Kreitmair M J, Draper S, Borthwick A G L, van den Bremer T S
School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, UK.
Faculty of Engineering, Computing and Mathematics, The University of Western Australia, Crawley Western Australia 6009, Australia.
R Soc Open Sci. 2019 Jan 9;6(1):180941. doi: 10.1098/rsos.180941. eCollection 2019 Jan.
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 , 2563-2572. (doi:10.1098/rspa.2005.1494); 2013 , 634-643. (doi:10.1017/jfm.2012.515)) and Vennell (2010 , 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.
不确定性影响着潮流发电潜力的估计，导致给定地点（如英国彭特兰湾）报告的数值范围很大。我们研究了底部摩擦这一最重要的不确定性来源之一的作用。我们通过使用微扰方法来找出底部摩擦不确定性在加勒特和卡明斯（2005年，第2563 - 2572页。（doi:10.1098/rspa.2005.1494）；2013年，第634 - 643页。（doi:10.1017/jfm.2012.515））以及维内尔（2010年，第587 - 604页。（doi:10.1017/S0022112010006191））的理论模型中的一阶效应，这些模型分别考虑了完全由潮汐涡轮机覆盖的通道中的准稳态流、一个类似的通道但保留惯性项以及横向无约束流中的圆形涡轮机农场。我们发现底部摩擦不确定性在完全覆盖的通道中会增加预期功率的估计值，但在横向无约束的农场中通常具有相反的效果。考虑到底部摩擦不确定性，完全覆盖通道的最佳涡轮机数量较少，而横向无约束农场的最佳涡轮机数量较多。我们估计了底部摩擦不确定性的典型量级，这表明其对预期功率估计的影响在 -5% 至 +30% 的范围内，但对于像彭特兰湾这样的深通道可能较小（5% - 10%）。在这样的通道中，由于底部摩擦不确定性导致的功率估计不确定性仍然相当大，我们估计相对标准偏差为30%，对于小通道则增加到50%。
