On the Extractable Power from a Tidal Channel

The drive to develop marine renewable energy has made resource assessments a matter of pressing need and ongoing research. In the case of tidal in-stream power generation, a central objective of such assessments is to estimate the maximum power that may be extracted from tidal motions based on observable properties of the flow in the natural undisturbed state. To this end, analytical models have been developed for simple geometries, such as a channel connecting the open ocean to an inner basin. A key assumption of these models is that the along-channel volume flux is nondivergent. This requires the channel length to be small in comparison to the tidal wavelength and also that $\mu \ll 1$ , where $\mu$ is the ratio of the surface area of the channel to that of the basin. A practical consequence of assuming nondivergent flow is that the extractable power is then independent of position along the channel. In the present study, a linear one-dimensional model is developed to study the power potential of a uniform tidal channel that is spanned by a turbine fence and that links a bay to the open ocean. The assumption of nondivergent flow is relaxed, permitting an exploration of the sensitivity of the extractable power to nondimensional parameters measuring the relative channel length and area. Depending on parameter values, the results show that assuming nondivergent flow may lead to an underestimation of the available power. For long waves, the maximum extractable power is shown to scale as $(1+\mu )$ , thus providing a simple correction to account for the effects of finite channel area. It is shown that the power potential may vary appreciably with the position along the channel. However, for long waves the optimal location of the turbine fence is always at the mouth where the magnitude of the along-channel flow is greatest.