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

机译：不确定的底部摩擦对潮流功率估计的影响

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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.
机译：不确定性会影响对潮流潜力的估计，从而导致给定站点（例如，英国Pentland Firth）的报告值存在较大范围。我们研究了底部摩擦的作用，底部摩擦是不确定性的最重要来源之一。为此，我们采用了摄动法来找到Garrett＆Cummins（2005 Proc。R. Soc。A 461，2563–2572。（doi：10.1098 / rspa.2005.1494））在理论模型中底部摩擦不确定性的前导效应。 2013 J.Fluid Mech.714，634-643。（doi：10.1017 / jfm.2012.515））和Vennell（2010 J.Fluid Mech.671，587-604。（doi：10.1017 / S0022112010006191）），考虑了准潮汐涡轮机完全覆盖的通道中有稳定的水流，类似的通道但保留了惯性项，​​而横向无限制流动的圆形涡轮机场。我们发现底部摩擦的不确定性会增加全跨通道中预期功率的估计，但通常在侧向无限制的农场中会产生相反的影响。考虑到底部摩擦不确定性的最佳涡轮机数量，对于全跨度通道而言较低，而在侧向无限制的农场中较高。我们估计了底部摩擦不确定度的典型大小，这表明对预期功率估计的影响在5％至+ 30％的范围内，但对于深水通道（如Pentland Firth）可能很小（5-10％）。在这样的通道中，由于底部摩擦的不确定性，功率估计的不确定性仍然很大，我们估计相对标准偏差为30％，对于小通道，则增加到50％。

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