Structure function

From Glossary of Meteorology

structure function

The variance of the difference of a turbulence quantity in space or time, given by
where q is a scalar or a velocity component.

For small separations (rz, where z is the height above the surface), this equation may be written
where b is about 0.7 for temperature and 0.76 for humidity, χq is the rate of destruction of q2/2 by molecular diffusion, and ε is the rate of dissipation of turbulence energy into heat. The coefficient
is called the structure constant of q. This formulation eliminates the mean component of a fluctuating quantity and provides a measure of fluctuation variance within a band of wavelengths (or frequencies) determined by the separation distance (or lag time).

Panofsky, H. A., and J. A. Dutton 1984. Atmospheric Turbulence. Wiley, . 182–183.