Velocity Spectra and Coherence Estimates in the Marine Atmospheric Boundary Layer

Abstract

Two years of continuous sonic anemometer measurements conducted in 2007 and 2008 at the FINO1 platform are used to investigate the characteristics of the single- and two-point velocity spectra in relation to the atmospheric stability in the marine atmospheric boundary layer. The goals are to reveal the limits of current turbulence models for the estimation of wind loads on offshore structures, and to propose a refined description of turbulence at altitudes where Monin–Obukhov similarity theory may be limited. Using local similarity theory, a composite spectrum model, combining a pointed and a blunt model, is proposed to describe the turbulence spectrum for unstable, neutral and stable conditions. Such a model captures the $-1$ power law followed by the velocity spectra at an intermediate frequency range in the marine atmospheric boundary layer. For the Monin–Obukhov similarity parameter $\zeta < 0.3$, the Davenport coherence model captures the vertical coherence of the horizontal velocity components well. A two-parameter exponential decay function is found more appropriate for modelling the coherence of the vertical velocity component. Under increasingly stable conditions, the size of the eddies in the vertical coordinate reduces, such that smaller separation distances than that covered in the present dataset may be required to study the coherence with sufficient accuracy.

Appendix 1

In Table 3, the parameters of the pointed–blunt model obtained by the least-squares fit method are displayed for the along-wind component. As this component does not follow Monin–Obukhov similarity theory under unstable conditions, the coefficients $a^u_i$ and $b^u_i$, $i = \left\{ 1,2 \right\}$ are height dependent at $\zeta < -0.1$. In contrast, the parameters are more or less height independent for a stable stratification as local similarity theory should be applicable in this case. The height dependency is also linked to the modelling of the $-1$ spectral range, which is more pronounced at lower heights and neutral conditions. For $\zeta >0.1$, the spectral plateau disappears, while the spectral gap and mesoscale spectral range become dominating features of the 1-h velocity spectrum, such that Eq. 26 can be approximated by Eq. 28.

Table 3 Parameters obtained by fitting Eq. 26 and Eq. 28 to the $S_u$ velocity spectrum in Fig. 6