Fast tidal streams are a promising source of clean and predictable power, but the task of arranging tidal turbines for maximum power capture is complicated. Actuator disc models have proven useful in seeking optimal turbine arrangements, yet these models assume flows which are frictionless and steady, and thus quite unlike the channel flow conditions that actual tidal turbines experience. In this paper, we use numerical methods to relax these assumptions and explore how optimal turbine arrangements change as the flow transitions from frictionless and steady to rough and oscillatory. In so doing, we show that, under certain conditions, the assumption of steady flow in models of tidal turbines may neglect leading-order physics. When the ratio of drag to inertial forces in the channel is very low, for instance, the optimal turbine arrangements are found to be quite different, and the potential for enhanced power capture much greater, than what is predicted by actuator disc theory.

In this paper, an upper bound approach is used to determine the maximum power available to tidal stream turbines placed at five sites along the west coast of Peninsular Malaysia. A depth-averaged hydrodynamic model of the Malacca Strait is built and validated against field measurements. Actuator disc theory is then used to introduce rows of tidal stream turbines as line sinks of momentum and to determine the maximum time-averaged power available to rows of both moderately sized and very large turbines, placed strategically at the locations of highest naturally occurring kinetic energy flux. Results suggest that although the Malaysian tidal stream energy resource is not large enough to make a significant contribution to the country's energy mix, there may yet be opportunities to use low-speed tidal turbines in small-scale and off-grid electricity generation schemes. Methods are described in detail and links to source codes and results are provided to encourage the application of this simple, yet effective resource assessment methodology to other promising tidal energy sites.

The limit of power extraction by a device which makes use of constructive interference, i.e. local blockage, is investigated theoretically. The device is modelled using actuator disc theory in which we allow the device to be split into arrays and these then into sub-arrays an arbitrary number of times so as to construct an $n$ -level multi-scale device in which the original device undergoes $n-1$ sub-divisions. The alternative physical interpretation of the problem is a planar system of arrayed turbines in which groups of turbines are homogeneously arrayed at the smallest $n\mathrm {th}$ scale, and then these groups are homogeneously spaced relative to each other at the next smallest $n-1\mathrm {th}$ scale, with this pattern repeating at all subsequent larger scales. The scale-separation idea of Nishino & Willden (J. Fluid. Mech., vol. 708, 2012b, pp. 596–606) is employed, which assumes mixing within a sub-array occurs faster than mixing of the by-pass flow around that sub-array, so that in the $n$ -scale device mixing occurs from the inner scale to the outermost scale in that order. We investigate the behaviour of an arbitrary level multi-scale device, and determine the arrangement of actuator discs ( $n\mathrm {th}$ level devices) which maximises the power coefficient (ratio of power extracted to undisturbed kinetic energy flux through the net disc frontal area). We find that this optimal arrangement is close to fractal, and fractal arrangements give similar results. With the device placed in an infinitely wide channel, i.e. zero global blockage, we find that the optimum power coefficient tends to unity as the number of device scales tends to infinity, a 27/16 increase over the Lanchester–Betz limit of $0.593$ . For devices in finite width channels, i.e. non-zero global blockage, similar observations can be made with further uplift in the maximum power coefficient. We discuss the fluid mechanics of this energy extraction process and examine the scale distribution of thrust and wake velocity coefficients. Numerical demonstration of performance uplift due to multi-scale dynamics is also provided. We demonstrate that bypass flow remixing and ensuing energy losses increase the device power coefficient above the limits for single devices, so that although the power coefficient can be made to increase, this is at the expense of the overall efficiency of energy extraction which decreases as wake-scale remixing losses necessarily rise. For multi-scale devices in finite overall blockage two effects act to increase extractable power; an overall streamwise pressure gradient associated with finite blockage, and wake pressure recoveries associated with bypass-scale remixing.

There are two approaches to extracting power from tides — either turbines are placed in areas of strong flows or turbines are placed in barrages enabling the two sides of the barrage to be closed off and a head to build up across the barrage. Both of these energy extraction approaches will have a significant back effect on the flow, and it is vital that this is correctly modelled in any numerical simulation of tidal hydrodynamics. This paper presents the inclusion of both tidal stream turbines and tidal barrages in the depth-averaged shallow water equation model DG-SWEM. We represent the head loss due to tidal stream turbines as a line discontinuity — thus we consider the turbines, and the energy lost in local wake-mixing behind the turbines, to be a sub-grid scale processes. Our code allows the inclusion of turbine power and thrust coefficients which are dependent on Froude number, turbine blockage, and velocity, but can be obtained from analytical or numerical models as well as experimental data. The barrage model modifies the existing culvert model within the code, replacing the original cross-barrier pipe equations. At the location of this boundary, velocities through sluice gates are calculated according to the orifice equation. For simulating the turbines, a Hill Chart for low head bulb turbines provided by Andritz Hydro is used. We demonstrate the implementations on both idealised geometries where it is straightforward to compare against other models and numerical simulations of real candidate sites for tidal energy in Malaysia and the Bristol Channel.