A theoretically based relationship for the Darcy–Weisbach friction factor $f$ for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.

Large-eddy simulations (LES) of the flow over a non-uniformly roughened channel bed are carried out to study the effect of non-uniform bed roughness on turbulence driven secondary currents and turbulence statistics. The channel bed is comprised of alternating rough and smooth strips, the width of which corresponds to the water depth. The Reynolds number based on hydraulic radius and bulk velocity is 34,000. The LES are successfully validated using experimental data. The secondary flow and bed roughness have a significant effect on the streamwise velocity and second order turbulence statistics. Turbulence is enhanced over rough strips and suppressed over smooth strips. Significant lateral momentum transfer takes place due to both advection and turbulence. The bed shear stresses over the smooth strips are approximately four times less than over the rough strips a result of near bed low momentum fluid being transported from the rough strips to the smooth strips and high momentum fluid being convected from the surface towards the bed. The most significant terms in the streamwise momentum equation are quantified and discussed with regard to momentum transfer.

This paper starts by reviewing the most significant previous studies on fluid-structure interaction of flows past stationary and moving circular cylinders, including those undergoing fluid dynamic excitation in the form of vortex-

Results from large-eddy simulations and complementary flume experiments of turbulent open channel flows over bed-mounted square bars at intermediate submergence are presented. Scenarios with two bar spacings, corresponding to transitional and k-type roughness, and three flow rates, are investigated. Good agreement is observed between the simulations and the experiments in terms of mean free surface elevations and mean streamwise velocities. Contours of simulated time-averaged streamwise, streamfunction and turbulent kinetic energy are presented and these reveal the effect of the roughness geometry on the water surface response. The analysis of the vertical distribution of the streamwise velocity shows that in the lowest submergence cases no logarithmic layer is present, whereas in the higher submergence cases some evidence of such a layer is observed. For several of the flows moderate to significant water surface deformations are observed, including weak and/or undular hydraulic jumps which affect significantly to the overall streamwise momentum balance. Reynolds shear stress, form-induced stress and form drag are analysed with reference to the momentum balance to assess their contributions to the total hydraulic resistance of these flows. The results show that form-induced stresses are dominant at the water surface and can contribute significantly to the overall drag, but the total resistance in all cases is dominated by form drag due to the presence of the bars.

SUMMARYIn this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces.

This paper introduces and discusses numerical methods for free-surface flow simulations and applies a Large Eddy Simulation (LES) based free-surface-resolved CFD method to a couple of flows of hydraulic engineering interest. The advantages, disadvantages and limitations of the various methods are discussed. The review prioritises interface capturing methods over interface tracking methods, as these have shown themselves to be more generally applicable to viscous flows of practical engineering interest, particularly when complex and rapidly changing surface topologies are encountered. Then, a Large-eddy simulation solver that employs the Level Set Method to capture free-surface deformation in 3D flows is presented, as are results from two example calculations that concern complex low submergence turbulent flows over idealised roughness elements and bluff bodies. The results show that the method is capable of predicting very complex flows that are characterised by strong interactions between the bulk flow and the free-surface, and permits the identification of turbulent events and structures that would be very difficult to measure experimentally.

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Vertical Axis Tidal Turbines (VATTs) are an innovative way of harnessing renewable energy from tidal streams. Herein a novel numerical approach using a refined Large Eddy Simulation (LES) code to simulate the performance of a VATT is presented. The turbine blades are modelled with Lagrangian markers using the Immersed Boundary Method which offers several advantages especially concerning computational effort. Comparisons of the LES results with experimental and numerical data suggest reasonably good accuracy of the code. In addition, the stability of the method for high Reynolds number flows is also discussed. IntroductionIn recent years the pressing need to find alternative sources of renewable energy has given impetus to research in new fields. The fact that tidal energy is more predictable than, for example, wind energy makes it a promising renewable energy source. Vertical Axis Tidal Turbines (VATTs) are an attractive way to harness the hydrokinetic energy from tidal streams, however the technology is considered in its infancy and much research is still needed to improve current designs.Experimental testing of VATTs cannot provide a full explanation as to why certain turbine design parameters such as blade shape, angle of attack or number of blades work better than others. In addition, the complexity of the flow through and around the turbine cannot be predicted with analytical tools and hence requires more detailed predictions. Thus, high-resolution numerical simulations using Computational Fluid Dynamics (CFD) can provide an enormous amount of data and, if accurate, can give insight into the complex fluid-structure interaction of tidal