Geoscience Reference
In-Depth Information
3.3 Turbulence
3.3.1 Qualitative Description
Starting with the pioneering work of Reynolds (
1895
), turbulent lows have been the
subject of scientiic research ever since (for a review see, e.g., Monin and Yaglom,
1971
). From this research a more or less commonly accepted picture has evolved that
describes turbulent lows both qualitatively and quantitatively. Based on this picture
some general properties of turbulent lows can be summarized (after Tennekes and
Lumley (
1972
); Lesieur (
1993
)):
•
Turbulence occurs in lows where the nonlinear terms in the governing equations
2
dom-
inate over the linear viscous terms. Those nonlinear terms may involve momentum and/
or density (or temperature) variations.
Turbulent lows are irregular or chaotic in space and time: they are not reproducible in
•
detail.
Turbulent lows are diffusive: heat, momentum, as well as mass are mixed and trans-
•
ported eficiently by turbulent lows. In many practical applications this is a desirable
feature of turbulence.
Turbulence is essentially rotational and three-dimensional, which is a distinction to other
•
chaotic lows (like, e.g., cyclones). Rotating patches of luid (loosely called eddies) have
length scales ranging from the size of the low domain (in the ASL this would be the
height above the ground) down to the order of millimetres.
Turbulent lows are dissipative: the kinetic energy of the velocity luctuations, pro-
•
duced at the largest scales, is dissipated at the smallest scales into heat through viscous
forces.
As stated before, turbulence is essentially three dimensional (and time dependent).
But very often we are not able to capture the variability of a turbulent low in all those
four dimensions (except with very advanced measurement techniques, and in numer-
ical simulations). To obtain a irst glimpse of what turbulence looks like, we will dis-
cuss the observed time series
3
of vertical wind speed, temperature, humidity and CO
2
concentration as observed above a savannah vegetation in Ghana (see
Figure 3.4
).
The following remarks can be made:
1. The four signals are indeed chaotic. But some structure is apparent as well. Large
deviations from the mean are very rare, whereas smaller deviations are more common.
Furthermore, larger deviations from the mean last for some time (e.g., around 11.3, 11.4
and 11.6 hours): so scale and magnitude of the luctuations are related.
2. The signals of the scalars (i.e., temperature, humidity and CO
2
) are asymmetric in the
sense that there is a base level from which the signal deviates in only one direction. This
2
Nonlinear terms are those terms where a property of the low, in particular a velocity component or density (or tem-
perature) is multiplied with another (or the same property). An example of such a quadratic term is the advection
term
∂
∂
u
x
occurring in the differential equation that describes the change in time of velocity
u
.
3
A time series: so only one dimension varies and
x, y
and
z
are ixed.
u
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