistics
• urban boundary layer