With the rapid development of IoT, big data and artificial intelligence, the research and application of data-driven hydrological models are increasing. However, when conducting time series analysis, many prediction models are often directly based on the following assumptions: hydrologic time series are normal, homogeneous, smooth and non-trending, which are not always all true. To address the related issues, a solution for short-term hydrological forecasting is proposed. Firstly, a feature test is conducted to verify whether the hydrological time series are normal, homogeneous, smooth and non-trending; secondly, a sequence-to-sequence (seq2seq)-based short-term water level prediction model (LSTM-seq2seq) is proposed to improve the accuracy of hydrological prediction. The model uses a long short-term memory neural network (LSTM) as an encoding layer to encode the historical flow sequence into a context vector, and another LSTM as a decoding layer to decode the context vector in order to predict the target runoff, by superimposing on the attention mechanism, aiming at improving the prediction accuracy. Using the experimental data regarding the water level of the Chu River, the model is compared to other models based on the analysis of normality, smoothness, homogeneity and trending of different water level data. The results show that the prediction accuracy of the proposed model is greater than that of the data set without these characteristics for the data set with normality, smoothness, homogeneity and trend. Flow data at Runcheng, Wuzhi, Baima Temple, Longmen Town, Dongwan, Lu’s and Tongguan are used as input data sets to train and evaluate the model. Metrics RMSE and NSE are used to evaluate the prediction accuracy and convergence speed of the model. The results show that the prediction accuracy of LSTM-seq2seq and LSTM-BP models is higher than other models. Furthermore, the convergence process of the LSTM-seq2seq model is the fastest among the compared models.

Vortex-induced vibrations of dual-step cylinders in laminar flows at the Reynolds number of 200 based on a larger diameter are investigated through three-dimensional direct numerical simulations. Four larger-to-smaller diameter ratios (D/d) of 4.0, 2.0, 1.43, and 1.19 are considered for the cylinder with a low mass ratio of 2. Numerical results reveal that D/d significantly influences vibration responses and the vortex shedding process. The case with D/d = 1.43 can effectively reduce vibration amplitudes. The wake vortices are shed in cellular patterns along the cylinder span, with a distinct frequency for each cell. A direct and “X-shaped” connection of wake vortex-shedding modes occurs between different vortex cells, and a loop connection appears between the same cell vortices. A new wake pattern entitled the “out-of-phase vortex shedding” is found downstream of the smaller cylinder at D/d = 2.0. This is manifested by the wake vortices not being shed at a fixed frequency and intensity. The essential reason for this phenomenon lies in a non-lock-in condition between the structural vibration and vortex shedding frequencies of the smaller cylinder. As D/d decreases, a coherence between vortex cells is enhanced, leading to a disappearance of the “out-of-phase vortex shedding.”

In this paper, we present three-dimensional direct numerical simulations (3D DNS) of vortex-induced vibrations of an elastically mounted circular cylinder near a stationary wall at a subcritical Reynolds number of 500. The circular cylinder can oscillate in both the streamwise and transverse directions. A typical gap of 0.$8D$ between the cylinder surface and the stationary wall was selected to evaluate the characteristics of the responses and vortex dynamics in the presence of a stationary wall and boundary layer. We observe that the vibration response is two-branched, with two desynchronization regions lying at the ends of the simulated $U_r$ range. Because of the wall proximity, the dominant vibration frequencies in the two directions are generally identical, and the trajectories of the displacement significantly differ in each branch. Figure-eight, combined figure-eight and raindrop, raindrop, and chaotic trajectories appear successively with increasing $U_r$, dominating the first desynchronization region, initial branch, lower branch (LB), and second desynchronization region (DS-II), respectively. In addition, the phase lag between the lift and displacement jumps from 0° to 180° at the transition between the LB and DS-II. Furthermore, we evaluated the three-dimensionality of the wake through the instantaneous vortical structures, spanwise-averaged vorticity contours, and statistics of the enstrophies. We found that the three-dimensionality increases linearly with the amplitude, leading to substantial variations in the vortex dynamics. The statistics of the gap flow indicates that the mean gap flow velocity is determined by only the time-averaged gap, whereas the fluctuating gap flow velocity is governed by the amplitude. Finally, the flow physics behind the response was analyzed using the time histories of the displacement, gap flow velocity, drag and lift coefficients, and vorticity contours in one vibration period. We observed that the interactions of the vortices with the wall-generated boundary layer play significant roles in altering the cylinder vibration. In the small-amplitude case, the boundary layer merges with the freestream-side vortex of the cylinder, forcing the gap-side vortex to pair with the freestream-side vortex. In contrast, in the large-amplitude case, the gap-side shear layer collides with the boundary layer and disintegrates into small parts, resulting in negative vortices in the wake.

Flow-induced vibrations of two side-by-side circular cylinders are numerically studied using the immersed boundary method for Reynolds numbers of 60–200. The two cylinders are constrained to vibrate only in the transverse direction. The center-to-center spacing ratio (s/D) is in the range 2.0–5.0, and the reduced velocity (U_r) is in the range 2.0–10.0. The smallest increments for s/D and U_r are 0.02 and 0.01, respectively. It was found that the vibration amplitudes, mean position shifts, lift and drag forces, spectral frequencies, and phase lags between the lift and displacement are significantly influenced by s/D and U_r, supported by (a) a wider lock-in region compared to the case of a single cylinder, (b) emergence of asymmetric vibration where the amplitudes of two cylinders are not identical, (c) the phase jump between the lift and displacement resulting from multiple harmonic frequencies, and (d) a significant drop in mean position shift accompanied by the changes in the frequency or wake pattern. Furthermore, the influences of the spacing ratio, Reynolds number, blockage ratio, and mass ratio, on asymmetric vibration with single-sided hysteresis (AV-I), are examined in detail. The AV-I with double-sided hysteresis was confirmed for the first time when the cylinder mass ratio is larger than 5.0.