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Vortex-induced vibration (VIV) test of a tensioned flexible pipe in oscillatory sheared flow was performed in an ocean basin. The model was 28.41 mm in diameter and 3.88 m in length. The test was performed on a rotating test rig to simulate oscillatory sheared flow conditions. One end of the test pipe is fixed, and one end is forced to harmonically oscillate to simulate oscillatory sheared flows with various combinations of amplitudes and periods, Keulegan-Carpenter ($KC$) numbers from $25$ to $160$ and five kinds of reduced velocities $Vr$ from $6$ to $14$. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. The VIV response in the cross flow (CF) direction is investigated. The results show that VIV under oscillatory sheared flow exhibit amplitude modulation and hysteresis phenomena. Compared with oscillatory uniform flow-induced VIV, the Strouhal number is smaller in oscillatory sheared flow-induced VIVs. The VIV developing process in oscillatory sheared flow is analyzed, and critical $KC$ is proposed to describe the occurrence of modulated VIV under oscillatory sheared flow., Comment: 19 pages, 18 figures

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) [Ling et al. (2016)] are established. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier-Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user's defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge., Comment: 23 pages