In this paper we extend linear momentum actuator disc theory to consider two rows of tidal turbines placed in a centred or staggered arrangement. The extensions assume a streamwise spacing between rows that is sufficient for pressure equalization, but is not too large for significant mixing of the upstream turbine wake before the second row. We first consider a given number of turbines in a tidal channel; in this case the average power for a staggered arrangement over two rows is found to be higher than that for a centred arrangement, but lower than can be obtained by placing all turbines side-by-side in one row (if all turbines have the same local resistance). Furthermore, staggered arrangements extract power more efficiently than centred arrangements, but less efficiently than a single row with the same number of turbines, and this has implications for ranking different arrangements of tidal turbines. We also use the extended actuator disc models (together with an argument of scale separation) to consider some example arrangements of tidal turbines in laterally unconfined flow. Specifically, it is shown that locally staggering a fixed number of turbines in an array to form a tidal farm generates less power than placing the same number of turbines side-by-side. However, if more than one row of turbines is adopted (perhaps to keep the farm spatially compact) then the optimum turbine spacing within a row increases significantly with addition of a second row. This trend suggests that multi-row tidal turbine farms would require wide turbine spacing within each row to maximize the power per turbine, similarly to existing offshore wind farms.

Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines.

On-bottom stability design of subsea pipelines transporting hydrocarbons is important to ensure safety and reliability but is challenging to achieve in the onerous metocean (meteorological and oceanographic) conditions typical of large storms (such as tropical cyclones, hurricanes or typhoons). This challenge is increased by the fact that industry design guidelines presently give no guidance on how to incorporate the potential benefits of seabed mobility, which can lead to lowering and self-burial of the pipeline on a sandy seabed. In this paper, we demonstrate recent advances in experimental modelling of pipeline scour and present results investigating how pipeline stability can change in a large storm. An emphasis is placed on the initial development of the storm, where scour is inevitable on an erodible bed as the storm velocities build up to peak conditions. During this initial development, we compare the rate at which peak near-bed velocities increase in a large storm (typically less than 10 ⁻³ m s ⁻² ) to the rate at which a pipeline scours and subsequently lowers (which is dependent not only on the storm velocities, but also on the mechanism of lowering and the pipeline properties). We show that the relative magnitude of these rates influences pipeline embedment during a storm and the stability of the pipeline.