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.