Stability modifications of the Frøya wind spectrum

Abstract

A general-stability wind spectrum for the marine boundary layer being an extension of the Frøya wind spectrum (Andersen and Løvseth, 2006) is proposed in order to quantify spectral stability modifications for marine operations and wind turbines.

The analysis of the Frøya data was based on results from the literature: Stability modifications are given by the ratio of a geometrical length scale Z_SC increasing linearly with height to a crude representation of the Monin–Obukhov length L. It was a problem that the Frøya data were not available in digital form.

Based on a slightly conservative approach restricted to periods below 6 min, the major spectral stability modification was found to be a linear scaling, whereas frequency shifting was less evident. A smooth representation of the linear scaling factor versus the above ratio was found correspond to monotonic decrease for stable conditions and unlimited monotonic increase for unstable conditions. The modification vanishes as the wind speed increases.

In view of the large scatter in the results for near-neutral stability and the need for better resolution for wind speed and static stability, it is necessary to re-analyse the Frøya database (in digital form) or to analyse some other relevant data set.

Introduction

A wind spectrum for the maritime boundary layer (MBL) during severe weather conditions with relevance for floating marine structures was the most important result from the Frøya project (Andersen and Løvseth, 2006). The Frøya spectrum is mainly a description of the fluctuations of the horizontal wind speed during neutral conditions and in the height range 10–100 m above sea level and has been incorporated in the guidelines NORSOK (1999), API RP2A, and ISO/DIS 19901. For wind speed (10 m, 1 h) stronger than gale (15 m/s), the MBL becomes gradually better mixed and therefore neutrally stratified. The main focus when establishing this description was low frequency wind fluctuations (periods around 20 s–5 min) during near-neutral conditions for measured reference wind speed in the range 10–26 m/s. This reflects the need to obtain a spectral description for floating structures with natural periods in the range around 0.5–2 min during severe weather 35–40 m/s.

The low frequency range is generally associated with significant uncertainty. This is so both because most investigations (Andersen, 1991) have focused on higher frequencies reflecting the needs for most land based structures, but also because very few studies have been made over the ocean (Wills et al., 1986; Shiotani, 1975; Ochi and Shin, 1988). Also, the low frequency range is known to be very sensitive to the effects of MBL stability (Plate, 1982). Thus, very accurate temperature profile measurements are required to ensure that near-neutral data only are included in the analysis and that the spectrum can adequately be extrapolated to severe conditions. Insufficient temperature profile data were a severe shortcoming of some earlier studies (Wills et al., 1986; Shiotani, 1975; Ochi and Shin, 1988).

In the present study, the focus is still on the height and frequency ranges indicated above. However, it is now the operational wind speed range (<15–20 m/s) which is emphasized. This range is important for marine operations and wind turbines and is sensitive to stability effects. This means that a generalization of the Frøya wind spectrum quantifying these effects is needed to provide an adequate spectral description in this range. In view of the engineering practice to use wind spectra based on neutral conditions (NORSOK, 1999; API RP2A; and ISO/DIS 19901), the present generalization will provide a measure of the contribution to the uncertainty of such spectra due to stability effects. It is desirable that this generalization is made within findings from the literature, particularly with attention given to deviations from the neutral Frøya spectrum in terms of simple parameterizations.

As for the Frøya wind spectrum, the data used presently are those from the Frøya project. The main reason for this is the excellent quality of this 15 year old data set both with respect to wind speed and stability. Also, the data set had not been fully and consistently analysed with respect to the effects of stability. However, due to numerous computer system revisions over the years the data are no longer easily available on digital form. Thus, for the present study they had to be extracted from a report (Andersen and Løvseth, 1992) where they were available on graphs with insufficient resolution. The quality of the data presently used, the analysis and the results of the present study are likely to suffer from this.