Publishers version - DTU Orbit

Figure 9: Large spatial scale variability for atmospheric flow at upper left, multiple temporal
scale variability at upper right, and vertical multiple spatial scale Tethersonde data at lower
left. A common name for the much of flow fluctuations in meteorology and fluid dynamics
is turbulence, a term that further implies that at least part of its analysis and description is
statistical. Production of turbulence from mean shear is illustrated at lower right (Tennekes
et al., 1972)
.
• co-variances and turbulent transport: < u ′ i u′ j >: Transport of ui in the j direction (and
vice versa).
• < uiT ′ >, and < uiq ′ > :Transport of temperature and water vapor in the ui direction.
Multiplying the velocity co-variances by the air density, ρ ,we can say that the velocity
transport can be considered a momentum transport, similarly multiplying the temperature
transport by ρCp is converted to a heat transport, and multiplying the water vapor transport
by ρL is converted to transport of latent heat. Here Cp is the heat capacity of the air at
constant pressure, L is the heat of evaporation for water. Indeed these terms are often used
in the description, since they reflect the physical importance better than the statistical term
correlation.
Alternatively can be denoted with capital letters or over-bars. The coordinate system
can be described at xi,i = 1,2,3 or with x,y,z , with the corresponding ui or u,v,w where
u now is along the mean wind direction, w is vertical and v lateral (the second horizontal
component).
A typical behavior of 600 seconds of ABL velocity components and temperature are shown
on fig. 10.
DTU Wind Energy-E-Report-0029(EN) 27