Log wind profile

Wind currents are influenced by the surface roughness. Depending on the type of soil roughness or the development result in different velocity profiles. The logarithmic wind profile is used as an approximation for the description of such profiles. It is in near-surface layer ( up to 60 m ), which is referred to as Prandtlschicht. This is for the wind energy is important.

In the Prandtlschicht the wind speed increases with altitude ( approximately ) logarithmically, so at first very rapidly and then more slowly. In this case, the following relationship applies:

The wind speed at height (within the Prandtlschicht ), the friction velocity (ie, the square root of the specific vertical momentum flux ), the von Karman constant ( about 0.4 ) and the dynamic roughness length (specifies the level at which about the reason, the vertical logarithmic wind profile assumes the value 0 ).

Often, the logarithmic profile is specified relative to the wind speed at a reference height. The data of the German Weather Service DWD data related to a height of 10 m above ground. Using the formula in the box opposite the conversion to any other reference height can be done.

The logarithmic vertical wind profile is valid only for neutral stratification (that is neither stable nor unstable ). In a non-neutral stratification, the relationship loses its validity.

The strong, logarithmic wind increase with height ( vertical wind shear ) in the Prandtlschicht and the wind rotation in the Ekmanschicht above the Prandtlschicht is to consider, for example, the construction of wind turbines. Due to the uneven wind pressure high voltages on the individual rotor blades can act.

Derivation

The atmospheric boundary layer is dominated by turbulence and the vertical turbulent flux horizontal pulse results from the Reynolds equations as covariance between vertical and horizontal speed. Assuming that average wind direction and average shear stress coincide, then we can write:

With the shear velocity, air density, u and w are the horizontal and vertical wind speed and for example the deviations or variations from the mean.

Mischungsweglängenansatz

The original derivation by Ludwig Prandtl is very descriptive and is based on the assumption that the turbulence transports certain flow properties from a different level to a particular place:

Assuming that the fluctuations u ' and w' of vertical, turbulent transport arise over a mixing length or out of the horizontal wind, so that one

Can approach, this leads by inserting the equation:

The Mischungsweglängen should increase with the height z (larger turbulence elements) and be positively correlated (the same up or downdraft transports the u ' and w' fault approach ). The simplest approach to this is:

With a proportionality constant. Insertion leads to

If is constant with height, then can integrate this equation. The lower limit of integration is defined such that here the horizontal wind disappears. This gives the logarithmic wind profile:

In the atmospheric boundary layer increases in the lowest 100 m from only a few percent, so that the assumption of a constant friction velocity is justified. In honor of Prandtl, who first derived the logarithmic wind profile, the lowest hundred meters of the atmospheric boundary layer in which the turbulent fluxes are approximately constant, referred to as the Prandtl layer.

The logarithmic wind profile can be found in nature in neutral stratification, that is, when the potential temperature does not change with height. In other stratifications find Deviations, which are described in the Monin -Obukhov theory. The above equation, the associated gradient and friction velocity, then contains a correction function, which can be interpreted as a correction of the mixing length:

The parameter is called Obukhov length and describes the thermal stratification of the atmosphere. It is positive in stable (temperature takes up to ) and negative for unstable stratification ( temperature decreases upward from the ground-level air is warmer ). With stable stratification vertical movements can be suppressed, the mixing length must be smaller than neutral layering and hence must be greater than one. For unstable stratification rich vertical movements further than for neutral stratification, the mixing length must be larger and hence less than one.

Swell

  • Http://www.top-wetter.de/lexikon/l/logarithmischeswindgesetz.htm
  • Helmut Pichler, ' Dynamics of the Atmosphere '
  • John A. Dutton, ' Dynamics of Atmospheric Motion'
  • Wind
  • Meteorological concept
  • Wind Energy Technology
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