number ranges, corresponding to the smaller eddies with isotropic turbulence
(Blackadar 1997).
The influence of thermal stability in the spectral power can be graphically
analyzed by curves in Fig. 3.7, where the frequency appears dimensionless as f z=u
in the abscissa, and the spectral power S(f), dimensionless in the form
f S u ðf Þ=u à /
2=3
e
is in the ordinates. The spectral power is expressed in L
3 T
À2 units.
The dimensionless dissipation factor / e , is defined by Eq. (3.96).
Figure 3.7 shows a family of curves for distinct conditions of thermal stability
represented by different values of z/L (k is the von Karman constant and L is the
Monin-Obhukov length).
The lower values of dimensionless frequency in the anisotropic range are more
dependent on surface heating and stability conditions. On the other hand, in the
inertial and dissipative subranges, the spectral curves converge towards a line with
slope of about −2/3 (Fig. 3.7). This shows that at higher frequencies, the spectral
intensity is no longer as dependent on conditions of thermal stability and that the
smaller eddies receive energy from the inertial subrange without direct interaction
with the mean flow. A convergence shown in graphs arises of the spectral curves
into a line with a slope of −5/3, in which the natural log of the scalar spectral
density energy in the ordinates is plotted against the ln(j) as abscissa.
Fig. 3.7 Normalized spectra for a u; b v; c w; and d T air of air velocity and temperature potential
(after Kaimal and Finnigan 1994)
3.6 Spectral Analysis
75
(Blackadar 1997).
The influence of thermal stability in the spectral power can be graphically
analyzed by curves in Fig. 3.7, where the frequency appears dimensionless as f z=u
in the abscissa, and the spectral power S(f), dimensionless in the form
f S u ðf Þ=u à /
2=3
e
is in the ordinates. The spectral power is expressed in L
3 T
À2 units.
The dimensionless dissipation factor / e , is defined by Eq. (3.96).
Figure 3.7 shows a family of curves for distinct conditions of thermal stability
represented by different values of z/L (k is the von Karman constant and L is the
Monin-Obhukov length).
The lower values of dimensionless frequency in the anisotropic range are more
dependent on surface heating and stability conditions. On the other hand, in the
inertial and dissipative subranges, the spectral curves converge towards a line with
slope of about −2/3 (Fig. 3.7). This shows that at higher frequencies, the spectral
intensity is no longer as dependent on conditions of thermal stability and that the
smaller eddies receive energy from the inertial subrange without direct interaction
with the mean flow. A convergence shown in graphs arises of the spectral curves
into a line with a slope of −5/3, in which the natural log of the scalar spectral
density energy in the ordinates is plotted against the ln(j) as abscissa.
Fig. 3.7 Normalized spectra for a u; b v; c w; and d T air of air velocity and temperature potential
(after Kaimal and Finnigan 1994)
3.6 Spectral Analysis
75