Exceeding the Betz limit with tidal turbines

The Betz limit sets a theoretical upper limit for the power production by turbines expressed as a maximum power coefficient of 16/27. While power production by wind turbines falls short of the Betz limit, tidal turbines in a channel can theoretically have a power coefficient several times larger than 16/27. However, power extraction by turbines in large tidal farms also reduces the flow along the channel, limiting their maximum output. Despite this flow reduction, turbines in tidal farms can produce enough power to meet a stricter definition of what it means to exceed the Betz limit, one where the maximum power output of a turbine at the reduced flow exceeds the maximum output from a single Betz turbine operating in the unreduced flow. While having a power coefficient >16/27 is easily achieved by turbines in a channel, generating enough power to meet this stricter definition of exceedance is much more difficult. Whether turbines meet this stricter definition depends on their number, how they are arranged and tuned, and the dynamical balance of the channel. Arranging a tidal turbine farm so that the turbines within it exceed the stricter Betz limit would give tidal turbine farms an economic advantage over similarly sized wind farms. However, exceeding the stricter limit comes at a cost of both higher structural loads on the tidal turbines and the need to produce power from weaker flows. Farms in a channel loosely based on the Pentland Firth are used to discuss exceedance and structural loads.