PHYSICAL REVIEW FLUIDS 4, 054601 (2019) Very large-scale motions in turbulent flows over streamwise traveling wavy boundaries Wu-Yang Zhang, Wei-Xi Huang, * and Chun-Xiao Xu AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People’s Republic of China (Received 6 December 2018; published 7 May 2019) Turbulent flows over streamwise traveling wavy boundaries are investigated by large eddy simulations at a friction Reynolds number of Re τ = 1000. Four wave ages (i.e., the ratio between wave phase speed and bulk mean velocity) are considered, sequentially corresponding to the wave moving against the wind, stationary wavy wall, and intermediate and fast waves. A triple decomposition is performed to extract the mean, wave-induced, and turbulent components of the flow field. Very large-scale motions (VLSMs) of turbulent flow are identified by using the one-dimensional premultiplied energy spectra, instantaneous flow fields and conditionally averaged results. Compared with the flat-wall case, VLSMs in the negative wave age and stationary wavy wall cases are stronger, with larger length scales in both the streamwise and spanwise directions. The length scale and intensity of these motions decrease as the wave age increases. The conditionally averaged VLSMs involve the elongated low- and high-speed momentum regions and the roll cells in the streamwise direction. The transport equation of the two-point velocity correlation is investigated in different length scales by applying a spectral analysis. The wave-induced production that represents the interaction between the wave-induced and turbulent components of flow velocities provides extra input for the large-scale energy at low wave ages but play an opposite role at high wave ages. DOI: 10.1103/PhysRevFluids.4.054601 I. INTRODUCTION The coupling dynamic process between surface wave and turbulent flow exists widely in engineering and environmental flow phenomena and therefore is of great interest in many studies. Turbulent flow over a stationary wavy wall can be applied for heat transfer enhancement in some industrial devices [1,2]. It is also related to geophysical flows, such as oceanic flow over sandbars [3] and wind flow over wavy terrains [4]. However, turbulent flow over a surface undergoing a traveling wave motion can be considered as a control scheme for drag reduction [5–7]. This system has also been widely used as an idealized model of wind flowing over water surface in environmental research, such as energy transfer from wind to wave [8–11], wind-wave interaction [12–15], heat/mass mixing and exchange between atmosphere and sea [16–19]), and wind over breaking waves [20]. The previous studies showed that there were substantial differences between the turbulent flow over the wavy boundary and that over the flat wall. The influences of the surface wave on the turbulent momentum [12] and scalar [19] transport have complicated dependence on the geometry, length scale, and kinematics of the surface wave. Some open questions, such as applicability of the turbulence scaling law and estimation of the drag and mass/heat flux, are the key issues in the practical fields, e.g., the turbulence closure model in wavy boundary flow * hwx@tsinghua.edu.cn 2469-990X/2019/4(5)/054601(29) 054601-1 ©2019 American Physical Society