Recent studies show that near-bed turbulence may be better scaled using a mixed velocity scale u*U, where u* is the shear velocity and U denotes the characteristic bulk flow velocity. This implies that the classical scaling consideration for sediment transport rates could be improved by redefining the Shields number based on the mixed velocity scale. To investigate this potential improvement, a series of analyses was performed with laboratory data from 25 sources of sediment discharge studies. The data were carefully selected by minimizing effects of some factors including sidewall, particle gradation, particle density, and fluid viscosity. The findings indicate that the relationship between sediment discharges and flow conditions can be enhanced significantly when the analysis is carried out based on the redefined Shields number. The new relationship does not depend on the type of bedforms, and therefore facilitates the prediction of sediment discharge. Finally, by comparing with previous studies, it shows that the proposed formula markedly improves the prediction of bed-material sediment discharges.

Numerical methods generally need analytical solutions as test cases and validations in simplified problems. This work provides Laplace-domain explicit analytic solutions for fluid–structure interaction (FSI) water hammer waves within a pipe. Rather than applying the transfer matrix method (TMM) to the FSI four equations, it is transposed to the equivalent two-wave propagating problem considered instead. Using the classical wave matrix diagonalization approach permits decoupling the waves’ propagation while at the same time coupling boundary conditions in the diagonal base. This approach permits the transfer matrix for coupled waves boundary conditions to be provided so as to obtain a Laplace-domain solution for the pressure/stress vector solution. This solution is written in a general framework that can be adapted for general applied boundary conditions for a single pipe. Three sets of boundary conditions are considered as examples and illustrations from solving the inverse Laplace transform of the considered explicit solutions. Consistent results with recently proposed time-domain solutions are found, and a one-to-one mapping between Laplace-domain and time-domain approaches is also established. This permits finding the discrete spectrum of FSI water hammer wave mode decomposition from TMM solutions.

Improving the knowledge of the failure mechanism of riprap exposed to overtopping is valuable to enhance the construction and reinforcement techniques of rockfill dam defense systems. In this research, four experimental overtopping tests were carried out on 1∶10 rockfill dam models with placed riprap protection layers supported at the toe. Axial reaction loads were measured and 3D models were built using the structure from motion technique to study the displacement of riprap stones exposed to overtopping. The importance of throughflow in the rockfill shoulder is brought to light by comparing these results with previous data from a placed riprap model built on a ramp without throughflow. The structure from motion technique demonstrates to be very effective and highlights the existence of a buckling phenomenon, along with the compaction of the riprap. The displacement data show that the compaction mechanism is more important (both horizontally and vertically) and appears at lower overtopping discharges for less packed placed riprap layer. Finally, similar trends for vertical and horizontal riprap displacements are demonstrated between the initial position and the last position before failure. Such information suggests that the critical discharge value is not as critical as the riprap displacement to predict dam failure under overtopping conditions.

Boussinesq-type (BT) models play a major role in coastal engineering applications. Due to their asymptotic nature, these models have lent themselves to constant study and improvement based on the inclusion/removal of asymptotically small terms. In this work, we go back to the fundamental question of whether full nonlinearity in weakly dispersive BT models is a necessity. We reconsider the tests first used in the literature to address this issue, as well as a number of more demanding issues. We also consider different families of weakly nonlinear BT models, with different shoaling characteristics, especially when nonlinear waves are involved. Our study allows us to point out that for many cases, it is quite hard to conclude whether full nonlinearity is really necessary. There are a few discriminant cases, which are unfortunately not those mostly used in the literature proposing new models or new numerical methods.

Turbulent flows over bumpy walls are ubiquitous and pose a fundamental challenge to various engineering applications such as coastal boundary layers, drag on ships, hydraulic conveyance networks, and bluff body aerodynamics, to name a few. In this study, we used direct numerical simulations (DNS) along with a direct-forcing immersed boundary method (IBM) to understand the connection between the roughness geometry and the mean flow drag. A bumpy wall was constructed using an array of randomly oriented ellipsoids characterized by the Corey shape factor (Co). We found that our results exactly validated the experimental studies by Nikuradse for sand-grain type roughness (Co=1.0). Additionally, we observed that the mean flow drag increased for decreasing Co through an increase in the form-drag contribution and a decrease in the viscous drag. We also developed a relationship between the statistics of the bottom height distribution and the roughness parameter (z0) that may help explain the spread observed in the drag coefficient predicted when using conventional tools such as the Moody diagram.

The increasing number of interbasin diversion projects place high demands on fine-grained simulation and control of free-surface and transient mixed flow. Since the numerical oscillation of the transient mixed flow generates more with higher-order finite volume method (FVM), the study is based on a high-precision first-order Harten, Lax, and van Leer (HLL) Riemann solver that considers the source term (HLLS). This study modifies the original HLLS solver and introduces numerical viscosity in the vicinity of filling bores to suppress the numerical oscillations. Furthermore, this study explores the selection of wave velocity calculation methods. A first-order scheme with high accuracy of the free surface and transient flow was developed and verified through various experiments. The results show that the proposed scheme can deal with the bottom slope both in constant free-surface and mixed flow. This is because of the perfect conservation properties of this scheme. Furthermore, the formula shows good performance in transient mixed flow. Therefore, this method can satisfy the requirements for modelling a long-distance complex channel tunnel system.

The fix-grid method of characteristic (MOC) has been the main numerical scheme for modeling the transient pipe flows with an entrapped air pocket, where the Courant number Cr usually equals one (i.e., Cr=1) to ensure its accuracy and stability. However, Cr=1 cannot always be guaranteed in each pipe of real pipe systems; thus, the MOC needs to be approximated by interpolation or wavespeed adjustment. This could lead to large accumulated numerical errors and serious shape distortion of simulated pressure curves. To address this problem, an alternative coupled scheme, which combines the second-order Godunov-type scheme (GTS) and the MOC, is developed. Specifically, the conservation equations with unsteady friction of the water column are numerically solved by the GTS, and the moving air-water interface is modeled and captured by the coupled GTS-MOC scheme. The simulated pressure curves by the GTS-MOC scheme are compared with both MOC results and laboratory experiments. The proposed scheme with unsteady friction can better reproduce the experimental pressure oscillations, and is more robust and efficient than the MOC. The MOC scheme with Cr<1 and coarse grids causes more obvious numerical dissipation during an intensive transient induced by relatively high inlet pressure, in which more high-frequency waves occur.

A new empirical equation for free alternate bar length at the fully developed state is introduced. The equation is developed on the basis of dimensional analysis and all readily available data. A special effort is also made to align the formulation with findings from existing theoretical and numerical analyses of the development of alternate bars, and more specifically those resulting from a stability analysis of the phenomenon. When applied to the existing laboratory data, the equation results in significantly less dispersion around the best agreement line than that associated with previous empirical equations, yielding 70% of the data within the 20% error range, against 47% for previous equations. It is shown that previous equations perform notoriously poorly in the case of fully rough subcritical flows and all transitionally rough flows, with the present equation addressing this matter. When applied to field cases, the present equation yielded realistic values of bar length, including for large sand streams with high or very high values of relative depth (e.g., the Tagus and Mississippi Rivers).