Wind model

Wind is a turbulent flow of air; wind speed and direction vary in space and time. At a particular point in space wind may be considered to consist of a steady mean flow with an associated mean direction, and speeds that vary in time and direction around this mean. The velocity can thus be written in the form of the following vector equation:

wi w w

U ( x, y, z;t ) U ( x, y, z ) u ( x, y, z;t )= + (4.2-1)

where: Uwi = local and instantaneous wind velocity vector

Uw = mean wind velocity vector at point ( , , which is constant

in magnitude and direction over a period of time that is long compared to the time t

, )

x y z

uw = turbulent wind velocity vector around the mean velocity Uwat point

;

( , , )x y z

u_w varies in magnitude and direction as a function of time, while

the time average of uw is by definition zero.

There is normally insufficient data available to describe the spatial and time variations in great detail, while for most applications this is also unnecessary. Therefore, descriptions of the wind field are usually substantially simplified in that wind parameters are described in statistical terms such as the mean and the standard deviation of the speed as well as the direction. For the definition of such statistical parameters both length scales and time scales are needed.

Let us first consider the variation in time. When very long records of wind velocity are analysed it turns out that there are short-period variations due to turbulence, with periods ranging mainly from a few seconds to some 6 minutes, and long-period variations with periods ranging from several hours to many days. Figure 4.2-1 shows a typical power spectrum of the wind velocity determined by Van der Hoven [4.2-1] that clearly shows both variations. The long-term variations show a lower peak at around 12 hours associated with the daily thermal cycle and a higher peak at some 100 hours or 4 days, due to the succession of pressure systems passing the measurement station at the time that the measurements were taken. The figure further shows that the two variations are clearly separated by a spectral gap, i.e. a range of low wind energy, around a period of 1 hour. Therefore 1 hour is a suitable period for averaging of wind speeds (and directions). The long period variations will then manifest themselves as slow changes of the mean velocity Uw( , , )x y z , while the short-period

variations are rapid fluctuations uw( , , ; )x y z t about Uw( , , )x y z .

As to the spatial variation, observations show that on length scales that are typical of an offshore structure (even the largest ones) the mean and standard deviation of the wind speed and direction, averaged over durations of the order of an hour or so, do not vary horizontally. However, vertically they differ with elevation above the ground or above mean sea level

Due to its variability in space and time a wind velocity value is only meaningful if it is qualified by its elevation as well as the duration over which it is averaged. With regard to time averages wind velocities are classified as either:

• sustained wind velocities, which are averages over 1 minute or longer; • wind gust velocities, which are averages over less than 1 minute.

The mean velocity determined by averaging the wind velocity Uwi( , , ; )x y z t at a height of 10

m above MSL over a duration of 1 hour is used as a standard reference value . For shorter

averaging durations than 1 hour there will clearly be periods in which the mean wind velocity is higher. Examples are the 10 min. sustained wind, the 1 min. sustained wind and the 3 s wind gust velocity.

Uw0

The fluctuating velocity uw( , , ; )x y z t for appreciably shorter than the averaging duration is

usually referred to as a wind gust. It reflects the local turbulence in the atmospheric conditions. Detailed information about the full structure of the turbulent wind field will rarely be available. Therefore the spatial variation of

t

uw( , , ; )x y z t is generally assumed to be similar

to that of the sustained wind. In other words, uw( , , ; )x y z t is assumed to be a horizontal

velocity in the same direction as the mean wind with a vertical profile, i.e. it reduces to the

scalar quantity . As a function of time varies randomly about a zero mean in an

approximately gaussian manner. Further and more detailed information about mean and gust wind may e.g. be found in references [4.2-2] to [4.2-4].

uw( ; )z t uw( ; )z t

The importance of wind for the global environmental loading on offshore structures differs with the type of structure and the nature of a structure’s response (quasi-static or dynamic). Fixed structures are usually rather stiff and tend to respond quasi-statically to the environmental actions. Furthermore, wind loads form only a small contribution to the total environmental loads on these structures, typically less than some 15%. Hence a very simple

wind model and a sustained velocity U are adequate characterisations of the wind field

for calculating global wind loads on these structures. The 10 min or even the 1 hr sustained wind is usually an appropriate wind velocity to determine wind loading that is concurrent with the dominant wave and current loading. In case of doubt, or where a fixed structure experiences some dynamic response, the 1 min sustained wind may conservatively be used. For the quasi-static design of parts of the superstructure it should be observed that the three- dimensional spatial scales of wind turbulence in gusts varies with the duration of the gusts. For example, a 15 s gust is coherent over larger distances and thus affects larger elements than a 3 s gust. Local loads should hence be calculated using a shorter averaging duration than global loads. For individual structural members a 3 s gust velocity should preferably be used, while for parts of the superstructure with horizontal dimensions less than some 50 m the 5 s gust velocity is more appropriate. For larger parts the 15 s gust velocity can be considered to be adequate.

