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## The microstructure of the temperature field in the atmosphere

[Tatarskii] describes the microstructure of the temperature field in a fluid with homogeneous and isotropic turbulence, characterized in particular by its dissipation rate of kinetic energy , similarly to Kolmogorov's analysis of the turbulent velocity field. The analysis leads to the definition of an inner scale corresponding to the smallest temperature variations, which is determined by the thermal diffusivity and the dissipation rate :

Continuing the analogy with the velocity field, Tatarskii finds then an inertial domain, between the outer scale of turbulence L and l where the temperature structure function

has the form:

where is the temperature structure coefficient.
characterizes completely the local thermal turbulence at a give time, has units (K m) and is therefore formally defined as:

for a separation in the inertial domain.

is also related to the one-dimensional temperature spectrum which in the inertial domain has the form:

where is the streamwise component of wavenumber.
Moreover, [Tatarskii] notes that in the inertial domain should be a function of only , and the temperature dissipation rate . Dimensional reasoning leads then to

where is a constant found to be equal to about 3.

The value of at a given point can be measured by special temperature sensors. Sometimes two sensors are used, with a separation of the order or 1 meter, but often the measurement is taken with one sensor only. The data are then processed assuming the Taylor hypothesis of "frozen turbulence" in which time and spatial intervals are linked by the mean wind speed as:

This hypothesis implies that velocity fluctuations are small with respect to the mean value, which is generally the case with not exceedingly gusty winds of at least 4 5 m/s. The temperature structure coefficient can then be evaluated from the variations of temperature at a single point as:

The temperature sensors for the measurement of must have a high resolution and a large dynamic range. may vary from Km during the night on an excellent site to Km during the day and convection from the ground. The required bandwidth is determined by the -5/3 slope of the temperature spectrum () and will generally be at least 100 or 200 Hz.

Direct measurements of from a fixed setup are of course possible only close to the ground while one-time vertical profiles over a larger height can be obtained by aerostatic balloons. The already mentioned SODAR can measure refraction turbulent profiles in the boundary layer with a height range between 50 and 800 m. The profiles of in the high atmosphere and in the boundary layer have been also the objects of many studies aiming at determining their relationship with height and the atmosphere parameters (see for instance [Coulman 86], [Coulman 88] and [Consortini]).

Next: The microstructure of Up: Thermal turbulencelight Previous: Thermal turbulencelight

Lorenzo Zago, zago@elgc.epfl.ch, Sun Feb 26 22:57:31 GMT+0100 1995