waves and strong tangential stresses develop. These scattered structures coalesce
forming a continuous turbulent field.
Turbulence can be described as an integral part of the atmosphere and is mainly
random, requiring statistical methods. It follows that there should be a separation
between the mean and the turbulent flow components to determine the means and
standard deviations of scalar and vector quantities in calculating statistical parameters. Among these parameters are variance representative of the intensity of turbulence or kinetic energy, and covariance for vertical fluxes or shear stress.
These parameters can be represented using algebraic summation equations of
budget, e.g., mass, linear momentum, variances, or kinetic energy. The terms of the
equations make it possible to introduce various parameters that collectively make
up the budget.
Spectral analysis is another mathematical tool that makes it possible to analyze
the sizes and frequencies of eddies that make up the turbulent velocity field.
3.2 Mean and Flutuation Components for Turbulent
Flows
Atmospheric turbulent flow is characterized by a continuous variation of the vector
or scalar parameters, inherent to the dynamics of movement around a mean value
calculated from data obtained over periods of about half hour. Any time-dependent
quantity A can then be written as follows:
A ¼ A þ a
0
ð3:1Þ
where A represents the mean value and a′ the instantaneous fluctuation.
Some of the rules for defining means for time-dependent quantities of products
or derivatives, considering that fluxes and variances are products of fluctuations are
as follows:
c ¼ c
ð3:2Þ
where c is a constant.
cA ¼ cA
ð3:3Þ
A
À Á ¼ A
ð3:4Þ
AB
À Á ¼ AB
ð3:5Þ
3.1 Introduction
35
forming a continuous turbulent field.
Turbulence can be described as an integral part of the atmosphere and is mainly
random, requiring statistical methods. It follows that there should be a separation
between the mean and the turbulent flow components to determine the means and
standard deviations of scalar and vector quantities in calculating statistical parameters. Among these parameters are variance representative of the intensity of turbulence or kinetic energy, and covariance for vertical fluxes or shear stress.
These parameters can be represented using algebraic summation equations of
budget, e.g., mass, linear momentum, variances, or kinetic energy. The terms of the
equations make it possible to introduce various parameters that collectively make
up the budget.
Spectral analysis is another mathematical tool that makes it possible to analyze
the sizes and frequencies of eddies that make up the turbulent velocity field.
3.2 Mean and Flutuation Components for Turbulent
Flows
Atmospheric turbulent flow is characterized by a continuous variation of the vector
or scalar parameters, inherent to the dynamics of movement around a mean value
calculated from data obtained over periods of about half hour. Any time-dependent
quantity A can then be written as follows:
A ¼ A þ a
0
ð3:1Þ
where A represents the mean value and a′ the instantaneous fluctuation.
Some of the rules for defining means for time-dependent quantities of products
or derivatives, considering that fluxes and variances are products of fluctuations are
as follows:
c ¼ c
ð3:2Þ
where c is a constant.
cA ¼ cA
ð3:3Þ
A
À Á ¼ A
ð3:4Þ
AB
À Á ¼ AB
ð3:5Þ
3.1 Introduction
35