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.

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Until recently tidal stream turbine design has been carried out mainly by experimental prototype testing aiming at maximum turbine efficiency. The harsh and highly turbulent environments in which tidal stream turbines operate in poses a design challenge mainly with regards to survivability of the turbine owing to the fact that tidal turbines are exposed to significant intermittent hydrodynamic loads. Credible numerical models can be used as a complement to experiments during the design process of tidal stream turbines. They can provide insights into the hydrodynamics, predict tidal turbine performance and clarify their fluid-structure interaction as well as quantify the hydrodynamic loadings on the rotor. The latter can lead to design enhancements aiming at increased robustness and survivability of the turbine. Physical experiments and complementary large-eddy simulations of flow around a horizontal axis tidal turbine rotor are presented. The goal is to provide details of the hydrodynamics around the rotor, the performance of the turbine and acting hydrodynamic forces on the rotor blades. The simulation results are first compared with the

The wake recovery downstream of a vertical axis turbine operating in a turbulent channel flow is investigated via detailed velocity measurements using an Acoustic Doppler Velocimeter. Three distinct wake regions are identified: (i) a near-wake region which extends until two rotor diameters (2D) downstream and characterised by a low-momentum area isolated from the ambient flow and the presence of energetic dynamic stall vortices; (ii) a transition region (2D-5D), characterised by a fast momentum recovery, high turbulence intensity levels and vertical expansion of the wake; and (iii) a far-wake region beyond 5D where the velocity recovers to approximately 95% of the free-stream velocity. Albeit the wake deficit recovery is mostly accomplished at 5D behind the turbine, rotorinduced effects are still present beyond 10D as indicated by high-order flow statistics, such as high velocity fluctuations and flow skewness. Analysis of the streamwise momentum budget reveal that advection terms are mainly responsible for momentum replenishment through most of the wake and turbulent transport terms play only a minor role. This study evidences the anisotropic nature of the turbulence and asymmetry of the flow in horizontal, vertical and cross-sectional planes downstream of the vertical axis turbine.

A large-eddy simulation (LES) of a laboratory-scale horizontal axis tidal stream turbine operating over an irregular bathymetry in the form of dunes is performed. The Reynolds number based on the approach velocity and the chord length of the turbine blades is approximately 60,000. The simulated turbine is a 1:30 scale model of a full-scale prototype and both turbines operate at very similar tip-speed ratio of λ ≈ 3. The simulations provide quantitative evidence of the effect of seabed-induced turbulence on the instantaneous performance and structural loadings of the turbine revealing how large-scale, energetic turbulence structures affect turbine performance and bending moments of the rotor blades. The data analysis shows that wake recovery is notably enhanced in comparison to the same turbine operating above a flat-bed and this is due to the higher turbulence levels generated by the dune. The results demonstrate the need for studying in detail the flow and turbulence characteristics at potential tidal turbine deployment sites and to incorporate observed large-scale velocity and pressure fluctuations into the structural design of the turbines.