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On the Apparent “Imbalance” Term in the Turbulent Kinetic Energy Budget

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  • 1 Southampton Oceanography Centre, Southampton, United Kingdom
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Abstract

A synthetic dataset is used to show that apparent variations between different stability classes in the mean drag coefficient, CD10n, to wind speed relationship can be explained by random errors in determining the friction velocity u∗. Where the latter has been obtained by the inertial dissipation method, the variations in CD10n have previously been ascribed to an imbalance between production and dissipation in the turbulent kinetic energy budget. It follows that the application of “imbalance corrections” when calculating u∗ is incorrect and will cause a positive bias in CD10n, by about 10−4.

With no imbalance correction, random errors in u∗ result in scatter in the CD10n values, but for most wind speeds, there is no mean bias. However, in light winds under unstable conditions random errors in u∗ act to positively bias the calculated CD10n values. This is because the stability related effects are nonlinear and also because for some records for which CD10n would be decreased, the iteration scheme does not converge. The threshold wind speed is typically 7 m s−1, less for cleaner datasets. The biased CD10n values can be avoided by using a u∗ value calculated from a mean CD10nU10n relationship to determine the stability. The choice of the particular relationship is not critical. Recalculating previously published CD10n values without imbalance correction, but with anemometer response correction, results in a decrease of CD10n but only by about 0.05 × 10−3.

In addition to removing a previous cause of scatter and uncertainty in inertial dissipation data, the results suggest that spurious stability effects and low wind speed biases may be present in CD10n estimates obtained by other methods.

Corresponding author address: Dr. Peter K. Taylor, Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, United Kingdom.

Email: Peter.K.Taylor@soc.soton.ac.uk

Abstract

A synthetic dataset is used to show that apparent variations between different stability classes in the mean drag coefficient, CD10n, to wind speed relationship can be explained by random errors in determining the friction velocity u∗. Where the latter has been obtained by the inertial dissipation method, the variations in CD10n have previously been ascribed to an imbalance between production and dissipation in the turbulent kinetic energy budget. It follows that the application of “imbalance corrections” when calculating u∗ is incorrect and will cause a positive bias in CD10n, by about 10−4.

With no imbalance correction, random errors in u∗ result in scatter in the CD10n values, but for most wind speeds, there is no mean bias. However, in light winds under unstable conditions random errors in u∗ act to positively bias the calculated CD10n values. This is because the stability related effects are nonlinear and also because for some records for which CD10n would be decreased, the iteration scheme does not converge. The threshold wind speed is typically 7 m s−1, less for cleaner datasets. The biased CD10n values can be avoided by using a u∗ value calculated from a mean CD10nU10n relationship to determine the stability. The choice of the particular relationship is not critical. Recalculating previously published CD10n values without imbalance correction, but with anemometer response correction, results in a decrease of CD10n but only by about 0.05 × 10−3.

In addition to removing a previous cause of scatter and uncertainty in inertial dissipation data, the results suggest that spurious stability effects and low wind speed biases may be present in CD10n estimates obtained by other methods.

Corresponding author address: Dr. Peter K. Taylor, Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, United Kingdom.

Email: Peter.K.Taylor@soc.soton.ac.uk

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