### Abstract

Uncertainty affects estimates of the power potential of tidal currents, resulting in large ranges in values reported for a given site, such as the Pentland Firth, UK. We examine the role of bottom friction, one of the most important sources of uncertainty. We do so by using perturbation methods to find the leading-order effect of bottom friction uncertainty in theoretical models by Garrett & Cummins (2005 Proc. R. Soc. A 461, 2563-2572. (doi:10.1098/rspa.2005.1494); 2013 J. Fluid Mech. 714, 634-643. (doi:10.1017/jfm.2012.515)) and Vennell (2010 J. Fluid Mech. 671, 587-604. (doi:10.1017/S0022112010006191)), which consider quasi-steady flow in a channel completely spanned by tidal turbines, a similar channel but retaining the inertial term, and a circular turbine farm in laterally unconfined flow. We find that bottom friction uncertainty acts to increase estimates of expected power in a fully spanned channel, but generally has the reverse effect in laterally unconfined farms. The optimal number of turbines, accounting for bottom friction uncertainty, is lower for a fully spanned channel and higher in laterally unconfined farms. We estimate the typical magnitude of bottom friction uncertainty, which suggests that the effect on estimates of expected power lies in the range -5 to +30%, but is probably small for deep channels such as the Pentland Firth (5-10%). In such a channel, the uncertainty in power estimates due to bottom friction uncertainty remains considerable, and we estimate a relative standard deviation of 30%, increasing to 50% for small channels.

Original language | English |
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Article number | 180941 |

Number of pages | 20 |

Journal | Royal Society Open Science |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2019 |

### Cite this

*Royal Society Open Science*,

*6*(1), [180941]. https://doi.org/10.1098/rsos.180941

}

*Royal Society Open Science*, vol. 6, no. 1, 180941. https://doi.org/10.1098/rsos.180941

**The effect of uncertain bottom friction on estimates of tidal current power.** / Kreitmair, M. J.; Draper, S.; Borthwick, A. G. L.; van den Bremer, T. S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The effect of uncertain bottom friction on estimates of tidal current power

AU - Kreitmair, M. J.

AU - Draper, S.

AU - Borthwick, A. G. L.

AU - van den Bremer, T. S.

PY - 2019/1

Y1 - 2019/1

N2 - Uncertainty affects estimates of the power potential of tidal currents, resulting in large ranges in values reported for a given site, such as the Pentland Firth, UK. We examine the role of bottom friction, one of the most important sources of uncertainty. We do so by using perturbation methods to find the leading-order effect of bottom friction uncertainty in theoretical models by Garrett & Cummins (2005 Proc. R. Soc. A 461, 2563-2572. (doi:10.1098/rspa.2005.1494); 2013 J. Fluid Mech. 714, 634-643. (doi:10.1017/jfm.2012.515)) and Vennell (2010 J. Fluid Mech. 671, 587-604. (doi:10.1017/S0022112010006191)), which consider quasi-steady flow in a channel completely spanned by tidal turbines, a similar channel but retaining the inertial term, and a circular turbine farm in laterally unconfined flow. We find that bottom friction uncertainty acts to increase estimates of expected power in a fully spanned channel, but generally has the reverse effect in laterally unconfined farms. The optimal number of turbines, accounting for bottom friction uncertainty, is lower for a fully spanned channel and higher in laterally unconfined farms. We estimate the typical magnitude of bottom friction uncertainty, which suggests that the effect on estimates of expected power lies in the range -5 to +30%, but is probably small for deep channels such as the Pentland Firth (5-10%). In such a channel, the uncertainty in power estimates due to bottom friction uncertainty remains considerable, and we estimate a relative standard deviation of 30%, increasing to 50% for small channels.

AB - Uncertainty affects estimates of the power potential of tidal currents, resulting in large ranges in values reported for a given site, such as the Pentland Firth, UK. We examine the role of bottom friction, one of the most important sources of uncertainty. We do so by using perturbation methods to find the leading-order effect of bottom friction uncertainty in theoretical models by Garrett & Cummins (2005 Proc. R. Soc. A 461, 2563-2572. (doi:10.1098/rspa.2005.1494); 2013 J. Fluid Mech. 714, 634-643. (doi:10.1017/jfm.2012.515)) and Vennell (2010 J. Fluid Mech. 671, 587-604. (doi:10.1017/S0022112010006191)), which consider quasi-steady flow in a channel completely spanned by tidal turbines, a similar channel but retaining the inertial term, and a circular turbine farm in laterally unconfined flow. We find that bottom friction uncertainty acts to increase estimates of expected power in a fully spanned channel, but generally has the reverse effect in laterally unconfined farms. The optimal number of turbines, accounting for bottom friction uncertainty, is lower for a fully spanned channel and higher in laterally unconfined farms. We estimate the typical magnitude of bottom friction uncertainty, which suggests that the effect on estimates of expected power lies in the range -5 to +30%, but is probably small for deep channels such as the Pentland Firth (5-10%). In such a channel, the uncertainty in power estimates due to bottom friction uncertainty remains considerable, and we estimate a relative standard deviation of 30%, increasing to 50% for small channels.

KW - tidal power

KW - renewable energy

KW - resource assessment

KW - uncertainty

KW - bottom friction

KW - bed roughness

KW - CURRENT ENERGY

KW - TURBINES

KW - FARM

U2 - 10.1098/rsos.180941

DO - 10.1098/rsos.180941

M3 - Article

VL - 6

JO - Royal Society Open Science

JF - Royal Society Open Science

SN - 2054-5703

IS - 1

M1 - 180941

ER -