z

w( )

Fore compliant bottom founded structures, floating structures and mobile offshore units the response to wind action should be considered much more carefully and in much greater detail where appropriate . For floating structures mean wind loads are clearly important for their station keeping ability. These mean loads must be compensated by anchorline forces or the forces produced by thrusters; they determine the (static) equilibrium position of the floater. In view of the long natural periods of the horizontal motions of floating structures the 10 min

Chapter 4 – The offshore environment and environmental loading 4-6

Figure 4.2-2. Vertical profile of steady wind velocity, according to equations 4.2-2 and the logarithmic profile in Annex A.

sustained wind will usually be an appropriate choice for such applications. Finally, for structures that respond truly dynamically to wind action the time and spatial variation of the wind speed and its direction can be very important, especially when the wind field contains energy at frequencies close to a natural frequency of the structure. Therefore, the wind model to be used in such cases will likely need to be much more detailed to account for such variation. This requires knowledge of turbulence intensity, wind spectra and spatial coherence.

Structure types that may exhibit global dynamic response include compliant bottom founded structures and floating structures, i.e. 4 of the 5 types distinguished in chapter 2. Individual structural elements and structural parts such as masts and flare or communication towers may be subject to local dynamic response. The design of such elements and parts will therefore generally need to be based on their dynamic response to wind action.

The vertical profile of the mean wind speed has traditionally been expressed in the form of a power law:

Uw( )z =Uw( )10 ⋅

FHG

IKJ

10

α

(4.2-2)

where: Uw(z) = mean (sustained or gust) wind speed at z m above MSL [m/s]

Uw(10) = mean (sustained or gust) wind speed at 10 m above MSL [m/s]

(both averaged over the same time interval)

z = vertical distance above MSL [m]

0 Uw(z ) z Uw(10) 10 m α = 1/7 α = 1/8.5 logarithmic profile

For onshore conditions the exponent α is of the order of 1/7 (0.14). At sea the terrain is flatter

than on land so that the wind profile is steeper with a correspondingly lower value of α of the

order of 1/8.5 (0.12).

A theoretically preferred and more correct description of the vertical profile is based on a logarithmic function; see Annex A. For illustration, the wind profiles according to the power

law profile of equation 4.2-2 (for both exponents of α) and the logarithmic profile of Annex

A are shown in figure 4.2-2. As a result of the empirical nature of the wind field description, adjustments to the wind profile at a particular location or under certain conditions may be made when specific measured data from offshore locations are available.

As discussed, in many applications the time varying component is an unnecessary

sophistication and can be ignored, reducing the wind model to the steady wind with a vertical profile only. There are three main reasons why such a gross simplification is often entirely adequate. These are:

uw( ; )z t

1) The mean wind velocity and hence the steady mean wind load is usually rather large compared to the fluctuating velocity and the fluctuating load. Additionally, the steady load is correlated over the full exposed area as opposed to the fluctuating load, where the degree of correlation depends on the relative dimensions of the object and the atmospheric turbulence. As a result, the fluctuating loads on separate parts of the exposed area will tend to partly cancel one another, thus being of more local than global importance.

2) The time varying wind loads are small compared to the time varying wave loads, which is mainly due to the density of air being roughly a factor 800 times smaller than the density of water.

3) The periods contained in the fluctuating wind velocities and hence in the fluctuating wind loads range from a few seconds to several minutes, with most energy concentrated around a few minutes (see figure 4.2-1). The wind energy is therefore mainly concentrated at rather low frequencies that are generally outside the practical range of interest for most offshore structures. Exceptions to this may be long periodic motions of anchored floating vessels and the rigid body motions of compliant bottom supported structures. In these cases the wind load excitation may be an additional and important source of excitation, resulting in significant resonant response of a lightly damped system.

Chapter 4 – The offshore environment and environmental loading 4-8