DNS study of wall-pressure fluctuations in a turbulent boundary layer with large pressure gradients

DNS data are used to examine the behavior of wall-pressure fluctuations $p_w$ in a turbulent boundary layer with large adverse and favorable pressure gradients, thus involving separation and reattachment. The Reynolds number $Re_\theta$ based on momentum thickness is equal to 300, 600 and 900. Comparison is also made with recent experiment by Weiss et al. (2015) for $Re_\theta=5000$. Particular attention is given to the scaling law focusing on maximum value of each Reynolds stress. It is shown that rms value of $p_w$ normalized by dynamic pressure is about twice larger near separation and reattachment than for zero-pressure gradient. In the former regions, $p_w$ is affected noticeably by outer-layer pressure fluctuations where low pressure regions are closely associated with large-scale motions of negative streamwise velocity fluctuations. Among the scalings, rms value of $p_w$ normalized by maximum Reynolds shear stress (Simpson et al. 1987; Na \& Moin 1998) leads to near plateau in adverse pressure gradient and separated regions, indicating that shear stress makes significant contribution to $p_w$. This scaling also holds reasonably near reattachment where the scaling with maximum wall-normal Reynolds stress, pointed out by Ji \& Wang (2012) for steps, yields better collapse.