Pressure fluctuations are a key issue in hydraulic engineering. However, despite the large number of studies on the topic, their role in spatial hydraulic jumps is not yet fully understood. The results herein shed light on the formation of eddies and the derived pressure fluctuations in stilling basins with different expansion ratios. Laboratory tests are conducted in a horizontal rectangular flume with 0.5 m width and 10 m length. The range of approaching Froude numbers spans from 6.4 to 12.5 and the channel expansion ratios are 0.4, 0.6, 0.8, and 1. The effects of approaching flow conditions and expansion ratios are thoroughly analyzed, focusing on the dimensionless standard deviation of pressure fluctuations and extreme pressure fluctuations. The results reveal that these variables show a clear dependence on the Froude number and the distance to the hydraulic jump toe. The maximum values of extreme pressure fluctuations occur in the range $0.609<X<3.385$, where X is dimensionless distance from the toe of the hydraulic jump, which makes it highly advisable to reinforce the bed of stilling basins within this range.

Erosion in river bends causes loss of agricultural lands, adjacent facilities, and fish habitat. W-weir structures are recommended for controlling and reducing soil erosion as well as developing habitat for fish and other aquatic organisms. This paper presents the results of an experimental study carried out to investigate the effect of a W-weir structure on a sinusoidal channel with a sinuosity of 1.12 on the scour volume and type. The W-weir was applied in three heights (0.5, 1, and 1.5) with $H_o/h$ ratio (the height of weir to flow depth ratio) and different hydraulic conditions (inflow Froude numbers 0.107, 0.142, and 0.178) tested for each structure. Bed topography was measured at the end of each experiment, and from that the types of scouring, maximum scour depth and length, as well as maximum ripple height and length were computed. Furthermore, by decreasing the height of W-weir from $H_o/h$ = 1.5 to $H_o/h$ = 0.5, the scour volume decreased from 24 to 78 percent on average for different inflow Froude numbers. The angle of inner arms of W-weir was chosen as 50°, 64°, 86°, and 124°. Minimum scour volume occurred in the angle of inner arms of w-weir 64° for different heights of W-weir tested. Finally, two scour morphologies were observed. This study provides insights to guide and design W-weir structures for river restoration projects.

Scouring downstream of grade control structure is a common problem. W-weir structures are recommended for controlling, reducing soil erosion, and development aquatic organisms habitat. W-weir structures can provide energy dissipation, increased aquatic habitat, grade-control, and bank and bed stabilization through the diversion of conveyance with the river-channel center. The current study aimed at analyzing the scour geometry downstream of W-weirs in the sinuous channels using heuristic gene expression programming (GEP) and support vector machine (SVM) models. A comparison was also made between the GEP and SVM with traditional multi variable linear regression (MLR) technique. The cross-validation technique (i.e. k-fold testing) was used to assess the developed models. Observations revealed that the scour typology affects the maximum scour depth value. The obtained results showed that both the GEP and SVM models give promising results in simulating the scour depth and scour length magnitudes. Assessing the models confirmed that using the k-fold testing cross validation is very necessary as all the available patterns can participate in training and testing stages, which reduces the risk of over fitting.

The backward-facing step flow (BFSF) is a classical problem in fluid mechanics, hydraulic engineering, and environmental hydraulics. The nature of this flow, consisting of separation and reattachment, makes it a problem worthy of investigation. In this study, divided into two parts, the effect of a cylinder placed downstream of the step on the 2D flow structure was investigated. In Part 1, the classical 2D BFSF was validated by using OpenFOAM. The BFSF characteristics (reattachment, recirculation zone, velocity profile, skin friction coefficient, and pressure coefficient) were validated for a step-height Reynolds number in the range from 75 to 9000, covering both laminar and turbulent flow. The numerical results at different Reynolds numbers of laminar flow and four RANS turbulence models (standard k-ε, RNG k-ε, standard k-ω, and SST k-ω) were found to be in good agreement with the literature data. In laminar flow, the average error between the numerical results and experimental data for velocity profiles and reattachment lengths and the skin friction coefficient were lower than 8.1, 18, and 20%, respectively. In turbulent flow, the standard k-ε was the most accurate model in predicting pressure coefficients, skin friction coefficient, and reattachment length with an average error lower than 20.5, 17.5, and 6%, respectively. In Part 2, the effect on the 2D flow structure of a cylinder placed at different horizontal and vertical locations downstream of the step was investigated.

The hydraulic behavior of a hydraulic jump can be challenging to estimate in order to design gradually expanding stilling basins with roughness elements on the bed. In this study, five dependent variables were identified that comprise: (i) the sequent depth ratio; (ii) the relative length of the jump; (iii) the relative roller length of the jump; (iv) the relative energy dissipation; and (v) the water surface profile. This study undertook a set of formulations based on the regression analysis and Sugeno Fuzzy Logic (SFL) to predict these variables based upon experimental data. Results demonstrate that the trained SFLs predicted the behavior of the dependent variables with the Nash–Sutcliffe Coefficient (NSC) greater than 0.96 in the testing phase. In contrast, the NSC values for the regression models are greater than 0.79. The higher accuracy of SFL is attributed to its capability in managing uncertainty and imprecise data owing to water surface profile oscillations of the hydraulic jump. Also, the results indicate that the prediction residuals for SFL are homoscedastic for all hydraulic parameters investigated except for the water surface profile, the prediction residuals of which for the regression equations are heteroscedastic.

This study investigates the effect on the flow structure in a backward-facing step (BFSF) due to a cylinder placed downstream of the step. Numerical simulations were carried out using OpenFOAM with several turbulence models (standard k-ɛ, RNG k-ɛ, standard k-ω, and SST k-ω). The recirculating flow, the skin friction coefficient (C_f), and the pressure coefficient (C_p) of the bottom wall were comparatively analysed. The added cylinder modified the structure of flow and increased the skin friction coefficient (C_f) in the recirculation zone. Additionally, the pressure coefficient of the bottom wall increased immediately downstream of the cylinder and farther downstream of the reattachment point remained stable in the flow recovery process.