This study investigates turbulent flows over rough-wall periodic hills using large-eddy simulations with the curvilinear immersed boundary method. Five rough surface configurations (R1–R5) are generated by randomly oriented ellipsoids with minor semiaxes ranging from $r=0.048h$ to $0.160h$, where $h$ denotes the hill height, at a Reynolds number ${\mathrm{Re}}_b=10595$ (which is defined based on the bulk velocity and the hill height). The analysis reveals that surface roughness significantly alters flow statistics, reducing streamwise velocity, enhancing wall-normal momentum transfer, and redistributing Reynolds stresses. It monotonically increases the separation bubble length from the smooth-surface case to the R5 case, while inducing upward and downstream displacement of the bubble center $(x_c,$ $y_c)$. Notably, the downstream movement of $x_c$ saturates beyond R3. A key finding is the geometric similarity of separation bubbles under coordinate transformation. By aligning bubble centers and rescaling coordinates using semiaxes $d_x$ and $d_y$, we demonstrate the collapse of bubble outlines and zero-velocity isolines across rough surface configurations. Moreover, this similarity extends to smooth-surface cases at varying Reynolds numbers. Analysis based on momentum balance reveals a dual role of the rough surface: it reduces the available momentum in the near-wall region of lower hills, while simultaneously counteracting the adverse pressure gradient induced by hill slopes. This dual role alters the flow separation mechanism, with the adverse pressure gradient caused by hill slopes being the dominant factor under low surface roughness conditions and near-wall momentum loss due to surface roughness prevailing under high roughness conditions.

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• Turbulence
• Viscosity
• Immersed boundary methods
• Large eddy simulations
• Navier-Stokes equation