The vortex evolution behind a circular cylinder placed near a wall is investigated experimentally with particle image velocimetry. The Reynolds number based on the cylinder diameter D is $Re=1500$ , and the gap ratio $G/D$ varies from 0 to 2.5 (where G is the net gap between the lower surface of the cylinder and the wall). The proper orthogonal decomposition and the vortex identification method ${\lambda }_{ci}$ are applied to capture vortex structures, and the effects of the gap ratio on vortex evolution behind the cylinder are revealed. (i) For $G/D\le 0.25$ , the regular and alternate wake vortex shedding are suppressed, and the wake vortex shedding is associated with the upper shear layer of the cylinder. The wake vortex is shed from the curling of the upper shear layer and finally breaks down into some smaller vortices at G/D = 0. (ii) For $G/D=0.5$ , there is a vortex merging process among the upper wake vortex and the secondary vortex; meanwhile, some smaller vortices broken from the secondary vortex are entrained into the recirculation region. (iii) For $0.5<G/D\le 1$ , the lower wake vortex can directly interact with the secondary vortex while the direct interaction is reduced at $1<G/D\le 2$ . (iv) For $G/D>2$ , the flow of the region is similar to that of an isolated cylinder. The variation of the Strouhal number (St) is dependent on the gap ratio, and the St increases as the gap ratio decreases down to G/D = 0.25, and there is nearly a 92% increase from St = 0.192 at G/D = 2.5 to St = 0.369 at G/D = 0.25, which is caused by the deflection of the gap flow. Moreover, the regular and alternate vortex structure can be formed as the gap ratio increases, and the flow characteristics and the vortex evolution are strongly affected by the gap ratio.

The experimental investigation focuses on the effects of a short splitter plate on the flow physics of a circular cylinder in proximity to a wall by particle image velocimetry. The Reynolds number is Re = 3900, and the near-wall cylinder is immersed in turbulent boundary layer flow. Three gap ratios (i.e. $G/D$ = 0.25, 0.5 and 1) are considered, and the splitter plate length is $L/D=0$ , 0.25, 0.5, 0.75 and 1. For $G/D$ = 0.5 and 1, as $L/D$ increases from 0 to 1, the splitter plate facilitates the cylinder shear layers to elongate downstream, and the vortex formation length is increased, which leads to the increase of the range of the recirculation region. For $G/D$ = 0.25, the wall suppression on the wake vortex formation is enhanced, and the variations of the vortex formation length and the range of the recirculation region with $L/D$ are small. The Strouhal number St presents a decrease with increasing $L/D$ for the three gap ratios. The effects of $L/D$ on the vortex evolution are revealed. For $G/D$ = 0.5 and 1, as $L/D$ increases, the induction of the lower wake vortex on the wall secondary vortex becomes weaker due to the reduction in strength of the wake vortex and the increase of the vortex formation length. Additionally, the wake fluctuation intensity is decreased with the increase of $L/D$ due to the splitter plate suppression. For $G/D$ = 0.25, theL/D influences on evolution of the wake vortices and wall secondary vortex are small, which result in weaker variation of the wake fluctuation intensity with $L/D$ .

The flow characteristics and vortex evolution behind a circular cylinder near a wavy wall are studied using a large-eddy simulation framework. The Reynolds number based on the cylinder diameter D is Re_D = 1500, the gap ratio G/D is fixed to 1, and the slope S = λ/2k varies from 2 to 8 (where G is the distance between the lower surface of the cylinder and the crest, λ is the wavelength, and k is the wave amplitude). The flow field characteristics, hydrodynamic coefficients, pressure distributions, vortex evolution, and three-dimensional flow features are presented and discussed. The phase of the flow field is determined by proper orthogonal decomposition, and the vortex identification method is applied to capture vortex structures. Compared with a smooth wall, the wavy wall changes the pressure distribution of the flow field and decreases (increases) the mean drag (lift) coefficient. As the wall amplitude increases, the Strouhal number increases slightly, attaining values of 0.25 for S = 8, 0.25 for S = 4, and 0.26 for S = 2. The wall pressure coefficient has an approximately periodic distribution, while the wall friction coefficient varies according to the evolution of secondary vortices on the wall. Two small secondary vortices appear either side of the crest before merging into a new secondary vortex that moves downstream with the upper and lower wake vortices. The energy of the first two modes obtained by proper orthogonal decomposition decreases compared with the smooth-wall case, whereas that of the third and fourth modes increases, reflecting the greater large-scale vortex structures between the wavy walls. This is confirmed by examining the instantaneous three-dimensional vortex structures using the Q-criterion.

Accurate wind speed prediction is a premise that guarantees the reliable operation of the power grid. This study presents a combined prediction model that integrates data preprocessing, cascade optimization, and deep learning prediction to improve prediction performance. In data preprocessing, the wavelet soft threshold denoising (WSTD) is employed to filter the blurring noise of the original data. Then, the robust empirical mode decomposition (REMD) and adaptive variational mode decomposition (AVMD) are adopted to carry out a two-stage adaptive decomposition. Spearman correlation is used to quantify the mode that need to be decomposed for the second time. In the cascade optimization, the hybrid grey wolf algorithm (HGWO) is employed to optimize the parameters of the VMD and the gated recurrent unit (GRU), which overcomes the problem of empirical parameter adjustment. The HGWO is also adopted in the prediction strategy to optimize the GRU model to predict the grouped intrinsic mode functions (IMFs). Lastly, the final wind speed prediction result is obtained by superimposing the values of all the predicted models. The proposed model was validated with the measured wind speed data of the four quarters in the Bay area of China and was compared with 20 models of the classic method to further evaluate the effectiveness of the model. The results show that the whole process of the proposed model is adaptive, the final multi-step prediction performance is good, and high prediction accuracy can be attained.

In this paper, we introduce WindFormer, an innovative transformer-based model engineered for short-term wind speed forecasting, leveraging multivariate time series data. Unlike traditional approaches, WindFormer excels in processing diverse meteorological features—temperature, humidity, and power—to intricately map their spatiotemporal interdependencies with wind speeds. Utilizing a novel unsupervised pre-training strategy, WindFormer initially learns from vast volumes of unlabeled data to capture generalized feature representations. This foundation enhances the subsequent fine-tuning phase on labeled wind speed data, in which our model demonstrates exceptional predictive accuracy. Empirical evaluations across various public datasets illustrate that WindFormer markedly surpasses both conventional statistical models and contemporary deep learning techniques. The model not only achieves superior accuracy in forecasting wind speeds but also reveals a significant enhancement in handling complex spatiotemporal data dynamics. These advancements facilitate more effective wind farm management and power grid scheduling, making a substantial impact on operational efficiencies and renewable energy utilization. Our findings confirm the robustness of WindFormer in a real-world setting, underscoring its potential as a pivotal tool in meteorological and energy sectors. The integration of unsupervised pre-training with multi-task fine-tuning establishes a new benchmark for short-term wind speed prediction.