Internal tides are internal gravity waves generated in stratified waters by the interaction of barotropic tidal currents with variable bottom topography. They play a role in dissipating tidal energy and lead to mixing in the deep ocean. Key dimensionless parameters governing their generation include the tidal excursion compared with the scale of the topography, the bottom slope compared with the angle at which rays of internal waves of tidal frequency propagate, and the height of the topography compared with the depth of the ocean. Recent theoretical developments for parts of this parameter space particularly relevant to the deep ocean show that most of the energy flux is associated with low modes that propagate away from the generation region. For isolated features this energy flux is not strongly dependent on the bottom slope. Intense beams of internal tidal energy are expected near “critical slopes," bottom slopes equal to the ray slope, and lead to local mixing.

There is an upper bound to the amount of power that can be generated by turbines in tidal channels as too many turbines merely block the flow. One condition for achievement of the upper bound is that the turbines are deployed uniformly across the channel, with all the flow through them, but this may interfere with other uses of the channel. An isolated turbine is more effective in a channel than in an unbounded flow, but the current downstream is non-uniform between the wake of the turbines and the free stream. Hence some energy is lost when these streams merge, as may occur in a long channel. We show here, for ideal turbine models, that the fractional power loss increases from 1/3 to 2/3 as the fraction of the channel cross-section spanned by the turbines increases from 0 to close to 1. In another scenario, possibly appropriate for a short channel, the speed of the free stream outside the turbine wake is controlled by separation at the channel exit. In this case, the maximum power obtainable is slightly less than proportional to the fraction of the channel cross-section occupied by turbines.

Interest in sources of renewable energy has led to increasing attention being paid to the potential of strong tidal currents. There is a limit to the available power, however, as too many turbines will merely block the flow, reducing the power generated. The maximum average power available from a tidal stream along a channel, such as that between an island and the mainland, is estimated and found to be typically considerably less than the average kinetic energy flux in the undisturbed state through the most constricted cross-section of the channel. A general formula gives the maximum average power as between 20 and 24% of the peak tidal pressure head, from one end of the channel to the other, times the peak of the undisturbed mass flux through the channel. This maximum average power is independent of the location of the turbine ‘fences’ along the channel. The results may also be used to evaluate the power potential of steady ocean currents.

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