Impact of Flow Pulsation on Roughness Effects in Turbulent Channel Flows*

Modulation of roughness effects by pulsating pressure gradients (PG) is explored by DNS of turbulent channel flows. Sinusoidal pulsation of PG is examined for ω⁺ = 0 (steady), 0.02, and 0.04. The magnitude of the pulsation is ~25% of the mean PG, which drives the flow at $Re_{τ,o} = 1500$.  Comparisons are made between flows over the smooth wall and sandgrain roughness consisting of randomly distributed ellipsoids. The mean roughness height is $k/H=0.04$. A quintuple decomposition is proposed to isolate the pulsation- and roughness-induced fluctuations. Roughness appears to be the dominant factor characterizing the flow: Townsend's outer-layer similarity remain holds for the mean velocity and Reynolds stresses beyond a $2k$-thick roughness sublayer. Within the roughness sublayer, the mean wake (dispersive) flow stays the same regardless of the pulsation. However, pulsation creates a pulsating wake within the roughness sublayer which significantly amplifies the Reynolds stresses. The equivalent roughness height increases from $k_s^+ = $ 94 (steady) to 225 (ω⁺ = 0.04).  Without the roughness, Stoke layers are limited below the buffer layer for the frequencies examined. Roughness offsets them by 0.2-0.3$k$ and thickens by a factor of five, leading to wall-normal variations in pulsation amplitude and phase up to the mid log-law region.