## 3 Analysis  
Our recorded data sets were put into wind speed classes starting at 6 m/s, 12 m/s, and 16 m/s. Measurements were triggered manually if wind conditions were regarded as suitable. The bin size for each class was generally \(\pm 2\) m/s, and for some cases (offshore class 10 m/s, offshore class 12 m/s), it was less (lower limit: \(-1\) m/s). For each measurement, the statistical characteristics were analyzed with respect to the power-spectral density, incremental distributions, shape factors, structure functions, auto-correlations and Taylor's micro-scale. (It may be interesting to note that [PERSON]'s micro-scale may have an complementary interpretation to the _Markov-Einstein coherence length_[18]. To use this one seems to be much more physical than the somewhat vague interpretation of the average turbulent vortex size.) We now explain our methods in more detail. The increments of measured quantities were defined as  
\[\Delta u=u(t+\Delta t)-u(t)\qquad\Leftrightarrow\qquad\Delta p=p(t+\Delta t )-p(t), \tag{1}\]  
where \(u\) is the velocity, \(p\) is the pressure, \(t\) is the time, and \(\Delta t\) is a fixed time increment. The increments also eliminated the mean value of the time series and thus, stochastic fluctuations remained for a specific time scale (\(\Delta t\)). These increments were the basic statistical quantities used for more sophisticated analyses like structure functions or the so-called shape parameter. Reference [13] suggested that the distribution of increments may be described as a superposition of two distributions, one of them being lognormal. The shape factor then may be regarded as a measure of the level of intermittency. In accordance with [PERSON]'s approach from reference [12], the shape parameter can be calculated by the 2 nd and 4 th order moments of the distribution:  
\[s_{u}^{2}=\ln\left(\frac{1}{3}\frac{\left\langle\Delta u^{4}\right\rangle}{ \left\langle\Delta u^{2}\right\rangle^{2}}\right)\qquad\Rightarrow\qquad s_{ p}^{2}=\ln\left(\frac{1}{3}\frac{\left\langle\Delta p^{4}\right\rangle}{ \left\langle\Delta p^{2}\right\rangle^{2}}\right), \tag{2}\]  
where \(s_{u}^{2}\) is the shape factor for the velocity and \(s_{p}^{2}\) is the shape factor for the pressure. The brackets \(\left\langle x\right\rangle\) define the mean value of a quantity (\(x\)). Further properties are given in reference [12]. A value of \(s^{2}\approx 0\) indicates a normal distribution. It is worth noting that another important parameter for the deviation from Gaussian behavior, skewness, which is related to third-order moments, was found to be small [17]. It has well-known, at least since the work of reference [19], that turbulent velocities and pressures obey different scaling laws (\(\sim k^{-5/3}\) and \(\sim k^{-7/5}\), respectively), although they are seemingly related by \(p\sim v^{2}\) according to [PERSON]'s law. A direct comparison of a hot-wire with piezo-electric pressure sensor data showed comparable power density spectra up to 4 kHz (see [17], unpublished), however. Theoretical as well as experimental investigations of reference [20] are still incomplete, so that there is no clear answer so far about how \(s_{u}^{2}\) and \(s_{p}^{2}\) are related to each other. When heat transfer occurs, such as in the atmospheric boundary layer if the sea is warmer than the air (autumn), thermal stratification becomes more important. Simple static stability of the boundary layer may be used to characterize levels of turbulence. As was shown by reference [21], the turbulence intensity differs remarkably for stable and unstable flow when used to describe fatigue loads of wind turbines. A simple characterization of a stratified boundary layer exposed to heat transfer was introduced by reference [4] as being stable, neutral, or unstable. Different calculation methods have been used to distinguish these states ([4]) depending on what is known in terms of input. In our case, a Richardson's number approach was used, in accordance with common practice in wind energy meteorology [22; 23; 24].